(12) Patent Application Publication (10) Pub. No.: US 2015/0260527 A1 Fink (43) Pub

US 20150260527A1 (19) United States (12) Patent Application Publication (10) Pub. No.: US 2015/0260527 A1 Fink (43) Pub. Date: Sep. 17, 2015

(54) SYSTEMAND METHOD OF DETERMINING (52) U.S. Cl. A POSITION OF A REMOTE OBJECT VA CPC ...... G0IC 2 1/20 (2013.01) ONE ORMORE IMAGE SENSORS (57) ABSTRACT (71) Applicant: Ian Michael Fink, Austin, TX (US) In one or more embodiments, one or more systems, methods (72) Inventor: Ian Michael Fink, Austin, TX (US) and/or processes may determine a location of a remote object (e.g., a point and/or area of interest, landmark, structure that (21) Appl. No.: 14/716,817 “looks interesting, buoy, anchored boat, etc.). For example, the location of a remote object may be determined via a first (22) Filed: May 19, 2015 bearing, at a first location, and a second bearing, at a second O O location, to the remote object. For instance, the first and Related U.S. Application Data second locations can be determined via a position device, (63) Continuation of application No. 13/837,853, filed on Such as a global positioning system device. In one or more Mar. 15, 2013, now Pat. No. 9,074,892. embodiments, the location of the remote object may be based on the first location, the second location, the first bearing, and Publication Classification the second bearing. For example, the location of the remote object may be provided to a user via a map. For instance, (51) Int. Cl. turn-by-turn direction to the location of the remote object GOIC 2L/20 (2006.01) may be provided to the user.

Seria interface 54: iviemory Network 52 le59. 1549CAN

Processing it AR 341 543

Wireless interface 347 5. Patent Application Publication Sep. 17, 2015 Sheet 1 of 63 US 2015/0260527 A1

Patent Application Publication Sep. 17, 2015 Sheet 2 of 63 US 2015/0260527 A1

S S

-3.

- -

s & Š & & S

a axu Y-SS Patent Application Publication Sep. 17, 2015 Sheet 3 of 63 US 2015/0260527 A1

FG. 2 (Prior Art) Patent Application Publication Sep. 17, 2015 Sheet 4 of 63 US 2015/0260527 A1

Patent Application Publication Sep. 17, 2015 Sheet 5 of 63 US 2015/0260527 A1

o ress ser s

Patent Application Publication Sep. 17, 2015 Sheet 6 of 63 US 2015/0260527 A1

------

541C

3. F.G. 5A Patent Application Publication Sep. 17, 2015 Sheet 7 of 63 US 2015/0260527 A1

F.G. 5B Patent Application Publication Sep. 17, 2015 Sheet 8 of 63 US 2015/0260527 A1

6.30 3.

6. 83.

F.G. 6A Patent Application Publication Sep. 17, 2015 Sheet 9 of 63 US 2015/0260527 A1

805

34.

800 83)

F.G. 6B Patent Application Publication Sep. 17, 2015 Sheet 10 of 63 US 2015/0260527 A1

8): 83

F.G. 6C Patent Application Publication Sep. 17, 2015 Sheet 11 of 63 US 2015/0260527 A1

87)

| s

F.G. 6D Patent Application Publication Sep. 17, 2015 Sheet 12 of 63 US 2015/0260527 A1

SOGG 63

FIG. 6E Patent Application Publication Sep. 17, 2015 Sheet 13 of 63 US 2015/0260527 A1

8. 8:30

F.G. 6F Patent Application Publication Sep. 17, 2015 Sheet 14 of 63 US 2015/0260527 A1

554,

8 630

F.G. 6G Patent Application Publication Sep. 17, 2015 Sheet 15 of 63 US 2015/0260527 A1

K --- sees

were c

n D in

ser r s

res f s

w Y e

ex$8ws Patent Application Publication Sep. 17, 2015 Sheet 16 of 63 US 2015/0260527 A1

g Patent Application Publication Sep. 17, 2015 Sheet 17 of 63 US 2015/0260527 A1

FG, 9A Patent Application Publication Sep. 17, 2015 Sheet 18 of 63 US 2015/0260527 A1

905

s 8: 830

FIG. 9B Patent Application Publication Sep. 17, 2015 Sheet 19 of 63 US 2015/0260527 A1

387

6: 63

F.G. 9C Patent Application Publication Sep. 17, 2015 Sheet 20 of 63 US 2015/0260527 A1

83,80

Patent Application Publication Sep. 17, 2015 Sheet 21 of 63 US 2015/0260527 A1

**************************

Patent Application Publication Sep. 17, 2015 Sheet 22 of 63 US 2015/0260527 A1

39489Œ

Patent Application Publication Sep. 17, 2015 Sheet 23 of 63 US 2015/0260527 A1

8vice ( Network Network Memory 332 interface interface fiemory 39 303 WireeSS OS APP 1302 terface 33 303 3.

AP APP Wireless 3O32 333 interface

Processor 300

Usef Data 3035 Patent Application Publication Sep. 17, 2015 Sheet 24 of 63 US 2015/0260527 A1

Device vestory iO2 Memory Network inefaceifeless OS APP 14021 140go 4. 43 i33 Weess interface

Processing Unit 4}{

AR 3.

Memory 52 Device C2

OS APP interface 53 33 59 GPO :54,

ARP APP

532 5:33 Nieless

inteface APP Processing rit

ata 5. 50 338

S&ria interface 520 Position UART | UART || |2C 2C spy SP USB use Device 58 38 5 570 58 560 53 15:50 8 530

F.G. 15 Patent Application Publication Sep. 17, 2015 Sheet 25 of 63 US 2015/0260527 A1

Memory 32

Memory Network

OS APP 82 terface GPO 603 SO3. 3. 8):

APP APP

18032 16033 Wireless

As Processing init interface Data 60 8:0

8038

Seis interface 16210

AR Air 2C C 168 168 67 807

Memory 17.2 CS AP 73 3.

A P

reless intefface

AigiQ int Device 737,

F.G. 17 Patent Application Publication Sep. 17, 2015 Sheet 26 of 63 US 2015/0260527 A1

Position avia 53 Ser3 inte-face \leinery 542 Memory AC Network 34

OS APP 132 158. interface CAN S. 543 531 1549 1549 546

App APP

Processing it UART USB 54 5480 S450

2C Cock Wietess interiaice 54 5498 5:00

F.G. 18A

Position evice 53 After a 15495 Setia tefface Memory 1542 Memory AC Niewick Said APP 542 594 interface 1549

Processing init 5:

Cock Wireless interface 15498. 50 F.G. 18B Patent Application Publication Sep. 17, 2015 Sheet 27 of 63 US 2015/0260527 A1

Afteira 54.87

Network interface

Processing init 5.

interface 33

Processing Unit 9 Wireless

Gyroscope 953

ACCseeiO:lete 954 Bearing Device S F.G. 19 Patent Application Publication Sep. 17, 2015 Sheet 28 of 63 US 2015/0260527 A1

FG. 20 Patent Application Publication Sep. 17, 2015 Sheet 29 of 63 US 2015/0260527 A1

Pief Source 236

Power Supply 2284 Powe Sippy 2232 Weess Powe: Pier reass Poeis a Regulatof SOLFCe w O Tasite Receiver Secrea--- 228. | 22820 228.

Device 24 Device 232 Power Source Power Suppy Power Source 28 258). 2361

FG. 25

Power Sippy 268:

Wireless Poyer Y r Receivef va WieaSS Pow8 Regulator

2866 raisitar

Device 283 Patent Application Publication Sep. 17, 2015 Sheet 30 of 63 US 2015/0260527 A1

27. 273 - F.G. 27B

FG.27C Patent Application Publication Sep. 17, 2015 Sheet 31 of 63 US 2015/0260527 A1

Determine a position:

230t

Determine a first bearing Deterania, utilizing the to an object second bearing a second Compute a vectof based 290 w8cc that is nosta to On the deternin88 the origin, he titject, and position the second position 282 296 Detentire a first position 29) F.G. 28A Date:re a thic w8to that is oria to the first Betermine, stizing the vec{0} and the second firs: bearing, a first vector Wector that is no inal to an oxigin, 29 the object, and the first position 233. Deter nine a position 285 Determine a position of the object 298 Deesilise 3 secois Alier a vectof easing to the Ciject corresponding to and of 294, 3SSociated with tie positio:

23.8 Deefalise a secord gosition 2335) Corpute a vector northa to e.g., perpendictatio} the position 3rd the FIG. 29 aefed Westf 23.

FG. 28B Patent Application Publication Sep. 17, 2015 Sheet 32 of 63 US 2015/0260527 A1

82.

3}{

3. 8

800

F.G. 30A Patent Application Publication Sep. 17, 2015 Sheet 33 of 63 US 2015/0260527 A1

320

F.G. 3OB Patent Application Publication Sep. 17, 2015 Sheet 34 of 63 US 2015/0260527 A1

Si.

3.05 32

623

St.

FIG. 30C Patent Application Publication Sep. 17, 2015 Sheet 35 of 63 US 2015/0260527 A1

F.G. 31A Patent Application Publication Sep. 17, 2015 Sheet 36 of 63 US 2015/0260527 A1

FG. 31B Patent Application Publication Sep. 17, 2015 Sheet 37 of 63 US 2015/0260527 A1

FIG. 31C Patent Application Publication Sep. 17, 2015 Sheet 38 of 63 US 2015/0260527 A1

6220 SSSSSSsaxxx xxxxxs SSSSSSSSSSSS SSS

SSSSSSSSSSSSSSSSS sys-xx-x-xxx-xx-xxxSSSSSSSSSSSSSS S&S a SSSSSSSSS SSSSSSSS SSSSSS$$$$.& SSSSSSSSSS SSSSSSSSS 3-SSSSSSSS SSSFSS

s S

SSSSSS SSSSSSS SS s & SSSSS S&S S SSSSS -SSSSS3SSSSSSSSSS-SSSSSSSSSSSSSS & SSS SSSSSSSSSSS S&& SSS SSSSSSSSSSSSSSSSSSSS S&SSSSSSSSSSSSSS & SS SSS 3&s SS SS SSS SSSSSSSSSSSSSXSSSSSSXSSSSSS S sšŠSSSS SS X SSSSSSSSSSSSSS S $$$$$$$$. S SSSSSSSSS&SSSSSSSS SSS SSSSSSSSSSSS&SSSSSS8SS 8 SSSSSSSSSSSSSŠ SSSSSSSSSSSSSSSSSSsssssssssssssssssssssssssssssssssssssss SSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSS&SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S.ŠSSSSSSSS SSSSSSSSSSSSSSSSSSsssssssssssssssssssssssssssssssssss

SSSSSSSSSSSSSSSSSS as-SSSssssssssssssssssssssssssssssssss SSSSSSSSSSSSSSSSSSSSSSSSSS Š S. &SSXXXXX&xxxxxxx-xxxxx SSSSSSSSSSSSSSSSS &S SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSXSSSSSSSSX SSSSSSSSSSSSSSSSSSSSSSSSSSSSSŠ &S&SSSSSSSS&S&syssssssssssssssssssssssssssssssssssss SSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSS xxxYxxxxxxxSxxxxxxSSSSSSSSS3x3x3-SS33 xxxxxxyyxxxsaxs SSSSSSS sixsssssssssssssssss&SS&SSSSS&SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSS:s SSssssssssssssssssssssssssssssss sssssssssssssssssssssssssssssssss SyS, XSSSSSSSSSSSS SSXXXxxxxxyyxxxx Ssssssssssssssssssssssssssssssss SSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSS S. Ssssssssssssssssssssssssss SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSS

ssssssssssssssssssssss SSSSSSSSSSSSSSSSSSSSSS S-3-3-3-3-3-3-SSS

SSSSSSSSSSSSSSSSSSSSSSSSS &

St.

FIG. 32A Patent Application Publication Sep. 17, 2015 Sheet 39 of 63 US 2015/0260527 A1

3264

3262: 8.

a-608

FIG. 32B Patent Application Publication Sep. 17, 2015 Sheet 40 of 63 US 2015/0260527 A1

3284.

3263 82

32612

326

SOGO

F.G. 32C Patent Application Publication Sep. 17, 2015 Sheet 41 of 63 US 2015/0260527 A1

Determine a first Determine a great

position of a first titject arc bounded by 3300 the first position aid the Second Deterine a position position: 37) 333

eternie a second position of a second eterise a disiace object from the position to a 332)

great arc F.G. 33 F.G. 37

Determine a first position of a first object 340: Deter nine a positio: 38

)eterine a Second Deternie a distance position of a second from the positic: :o a object giane 342. 332

Determine, utizing the first position and the second position, a plate 34.3

FG, 34 Patent Application Publication Sep. 17, 2015 Sheet 42 of 63 US 2015/0260527 A1

800 3.55: 3552

FIG. 35 Patent Application Publication Sep. 17, 2015 Sheet 43 of 63 US 2015/0260527 A1

O 82. 36.3 SR

622,

38.2 38:

six-x-xx is...SSSSSSSS

Exx.

-6

F.G. 36 Patent Application Publication Sep. 17, 2015 Sheet 44 of 63 US 2015/0260527 A1

Deterime a first )eterie 3 if Determine a geat beating from a first rest of an invese circle intercept position to an object at D tangent function of tilizing a poie of a a second position 8 forth fest sphere and a first 39 398 position 392

Detefire a first result Deesire a sixth of a tanger: fiction rest of the fifth ete is a first Wecio Grait the of it result Sttracted Origin, the poie, and 332 from Positions the equator intercept 39 3S2

Detefine a secord esult of Position1p Establish a Determine, utilizing the Subtracted fro: Ti2 magnitude of the Oigin and the position, 333 great circle intercept an axis of rotation 398 3923

etermine a third Estatist a Second rest of a site function Determine, utilizing the angle of the great first bearing, a second of the second resuit circle intercept 334 vector via rotating the 393 first vector about the axis 3924 aerie a foith rest the hird result ruitiplied by the FIG. 39C first festi 395 FG. 39A Patent Application Publication Sep. 17, 2015 Sheet 45 of 63 US 2015/0260527 A1

eietire a second eetire a fifth bearing for a second result of an inverse Acquire a first set of position to an object at tangent function of multiple data points on or a second positi the four fest: near a first great circle 398 47

Determine a first fest Deerfire a sixth of a tangent function Compute a first plane from rest of he fifth the first sei of mittiple of 2 fe:St. Stifacted data points 38.2 from Position 472

eterfire a secons Acquire a second set of result of Positio2 Establish a imultiple cataggints or of subtracted from i2 Eagnitude of the near a second great circle 393 great circle intercept 473 398

Deering a tird Estatist a S&COf Compute a second piane fest Of a sile fictii ange of the great fron the SecGid sei of of the second result circle intercept multipe data points 334 339 474)

Detering a fourt Compute an intersection jesuit of the third of the first plane, the rest mitiplied by the Second plane aid a fiS rest sphee associated with the 395 fifs: great circle and the Second geat circle 475 FIG. 39B F.G. 47 Patent Application Publication Sep. 17, 2015 Sheet 46 of 63 US 2015/0260527 A1

3.25 302C

|l 82 {

6 (-

4520 6 : 405 445)

4053

FG. 40 Patent Application Publication Sep. 17, 2015 Sheet 47 of 63 US 2015/0260527 A1

900- 3.25

2 445 o 4.52 SCO

45)

38.33

32 S

FG. 41 Patent Application Publication Sep. 17, 2015 Sheet 48 of 63 US 2015/0260527 A1

Compute a dot product of a first row of matrix via with vecto: Wi: 4300 Corpute, Lizing the first Compute, base of the position, a first quaiernion first position, a third 42 Latefiot Compute a dot 25 product of a second row of matrix is with vector Weg Compute, utilizing the first 43020 position, an equator Coipute, utilizing the first intercept quaieffign and the second quaternion, a $22. fourth quatestion Congute a dot product of a third row of matrix M with Compute, tilizing the vector Weg equator intercept, a first 43O3C yet:Eoforia to the Coipute, utilizing the Origin, the first position, flirth (38teinigi and the and the equator intercept third quaternion, a fifth 230 diaei nioi Compute a dot if product of a fourth ECW of matrix Ali with vector W. Compute, utilizing a vector 43)4C norma to the origin and the equator intercept, a (Coipute, utilizing the fifth second quaieffion qualer?ion, a second 2. YeCEO F.G. 43 428O

FIG. 42 Patent Application Publication Sep. 17, 2015 Sheet 49 of 63 US 2015/0260527 A1

Compute, stilizing the beating. 3 Cosine of an angle Compute a third vector etetaine via a the difference if the rotatio; is ii. between one and the cockwise Cosine of the angle, the i dot product of the first vector aid the S&Cond Co?pite a dies eace yector, aid the first vector is Si

setween one and the cosine of the age is 2

Determine a sixth yector Compute a fourth vector via difference between a Coipute, utilizing the via a the Cosie of the st of third vector the angle and the second foLifth vector 38 the fift origin and the first yer wecšof position, a first vector 4. s:43 AAEF

Compute a sine of the ete Ete the sixth vectof Cornputs a second vecto: age was it of third yeco, that is to a to the first 8. ite foil festof, and the positionard at eas: one fifth vector of an equator intercept and a pole intercept 4.4 Compute a fifth vector via the sine of the angle and a cross product of the first vector and the second Compute a dot product of ecio the first vector and the O3 Second Wector iii.5)

FIG. 44 Patent Application Publication Sep. 17, 2015 Sheet 50 of 63 US 2015/0260527 A1

Determine, utizing etermine a fourth Determine, the hearing, a cosine flatix based the utizing a first of an angie Second vectof position and a 38 second position, s a first piane 480

Deterine a Determine, utilizing difference between the bearing, a sine of Deteanine, One as the Cosie an angie utilizing the first positio; and a of the aigie first equator i52 intercept, a Second pia;e £320 Deterine a first le:Big aff fairix based or a statix as a product of SeCQadi vectof since and the fourth Determine, 4503 rairix utilizing the 458 second positio: 3rd a secoid eier;i& a S&CO;h equatof matrix as a foduct intercept, a third Deterie & Six gaine o tratix as a tatrix {-cos(0)} and the St. of the Seco, $83. fi's fatrix matrix, the third 45. Fiatrix, and the fifth atfix Detenlie, 3590 iitizing a user laterine a third position and a atrix based of W&ctor Cos(8) asSociated with a 450SE etermine a third pians, a side oia vecto: from a product great circle of the sixth matrix and 484 the first vector iSO F.G. 46 FG. 45 Patent Application Publication Sep. 17, 2015 Sheet 51 of 63 US 2015/0260527 A1

Deterfire a first position Compute a fifth festi via Compute an eleventh 380 computing a sine of ps fest livia a Cosite of the 878 test resi i83) genre a Second position 432 Congate a sixth rest: Compute a twelfth result via Corpisting a Cosine of via a product of the eight: (g {esuit, the ninth fesuit, 4808. and the eeven eSt. Compute a first resuit via 48 an angular difference 4803 Compute a seventh result via a product of the fifth Compute a thitteenth result and the sixth resuit result via a difference of 489 the Seventh fesuit and the Compute a second fesuit twelfth gest via a sine of the first result i850 : $84.

Compute an eighth result via Computing a cosihe of Create a complex nuiber {Qinpute a thi? (ifesuit via { 48 for the oth fest and corputing a sine of (pg the thirteenth fesuit i850 488 Compute a ninth resuit via computing a sine of (p2 43 Compute an argument Compute a fourth Fesui e.g., a phase of the via a product of the Conpex unles second resultant the 48 third rest Coipue a teth fesuit 4308 via an agilar difference

F.G. 48 Patent Application Publication Sep. 17, 2015 Sheet 52 of 63 US 2015/0260527 A1

A3C 49.20

4922 Y 82

892 N 4)

88: 32

FG. 49 Patent Application Publication Sep. 17, 2015 Sheet 53 of 63 US 2015/0260527 A1

deteriaine a first position S5 Determine a position steriaine a positios 5 (. SEC Determine a first bearing to a retrote object Determine a bearing to Compute a plane that the second great circie incities at east two 52 positions and a Origin eiennie 3 second 52 position 853 Compute a plane that incides the position, an Corpute a distance along eie'nine & Second Origin, and a p0te the fist great Cice from bearing to the femote 5:3. the position to the second objeci great Circle 654 53 Coagute a rotation of the Corpute a position the plane, about the position, feiriote gject based of by the bearing FIG. 51 the first position, the first 5040 beating, the second position, and the second beasing Coipute &n intersection SS of the plane, rotated about the position by the bearing and a pare that Provide the position of the includes at 8asi &G remote object to a usef positions and the origin via a tap 300S 658

Cornpite a distance along Owide, to he use, the first great circle from informatic: based of the the position to the second gositio of the eigte great circie object SC3 857

FIG. 50 F.G. 65 Patent Application Publication Sep. 17, 2015 Sheet 54 of 63 US 2015/0260527 A1

Wettice 52

FG, 52A

F.G. 52B Patent Application Publication Sep. 17, 2015 Sheet 55 of 63 US 2015/0260527 A1

F.G. 53

take Austir Eyd EX 12 LE Patent Application Publication Sep. 17, 2015 Sheet 56 of 63 US 2015/0260527 A1

S S S s

s Patent Application Publication Sep. 17, 2015 Sheet 57 of 63 US 2015/0260527 A1

S: V | system. F.a^.

FIG. 57

SS 882 Display E30 Ester a decinatio: angle,

Enter a park position: leave the mark to poi:

Efter a CO'Se:

F.G. 66 Patent Application Publication Sep. 17, 2015 Sheet 58 of 63 US 2015/0260527 A1

Determine a first position via a first siewice 39 Determine a fits position Acquire a second image 58 hai Cixies the fier8te object Determine, at the first postion, a 588 first bearing to a remote object via a Second device Deteemine a first heading 582 582 Determine a positio of the remote object within Determine a second position via a the second in age hid device Acquire a first image that 589. 53.30 includes a reiroie object 58O3. Detefinine, at the second position, CoE spute a Second a second bearing to the remote bearing to the remote object via a fourt device Determine a position of objec: 53.4 the fernote object within the first image 58. 584) Provide position infortation and bearing information to a fifth device Coipute a position the 595 Compute a first bearing to emote object based or the remote object the first position, the first 803 bearing, the second Receive the position information position, and the second and the bearing information via bearing the fift siewice 58: 598 Reieffie a secCad

gosition 58O8. CQingite, via the fifth evice, a position of the femote object via the first positios, the first beating, eterine a S&CC: the second position, and the heading second bearing 397 F.G. 58 F.G. 59 Patent Application Publication Sep. 17, 2015 Sheet 59 of 63 US 2015/0260527 A1

Patent Application Publication Sep. 17, 2015 Sheet 60 of 63 US 2015/0260527 A1

Patent Application Publication Sep. 17, 2015 Sheet 61 of 63 US 2015/0260527 A1

8201)

F.G. 62A Patent Application Publication Sep. 17, 2015 Sheet 62 of 63 US 2015/0260527 A1

F.G. 62B Patent Application Publication Sep. 17, 2015 Sheet 63 of 63 US 2015/0260527 A1

Bisplay 830

information 33.

FG, 63

Mapping Service Computing evice 841C

Network tionatio: Service

- - - - -"... “ - Computing Device 84)2

Promotion

Advertiserient information Service formation Service Computing Device Computing Device 8:33). 649:

F.G. 64 US 2015/0260527 A1 Sep. 17, 2015

SYSTEMAND METHOD OF DETERMINING BRIEF DESCRIPTION OF THE DRAWINGS A POSITION OF A REMOTE OBJECT VA 0008. The embodiments will become apparent upon read ONE ORMORE IMAGE SENSORS ing the following detailed description and upon reference to 0001. This Application claims priority to and is a Continu the accompanying drawings as follows: ation of U.S. patent application Ser. No. 13/837,853, filed on 0009 FIG. 1A provides a prior art illustration of a starting 15 Mar. 2013, titled “System and Method of Determining a line of a sailboat race; Position of a Remote Object', which is hereby incorporated 0010 FIG. 1B provides a prior art illustration of a starting by reference. line of a sailboat race with multiple sailboats participating in a start of a sailboat race; 0011 FIG. 2 provides a prior art illustration of a remote BACKGROUND object; 0002 1. Technical Field 0012 FIG.3 provides an exemplary illustration of a vessel 0003. This disclosure relates generally to the field of navi sighting a first object from a first position, according to one or gation systems, and, more specifically, this disclosure per more embodiments; tains to the field of determining a position of a remote object 0013 FIG. 4 provides an alternate exemplary illustration via one or more mobile devices. of a vessel sighting a first object from a first position, accord ing to one or more embodiments; 0004 2. Description of the Related Art 0014 FIG.SA provides an exemplary illustration of a user 0005. In the past, determining a position of an end of a sighting a remote object, according to one or more embodi starting line of a sailboat race included maneuvering and/or ments; positioning a vessel to a point proximate to the end of the (0015 FIG. 5B provide provides another exemplary illus starting line. As illustrated in FIG. 1A, a vessel 1010 may tration of a user sighting a remote object, according to one or include a position device (e.g., a global positioning system more embodiments; (GPS) receiver and processor) that may determine a position 0016 FIG. 6A illustrates an exemplary sphere and first of an antenna included in or coupled to the position device, exemplary positions associated with the sphere, according to where vessel 1010 is positioned proximate to staff 1210 one or more embodiments; which is used to form a first end of a starting line 1310. As 0017 FIG. 6B illustrates an exemplary sphere and second shown, staff 1210 may be mounted on a vessel 1110 (e.g., a exemplary positions associated with the sphere, according to race committee boat). A second end of starting line 1310 is one or more embodiments; formed using object 1220 (e.g., a buoy, a floating tetrahedron, 0018 FIG. 6C illustrates an exemplary sphere and third a vessel, etc.). As illustrated in FIG. 1B, vessel 1010 is posi exemplary positions associated with the sphere, according to tioned proximate to object 1220 which is used to form the one or more embodiments; second end of starting line 1310. After two positions respec 0019 FIG. 6D illustrates an exemplary planet, according tively corresponding to the two ends of starting line 1310 are to one or more embodiments; determined, a distance to starting line 1310 may be deter 0020 FIG. 6E illustrates an exemplary spherical model of mined from another position of vessel 1110. a planet, according to one or more embodiments; 0006. One or more issues may be or become problematic 0021 FIG. 6F illustrates an exemplary sphere and axes of when utilizing one or more systems and/or methods of the a Cartesian coordinate system, according to one or more past. In one example, a starting area may be “crowded. For embodiments: instance, the starting area may be “crowded with multiple 0022 FIG. 6G illustrates an exemplary sphere and axes of vessels, such as vessels 1010-1018, and an amount of time a spherical coordinate system, according to one or more may not exist for one or more of the multiple vessels 1010 embodiments; 1018 to determine the two ends of the line. In a second 0023 FIG.7 provides an exemplary illustration of a vessel example, one or more ends of the starting line may be moved sighting a first object from a second position, according to one by the race committee, and an amount of time may not exist or more embodiments; for one or more of the multiple vessels 1010-1018 to deter 0024 FIG. 8 provides an alternate exemplary illustration mine the two ends of the line. For instance, the race commit of a vessel sighting a first object from a second position, tee may move object 1220 from a first position to a second according to one or more embodiments; position and starta race shortly (e.g., one to five minutes) after 0025 FIG. 9A provides an exemplary sphere, first posi moving object 1220 from the first position to the second tions associated with the sphere, and a sight line between two position. In another example, multiple starts may occur, and a positions, according to one or more embodiments; vessel may not be allowed near the starting area until the 0026 FIG.9B provides an exemplary sphere, second posi vessel's starting sequence. tions associated with the sphere, and a sight line between two 0007 Also in the past, determining a position of a point positions, according to one or more embodiments; and/or area of interest (e.g., a landmark, a structure that 0027 FIG. 9C provides an exemplary sphere, third posi “looks interesting, a remote object, etc.) at a distance was not tions associated with the sphere, and a sight line between two possible for Some (e.g., tourists, non-locals, etc.). For positions, according to one or more embodiments; example, a family could be driving along a highway and spot 0028 FIG. 10 provides an exemplary illustration of exem a structure at a distance. Not knowing where and what the plary devices in a first exemplary configuration, according to structure at the distance is, the family may not know where the one or more embodiments; structure at the distance is. For instance, structure 2010, as 0029 FIG. 11 provides an exemplary illustration of exem illustrated in FIG. 2, may not be known and/or its location plary devices in a second exemplary configuration, according may not be known to some. to one or more embodiments; US 2015/0260527 A1 Sep. 17, 2015

0030 FIG. 12 provides an exemplary illustration of exem 0051 FIG. 28B illustrates an exemplary method of deter plary devices in a third exemplary configuration, according to mining a plane that includes a determined position, according one or more embodiments; to one or more embodiments; 0031 FIG. 13 provides an illustration with further detail of 0052 FIG. 29 illustrates an exemplary method of deter an exemplary device, according to one or more embodiments; mining a position of a remote object, according to one or more 0032 FIG. 14 provides an illustration with further detail of embodiments; an exemplary device configured to include a display, accord 0053 FIG. 30A provides an exemplary illustration of a ing to one or more embodiments; first determined vector associated with a first plane, according 0033 FIG. 15 provides an illustration with further detail of to one or more embodiments; an exemplary device configured to be coupled to a position 0054 FIG. 30B provides an exemplary illustration of an device, according to one or more embodiments; intersection of a first plane with a surface of a sphere at a first 0034 FIG.16 provides an illustration with further detail of angle with respect to apole, according to one or more embodi an exemplary device configured to be coupled to a heading ments; device, according to one or more embodiments; 0055 FIG. 30C provides an exemplary illustration of a 0035 FIG. 17 provides an illustration with further detail of first plane that includes an origin of a sphere, a first position an exemplary device configured to coupled to one or more and a first equator intercept, according to one or more audio devices, according to one or more embodiments; embodiments; 0036 FIG. 18A provides an illustration with further detail 0056 FIG. 31A provides an exemplary illustration of a of an exemplary position device configured to be coupled to second determined vector associated with a second plane, an antenna, according to one or more embodiments; according to one or more embodiments; 0037 FIG. 18B provides an illustration with further detail 0057 FIG. 31B provides an exemplary illustration of an of an exemplary position device configured to include an intersection of a second plane with a surface of a sphere at a antenna, according to one or more embodiments: second angle with respect to a pole, according to one or more 0038 FIG. 18C provides an illustration with further detail embodiments; of an exemplary position device configured to be coupled to 0058 FIG. 31C provides an exemplary illustration of a two or more antennas, according to one or more embodi second plane that includes an origin of a sphere, a second ments; position and a second equator intercept, according to one or 0039 FIG. 19 provides an illustration with further detail of more embodiments; an exemplary bearing device, according to one or more 0059 FIG. 32A provides an exemplary illustration of an embodiments; intersection of a first plane and a second plane that indicates 0040 FIG. 20 illustrates exemplary axes of exemplary a position of a remote object, according to one or more devices, according to one or more embodiments; embodiments; 0041 FIG. 21 illustrates an exemplary power supply con 0060 FIG. 32B provides an exemplary illustration of a figured to be coupled to an exemplary power Source, accord third determined vector, according to one or more embodi ing to one or more embodiments; ments; 0042 FIG. 22 illustrates an exemplary power system, 0061 FIG. 32C provides an exemplary illustration of a according to one or more embodiments; third determined vector scaled via a scalar or radius, accord 0043 FIG. 23 illustrates an exemplary mobile device con ing to one or more embodiments; figured to include an exemplary power Supply configured to 0062 FIG.33 provides an exemplary method of determin be coupled to an exemplary power source, according to one or ing a great arc, according to one or more embodiments; more embodiments; 0063 FIG.34 provides an exemplary method of determin 0044 FIG. 24 illustrates an exemplary mobile device con ing a plane, according to one or more embodiments; figured to include an exemplary power Supply and an exem 0064 FIG. 35 provides an exemplary illustration of deter plary power source, according to one or more embodiments; mined positions, according to one or more embodiments: 0045 FIG.25 illustrates an exemplary mobile device con 0065 FIG. 36 provides an exemplary illustration of a figured to include an exemplary power Supply coupled to an plane that includes determined positions, according to one or exemplary power source, according to one or more embodi more embodiments; ments; 0.066 FIG.37 provides an exemplary method of determin 0046 FIG. 26 illustrates an exemplary mobile device con ing a distance, according to one or more embodiments; figured to include an exemplary power Supply that includes a 0067 FIG.38 provides an exemplary method of determin wireless power receiver, according to one or more embodi ing a distance to a plane, according to one or more embodi ments; ments; 0047 FIG. 27A provides an exemplary illustration of an 0068 FIG. 39A provides an exemplary method of deter exemplary wearable mobile device of a first configuration, mining, utilizing a first bearing from a first position to an according to one or more embodiments; object at a second position, a first great circle intercept, 0048 FIG. 27B provides an exemplary illustration of an according to one or more embodiments; exemplary wearable mobile device of a second configuration, 0069 FIG. 39B provides an exemplary method of deter according to one or more embodiments; mining, utilizing a second bearing from a second position to 0049 FIG. 27C provides an exemplary illustration of an an object at a second position, a second great circle intercept, exemplary mobile device, according to one or more embodi according to one or more embodiments ments; (0070 FIG. 39C provides an exemplary method of deter 0050 FIG. 28A illustrates an exemplary method of deter mining a vector that is normal to a first position, an origin, and mining a plane that includes a determined position and apole, a second position of a remote object, according to one or more according to one or more embodiments; embodiments; US 2015/0260527 A1 Sep. 17, 2015

0071 FIG. 40 provides an exemplary illustration that pro 0090 FIG. 58 provides an exemplary method of comput vides further details or a magnified view of a portion of FIG. ing, utilizing one or more image sensors, a position of a 30B, according to one or more embodiments; remote object from two positions, according to one or more 0072 FIG. 41 provides an exemplary illustration that pro embodiments vides further details or a magnified view of a portion of FIG. (0091 FIG.59 provides an exemplary method of determin 31B, according to one or more embodiments; ing a position of a remote object via utilizing multiple devices 0073 FIG. 42 provides an exemplary method of determin at multiple positions, according to one or more embodiments; ing, utilizing a bearing from a first position to an object at a 0092 FIG. 60 provides an exemplary illustration of a user, second position, a plane that includes the first position, an at a first position, sighting a remote object via a mobile device origin, and the second position, according to one or more at a first position, according to one or more embodiments: embodiments; 0093 FIG. 61 provides an exemplary illustration of a user, 0074 FIG. 43 provides an exemplary method of comput at a second position, sighting a remote object via a mobile ing a product of two quaternions via matrix multiplication, device, according to one or more embodiments; according to one or more embodiments: 0094 FIG. 62A provides an exemplary illustration of pro 0075 FIG. 44 provides an exemplary method of comput viding a position of a remote object via a map, according to ing, utilizing a bearing from a first position to an object at a one or more embodiments; second position, a plane that includes the first position, an 0.095 FIG. 62B provides an exemplary illustration of pro origin, and the second position, according to one or more viding an estimated position of a remote object via a map. embodiments; according to one or more embodiments; 0076 FIG.45 provides an exemplary method of determin 0096 FIG. 63 provides an exemplary illustration of pro ing, utilizing a bearing from a first position to an object at a viding a map and information based on a position of a remote second position and matrices, a plane that includes the first object via a display, according to one or more embodiments; position, the second position, and an origin, according to one 0097 FIG. 64 provides an exemplary illustration of con or more embodiments; figuration of a mobile device and one or more service com 0077 FIG. 46 provides an exemplary method of determin puting devices coupled to a network, according to one or more ing a position relative to one or more great circles, according embodiments; to one or more embodiments; 0.098 FIG. 65 provides an exemplary method of determin 0078 FIG.47 provides an exemplary method of determin ing a position of a remote object and providing the position to ingaposition may be determined from two planes determined a user via the map, according to one or more embodiments; via least squares, according to one or more embodiments: and 007.9 FIG. 48 provides an exemplary method of determin 0099 FIG. 66 provides an exemplary illustration of a dis ing a bearing to a remote object, according to one or more play that displays information, according to one or more embodiments; embodiments. 0080 FIG. 49 provides an exemplary illustration of posi 0100 While one or more embodiments, examples, and/or tions lying on great circles of a sphere, according to one or instances described may be susceptible to various modifica more embodiments; tions and alternative forms, specific embodiments thereofare 0081 FIG.50 provides an exemplary method of determin shown by way of example in the drawings and will herein be ing, utilizing a bearing, a distance along a first great circle described in detail. It should be understood, however, that the from a position to a second great circle, according to one or drawings and detailed description thereto are not intended to more embodiments; limit the disclosure to the particular form disclosed, but on the 0082 FIG.51 provides an exemplary method of determin contrary, the disclosure is to cover all modifications, equiva ing a distance along a first great circle from a position to a lents and alternatives falling within the spirit and scope of this second great circle, according to one or more embodiments disclosure. Moreover, some of the drawings and/or illustra 0083 FIG. 52A provides an exemplary illustration of a tions are not drawn to scale and are drawn and/or illustrated to vehicle and one or more cameras, according to one or more show and/or demonstrate by way of example as may be embodiments; expressed via drawings and/or illustrations. 0084 FIG. 52B provides an exemplary illustration of a mobile device and a camera, according to one or more DETAILED DESCRIPTION embodiments; 0101. In one or more embodiments, one or more systems, 0085 FIG. 53 provides an exemplary image of a remote methods, and/or processes described herein may compute a object acquired via a camera at a first position, according to position of a remote object. For example, computing the one or more embodiments; position of the remote object may be based on a first bearing I0086 FIG. 54 provides an exemplary image of a remote at a first position and a second bearing at a second position. In object acquired via a camera at a second position, according one or more embodiments, a bearing to the remote object may to one or more embodiments: be based on an angular difference between a geographic 0087 FIG. 55 provides an exemplary image of a remote position and the remote object. In one example, the bearing to object acquired via a camera at a first position, according to the remote object may be based on an angular difference one or more embodiments; between a geographic pole (e.g., a geographic north pole, a 0088 FIG. 56 provides an exemplary image of a remote geographic South pole, etc.) and the remote object. In another object acquired via a camera at a second position, according example, the bearing to the remote object may be based on an to one or more embodiments; angular difference between a magnetic pole (e.g., a magnetic 0089 FIG. 57 provides an exemplary image of a remote north pole, a magnetic South pole, etc.) and the remote object. object acquired via a camera at a third position, according to 0102. In one or more embodiments, computing the angu one or more embodiments; lar difference between the geographic pole and the remote US 2015/0260527 A1 Sep. 17, 2015 object may include computing an angular difference between object which may be utilized in computing the position of the a magnetic pole (e.g., a magnetic north pole, a magnetic South remote object. For example, one or more systems, methods, pole, etc.) and the remote object. For example, a bearing and/or processes described herein may compute an intersec device may be oriented with respect to the remote object, and tion of the first plane and the second plane, where the inter one or more measurements of a magnetic field of a planet may section of the first plane and the second plane includes a line be utilized in computing the angular difference between the that includes the position of the remote object. For instance, magnetic pole and the remote object. In one or more embodi the position of the remote object may be on a planet (e.g., ments, the magnetic pole may not be at a same position as the Earth), and the intersection of the first plane and the second geographic pole, and a declination angle and the angular plane may include the position of the remote object. In one or difference between the magnetic pole and the remote object more embodiments, computing the intersection of the first may be utilized in computing the angular difference between plane and the second plane may include computing a line the geographic pole and the remote object. and/or a vector. For example, computing the vector of the 0103) In one or more embodiments, a declination angle intersection of the first plane and the second plane may may depend on one or more of a position and a time, among include computing an angular latitude measure and an angu others. In one example, a declination angle at a first position larlongitude measure. For instance, the position of the remote may be different from a declination angle at a second position. object may be on the planet (e.g., at a radius from a center of In another example, a declination angle at a first point in time the planet) and at the angular latitude measure and at the may be different from a declination angle at a second point in angular longitude measure. time. For instance, one or more positions of respective one or 0108. In one or more embodiments, one or more devices more magnetic poles of a planet may change over a period of and/or systems described herein may communicate, utilizing time transpiring. one or more signals, in one or more of a wireless fashion and 0104. In one or more embodiments, a position of a remote a wired fashion. In one example, the bearing device may be a object may be computed without interrogating the remote handheld bearing device that may communicate bearing object with Sound waves or electromagnetic waves. In one information via one or more signals in a wireless fashion or in example, a position of a remote object may be computed a wired fashion. In a second example, a global positioning without interrogating the remote object with Sonar. In another device may communicate position information via one or example, a position of a remote object may be computed more signals in a wireless fashion or in a wired fashion. In without interrogating the remote object with radar (e.g., laser another example, a device, as described herein, may commu radar, microwave radar, etc.). In one or more embodiments, a nicate information via one or more signals in a wireless fash position of a remote object may be computed when the remote ion or in a wired fashion. object is position outside a constellation of ranging signal 0109. In one or more embodiments, one or more devices generating devices. For example, a position of a remote object and/or systems described herein may communicate utilizing outside a constellation of pseudolites or satellites may be one or more media and/or protocols that may include one or determined from a position within the constellation of more portions of one or more of NMEA (National Marine pseudolites or satellites. Electronics Association) 0180, NMEA 0182, NMEA 0183. 0105. In one or more embodiments, a position of a remote NMEA 2000, IEEE (Institute of Electrical and Electronics object may be determined from various positions. In one Engineers) 802.3, IEEE 802.11, IEEE 802.15, IEEE 802.15. example, a position of a remote object may be determined 4, Bluetooth, ZigBee, an open wireless protocol, and a pro from positions on land. In a second example, a position of a prietary wireless protocol, among others. In one example, one remote object may be determined from positions on water or more devices and/or systems described herein may com (e.g., sea, ocean, river, lake, etc.). In a third example, a posi municate, utilizing IEEE 802.11, with another device. For tion of a remote object may be determined from positions in instance, one or more devices and/or systems described air (e.g., from an aerial vehicle. Such as a glider, an airplane, herein may be or include a WiFi access point that may com a helicopter, etc.). In another example, a position of a remote municate information with one or more of a laptop computer, object may be determined from positions in space (e.g., from a personal digital assistant, a Smartphone, a tablet computing a satellite, a space station, a space ship, a space vehicle, etc.). device, a digital wearable device (e.g., a digital watch, a 0106. In one or more embodiments, one or more mobile device coupled to a lanyard, a device coupled to a headband, devices may be utilized in computing the position of the etc.), and a digital music player, among others. In another remote object based on the first bearing at the first position example, one or more devices and/or systems described and the second bearing at the second position. In one herein may communicate, utilizing one or more of Bluetooth, example, a position device (e.g., a global position system ZigBee, and IEEE 802.15.4, among others, with another device) may be utilized in computing one or more of the first device. For instance, one or more devices and/or systems position and the second position, among others. In another described herein may communicate information, via Blue example, a bearing device may be utilized computing one or tooth, ZigBee, and/or IEEE 802.15.4, with one or more of a more of the first bearing and the second bearing, among laptop computer, a personal digital assistant, a Smartphone, a others. For instance, the bearing device may be or include an tablet computing device, a digital wearable device (e.g., a electric compass that may transform an orientation of the digital watch, a device coupled to a lanyard, a device coupled bearing device into an angular difference between a magnetic to a headband), and a digital music player, among others. pole and the orientation of the bearing device. 0110. In one or more embodiments, one or more devices 0107. In one or more embodiments, one or more systems, and/or systems described herein may be controlled and/or methods, and/or processes described herein may compute a configured in one or more of a wireless fashion and a wired first plane that includes the first position, the position of the fashion. In one example, one or more devices and/or systems remote object, and an origin and may compute a second plane described herein may be or include a WiFi access point that that includes the second position, the position of the remote may receive configuration information (e.g., positions of US 2015/0260527 A1 Sep. 17, 2015

marks in a sailboat race, declination information, playlist example, the user may sight object 3210 utilizing a sighting information, etc.) from a laptop computer, a personal digital device. In one or more embodiments, object 3210 may be or assistant, a Smartphone, a tablet computing device, a digital include a staff (e.g., a flag staff), which may be mounted on a wearable device, and a digital music player, among others. In vessel 3110 (e.g., a race committee boat). As illustrated, the a second example, one or more devices and/or systems user may establish a sight line 3410 utilizing a sighting described herein may be controlled in a wireless fashion. In device. FIG. 4 illustrates another view of establishing sight one instance, one or more devices and/or systems described line 3410 utilizing the sighting device, according to one or herein may receive, in a wireless fashion or in a wired fashion, more embodiments. control information that indicates that a Volume of an audio 0115 Turning now to FIGS.5A and 5B, a user sighting a output device is to be increased or decreased. In a second remote object is illustrated, according to one or more embodi instance, one or more devices and/or systems described ments. As shown in FIG.5A, a user 5010 (e.g., an occupant, herein may receive, in a wireless fashion or in a wired fashion, a crew member, etc.) of vessel 3010 may, utilizing sighting control information that indicates that a next song is to be device 5110, sight a remote object. As illustrated, user 5010 output via an audio output device. may orient sighting device 5110 to establish a sight line 5410 0111. In a third example, one or more devices and/or sys to an object. In one example, user 5010 may orient sighting tems described herein may receive, in a wireless fashion or in device 5110 to establish a sight line to object 3210, and sight a wired fashion, control information that indicates that a clock line 5410 may be or include sight line 3410. In another may be started and/or initiated (e.g., a countdown clock to a example, user 5010 may orient sighting device 5110 to estab start of a sailboat race). In a fourth example, one or more lish a sight line to object 3220, and sight line 5410 may be or devices and/or systems described herein may receive, in a include sight line 7410. wireless fashion, configuration information that indicates that 0116. In one or more embodiments, sighting device 5110 a time (e.g., global positioning time, WWVB time, etc.) that may have or include a form that is similar to one or ore of a may be utilized in configuring one or more clocks, timing handheld firearm, a rifle, a hair dryer, and a handheld drill, mechanisms, and/or timing devices of the one or more among others. In one example, sighting device 5110 may devices and/or systems described herein. have or include a pistol grip that may be grasped by a user. In 0112. In a fifth example, one or more devices and/or sys another example, a top of sighting device 5110 may have or tems described herein may receive, via an audio interface include an alignment guide or a scope that may be utilized in (e.g., a microphone), control information that indicates con orienting sighting device 5110 such that sight line 5410 may trol information and/or configuration information. For be established from sighting device 5110 to an object. In one instance, one or more devices and/or systems described or more embodiments, sighting device 5110 may include a herein may include a speech to text device that may transform bearing device that may compute a magnetic bearing associ speech from a language from a human to one or more of text, ated with sight line 5410 and a magnetic pole. For example, numbers, configurations, and commands, among others. In the bearing device may compute the magnetic bearing asso another example, one or more devices and/or systems ciated with sight line 5410 and the magnetic pole via one or described herein may be coupled to a wide area network (e.g., more measurements of one or more magnetic fields associ an Internet) and may receive information from the wide area ated with the magnetic pole. For instance, the bearing device network. For instance, declination information, weather may measure a magnetic field associated with the magnetic information, Sea condition information, etc. may be received pole with respect to one or more axes and may compute the from the wide area network. In one or more embodiments, the magnetic bearing, associated with sight line 5410 and the wide area network may be accessed via one or more of local magnetic pole, utilizing one or more measurements of the area network, a public switched telephone network, a cellular magnetic field associated with the magnetic pole. telephone communications network, a satellite telephone 0117. As illustrated in FIG. 5B, user 5010 may utilize a communications network, and a satellite communications device 27610 to sight an object. In one or more embodiments, network, among others. device 27610 may be or include one or more of a personal 0113. In one or more embodiments, a position, as utilized digital assistant (PDA), a portable computer, a Smartphone, a herein, may mean an estimated position. In one example, a wireless telephone (e.g., a cellular telephone, a satellite tele position device may provide position information Such as a phone, etc.), a digital music player, a tablet computing device, computed position and a radius of uncertainty (e.g., a few a wearable computing device, a communications device, and centimeters to a few meters). In another example, a bearing other wired or wireless device, among others. As shown, user device may be accurate to a tenth to five tenths of a degree. For 5010 may orient device 27610 to establish a sight line 5410 to instance, the accuracy of the bearing device may measured an object. In one example, user 5010 may orient device 27610 via a RMS (root mean square) method or process. In one or to establish a sight line to object 3210, and sight line 5410 more embodiments, computing a position of a remote object may be or include sight line 3410. In another example, user may be computing an estimated position of a remote object, 5010 may orient device 27610 to establish a sight line to where an accuracy may be based on one or more accuracies of object 3220, and sight line 5410 may be or include sight line devices utilized in computing the estimated position of the 741O. remote object. 0118. In one or more embodiments, device 27610 may 0114 Turning now to FIG.3, a vessel sighting a first object include a bearing device that may compute a magnetic bear from a first position is illustrated, according to one or more ing associated with sight line 5410 and a magnetic pole. For embodiments. In one or more embodiments, a first object example, the bearing device may compute the magnetic bear 3210 may be or include a first end ofa starting line 3310, and ing associated with sight line 5410 and the magnetic pole via a second object 3220 may be or include a second end of one or more measurements of one or more magnetic fields starting line 3310. As shown, a user (e.g., an occupant, a crew associated with the magnetic pole. For instance, the bearing member, etc.) of a vessel 3010 may sight object 3210. For device may measure a magnetic field associated with the US 2015/0260527 A1 Sep. 17, 2015

magnetic pole with respect to one or more axes and may altitude may be or include an altitude (e.g., a height above a compute the magnetic bearing, associated with sight line sea level) of Lake Travis, Texas. In a second instance, the 5410 and the magnetic pole, utilizing one or more measure altitude may be or include an altitude (e.g., a height above a ments of the magnetic field associated with the magnetic pole. sea level) of Lake Tahoe, Nevada. In a third instance, the 0119. In one or more embodiments, device 27610 may altitude may be or include an altitude (e.g., a height below a include a position device that may provide one or more posi sea level) of the Dead Sea. In another example, the altitude tions. For example, the position device may be or include a may be or include an altitude (e.g., a height below a sea level) global positioning system device that may receive multiple of Death Valley. location signals and/or ranging signals and/or may compute 0.125. In another example, a radius of sphere 6000 may the one or more positions via the location signals and/or the changed according to a model. For instance, a model may ranging signals. In one or more embodiments, the position utilize a first radius for one or more calculations and may device may function as a bearing device. utilize a second radius for one or more other calculations 0120 Turning now to FIG. 6A, an exemplary sphere and and/or for modeling a planet (e.g., Earth). In one or more exemplary positions associated with the sphere are illus embodiments, a model may utilize a unit radius (e.g., a radius trated, according to one or more embodiments. As shown, a of a unity value or 'one' according to a metric and/or a sphere 6000 may be associated with one or more of an equator measure) and may utilize a radius of MSL, plus an altitude if 6110, a first pole 6120 (e.g., a north pole, etc.), and a second not at MSL. In one or more embodiments, an altitude may pole 6130 (e.g., a South pole), among others. In one or more include a positive or negative number or measure. embodiments, equator 6110 may be or include a great circle I0126. As illustrated in FIG. 6A, positions 6010, 6210, and of sphere 6000 and may be perpendicular to a line between 6220 may be associated with positions on a surface of sphere poles 6120 and 6130 and/or perpendicular to (e.g., normal to) 6000. In one example, position 6010 may be, include, and/or a plane that includes poles 6120 and 6130. In one or more be associated with a first position of vessel 3010 and/or a first embodiments, equator 6110 may be or include a great circle position of sighting device 5110. In a second example, posi of sphere 6000, where all points of the great circle are equi tion 6210 may be, include, and/or be associated with a posi distant to both poles 6120 and 6130. In one or more embodi tion of object 3210. In another example, position 6220 may ments, a great circle of a sphere may be an intersection of a be, include, and/or be associated with a position of object plane and points of the surface of the sphere, where the plane 3210. As shown, sight line 3410 may be a sight line between includes an origin of the sphere. In one or more embodiments, positions 6010 and 6210. a great circle of a sphere may be a Riemannian circle. I0127. As illustrated in FIG. 6B, positions 6015, 6215, and 0121. In one or more embodiments, a sphere. Such as 6225 may be associated with positions on a surface of sphere sphere 6000, may approximate a planet, may provide a model 6000. In one example, position 6015 may be, include, and/or of a planet, and/or may be utilized as an approximation and/or be associated with a first position of vessel 3010 and/or a first a model of a planet. For example, sphere 6000 may model a position of sighting device 5110. In a second example, posi planet, such as Earth (e.g., Earth 6710 of FIG. 6D), and/or tion 6215 may be, include, and/or be associated with a posi may provide an approximation of a planet, such as Earth 6710 tion of object 3210. In another example, position 6225 may illustrated in FIG. 6E. be, include, and/or be associated with a position of object 0122. In one or more embodiments, a planet (e.g., Earth) 3210. As shown, sight line 3410 may be a sight line between may be approximated by an ellipsoid. For example, Earth positions 6015 and 6215. may be associated with a mean equatorial radius of 6378.137 I0128. As illustrated in FIG. 6C, positions 6017, 6217, and km and may be associated with a mean polar radius (e.g., a 6227 may be associated with positions on a surface of sphere measure normal to the equatorial plane to a pole) of 6356. 6000. In one example, position 6017 may be, include, and/or 7523142 km. For instance, a cross-section of the Earth that is be associated with a first position of vessel 3010 and/or a first normal to its equatorial plane may be ellipsoidal. In one or position of sighting device 5110. In a second example, posi more embodiments, a sphere, such as sphere 6000, may tion 6217 may be, include, and/or be associated with a posi approximate an ellipsoid model of Earth. For example, deter tion of object 3210. In another example, position 6227 may mining distance measurements that are not over a horizon be, include, and/or be associated with a position of object (e.g., a horizon of Earth) may utilize the sphere. Such as 3210. As shown, sight line 3410 may be a sight line between sphere 6000, to approximate the ellipsoid model of Earth. For positions 6017 and 6217. instance, this approximation of the ellipsoid model of Earth 0129. In one or more embodiments, one or more coordi may reduce one or more computations in computing distance nate systems may be utilized. In one example, a Cartesian measurements that are not over the horizon. coordinate system may be utilized. For instance, as illustrated 0123. In one or more embodiments, modeling Earth may in FIG. 6F, axes 6610, 6612, and 6614 may be, include, include utilizing information from WGS 84 (World Geodetic correspond to, and/or be associated with an X-axis, a y-axis, System 1984) or another geodetic system. For example, a and a Z-axis, respectively. In a second example, a polar coor measure of a radius from an origin to a position may be a dinate system may be utilized. For instance, as illustrated in function of the position. FIG. 6G, a vector 6810 may be described with reference to a 0.124. In one or more embodiments, a radius of sphere length or magnitude p, a first angle, 0, to a first reference 6000 may vary according to a position on a planet and/or direction (e.g., a positive X-axis or axis 6610). and a second according to a model. In one example, a radius of sphere 6000 angle, p, to a second reference direction (e.g., a positive Z-axis may be or include a measure from an origin of sphere 6000 to or axis 6614). In one or more embodiments, an origin of an average sea level (e.g., a mean sea level (MSL)) of Earth. sphere 6000 be or include an origin of a coordinate system. In a second example, a radius of sphere 6000 may be or 0.130 Turning now to FIG.7, a vessel sighting a first object include a measure from an origin of sphere 6000 to an average from a second position is illustrated, according to one or more sea level of Earth adjusted by an altitude. In one instance, the embodiments. As shown, a user associated with vessel 3010 US 2015/0260527 A1 Sep. 17, 2015 may sight object 3210. For example, the user may sight object example, devices 10013, 10014, and 10017 may be coupled in 3210 utilizing sighting device 5110. As illustrated, the user a wired fashion utilizing a star configuration. In another may establish a sight line 7410 utilizing sighting device 5110. example, devices 10013-10014, and 10017 may be coupled in For example, sight line 5410 may be or include sight line a wired fashion utilizing a multiple star configuration. In one 7410. FIG. 8 illustrates another view of establishing sight line instance, device 10012 may communicate, in wired fashion, 74.10 utilizing sighting device 5110, according to one or more with one or more of devices 10014 and 10017 via device embodiments. 10013. In a second instance, device 10012 may communicate, 0131 Turning now to FIGS. 9A-9C, exemplary spheres in a wired and/or wireless fashion, with one or more of and positions associated with the sphere are illustrated, devices 10010, 10011, and 10015-10019 via devices 10013 according to one or more embodiments. As shown in FIG.9A, and 10017. In another instance, one or more of devices 10013 a position 9010 may be associated with positions on a surface and 10014 may communicate, in a wired and/or wireless of sphere 6000. In one example, position 9010 may be, fashion, with one or more of devices 10010, 10011, and include, and/or be associated with a second position of vessel 10015-10019 via device 10017. 3010 and/or a second position of sighting device 5110. As 0.137 As shown in FIG. 12, one or more of devices 10012 shown, sight line 7410 may be a sight line between positions 10014 and 10017 may communicate in a wired fashion uti 9010 and 6210. In one or more embodiments, position 6010, lizing a wired bus. In one or more embodiments, a wired bus a bearing associated with sight line 3410, position 9010, a 12010 may couple devices 10012-10014 and 10017. In one bearing associated with sight line 7410 may be utilized to example, wired bus 12010 may be or include a wired serial determine position 6210. bus. In another example, wired bus 12010 may be or include (0132). As shown in FIG.9B, a position 9015 may be asso a wired parallel bus. ciated with positions on a surface of sphere 6000. In one 0.138. In one or more embodiments, wired bus 12010 may example, position 9015 may be, include, and/or be associated communicate data utilizing and/or via at least one of wired with a second position of vessel 3010 and/or a second position Ethernet, 1-Wire, IC (inter-integrated circuit). USB (univer of sighting device 5110. As shown, sight line 7410 may be a sal serial bus), FireWire (e.g., IEEE 1394), SPI (serial periph sight line between positions 9015 and 6215. In one or more eral interconnect), UART (universal asynchronous receiver/ embodiments, position 6015, a bearing associated with sight transmitter), RS-232, RS-422, RS-485, CAN (controller area line 3410, position 9015, a bearing associated with sight line network), LIN (local interconnect network), FlexRay. NMEA 74.10 may be utilized to determine position 6215. (National Marine Electronics Association) 2000 Bus, MOST 0133. As shown in FIG. 9C, a position 9017 may be asso (media oriented systems transport), DVI (digital visual inter ciated with positions on a surface of sphere 6000. In one face), HDMI (high-definition multimedia interface), and example, position 9017 may be, include, and/or be associated D2B (domestic digital bus), among others. In one or more with a second position of vessel 3010 and/or a second position embodiments, a device of devices 10010-10019 may be or of sighting device 5110. As shown, sight line 7410 may be a include a mobile device (MD). In one or more embodiments, sight line between positions 9017 and 6217. In one or more a device of devices 10010-10019 may be or include one or embodiments, position 6017, a bearing associated with sight more of a structure and a component, among others, of line 3410, position 9017, a bearing associated with sight line another device of devices 10010-10019. In one or more 74.10 may be utilized to determine position 6217. embodiments, a device of devices 10010-10019 may include 0134 Turning now to FIGS. 10-12, exemplary devices are one or more functionalities of another device of devices illustrated, according to one or more embodiments. As shown 10010-1OO19. in FIG. 10, a device of devices 10010-10019 may wirelessly 0.139 Turning now to FIG. 13, an exemplary device is communicate with another device of devices 10010-10019. illustrated, according to one or more embodiments. As In one or more embodiments, devices 10010-10019 may shown, device 10010 may include one or more memories communicate in a wireless mesh fashion. In one or more 13020 and 13021 coupled to a processor 13010. In one or embodiments, devices 10010-10019 may communicate in a more embodiments, a processor, described herein, may fetch wireless bus fashion. For example, device 10017 may func and/or receive instructions from one or more of memories and tion as a center of a wireless Star configuration. In one or more execute the instructions to implement one or more of an embodiments, a first portion of devices 10010-10019 may exemplary method, a process, an exemplary method element, communicate in a wireless mesh fashion, and a second por a process element, a portion of an exemplary method element, tion of devices 10010-10019 may communicate in a wireless and a portion of a process element, described herein. For bus fashion. example, a processor may implement an instruction set archi 0135. In one or more embodiments, two or more of devices tecture (ISA) and may execute instructions from and/or asso 10010-10019 may wirelessly communicate utilizing one or ciated with the ISA. For instance, the ISA may include at least more of IEEE (Institute of Electrical and Electronics Engi one of an ARMISA, a MIPS32 ISA, a MSP430 ISA, an AVR neers) 802.11, IEEE 802.15, Bluetooth. IEEE 802.15.4, Zig ISA, an AVR-32 ISA, x86 ISA, a DSP (digital signal proces Bee, ZWave, wireless USB (universal serial bus), WMBUS sor) ISA, a PPC ISA, and an 8051 ISA, among others. (wireless meter bus), IEEE 11073, and a custom wireless 0140. In one or more embodiments, a processor may protocol and/or interface. In one or more embodiments, a implement a custom ISA, and the processor may be or include device that may communicate with another device may at least one of an ASIC (application specific integrated cir include one or more of a wireless transmitter, a wireless cuit) and a FPGA (field programmable gate array). In one or receiver, and a wireless transceiver. more embodiments, at least one of an ASIC and a FPGA may 0136. As illustrated in FIG. 11, one or more of devices be configured to implement one or more processes, methods, 10012-10014 and 10017 may communicate in a wired fash and/or systems described herein. In one or more embodi ion, and device 10017 may wirelessly communicate with one ments, a processor may include one or more processing cores or more of devices 10010, 10011, and 10015-10019. In one that implement at least one ISA. In one example, a processor US 2015/0260527 A1 Sep. 17, 2015

may include multiple cores that implement one ISA. In threads, Contiki, Sybian OS, ThreadX, or Windows CE, another example, a processor may include multiple cores, among others. In one or more embodiments. OS 1303.0 may where a first core may implement a first ISA and a second core include an embedded OS. For example, the embedded OS implements a second ISA, different from the first ISA. For may include a RTOS, embedded Linux, Linux, embedded instance, the first ISA may include an ARM ISA, and the FreeBSD, FreeBSD, embedded NetBSD, NetBSD, Apple second ISA may include a C28x ISA. iOS, Google Android, or Minix, among others. 0141. In one or more embodiments, a processor may 0145. In one or more embodiments, an OS may include a include a Havard architecture. For example, a processor may run-to-completion configuration, execution hierarchy, and/or fetch and/or execute instructions from a first memory and scheduler for a processor. For example, an OS may include may utilize a second memory, different from the first memory, Tiny/OS. In one or more embodiments, an OS may include a for dynamic data storage and/or retrieval. For instance, a first state machine (e.g., a Mealy state machine, a Moore state memory may be or include non-volatile memory, and a sec machine, a hierarchical state machine, a finite state machine, ond memory may be or include Volatile memory. In one or etc.) configuration, execution hierarchy, and/or scheduler for more embodiments, a processor may include a Von Neumann processor 13010. For example, OS 1303.0 may include a architecture. For example, a processor may fetch and/or hierarchical state machine kernel such as QP/C, QP/C++, or execute instructions from a first memory and/or a second QP-nano, among others. In one or more embodiments, an OS memory, and the processor may utilize the first memory and/ may not be included in a device, and one or more of APPs, a or the second memory for dynamic data storage and/or web server, may be or include a “bare metal configuration, retrieval. In one or more embodiments, multiple memories execution hierarchy, and/or scheduler for a processor. may be combined into a single device, or the multiple memo 0146 Turning now to FIG. 14, an exemplary device is ries may be included in two or more separate devices. In one illustrated, according to one or more embodiments. As example, one or more of memories may be included in a shown, device 10017 may include a memory 14020 coupled processor. In another example, one or more of memories may to a processing unit 14010. As illustrated, memory 14020 be external to a processor. may include one or more of an OS 14030, APPs 14031 0142. As illustrated, one or more of a GPIO (general pur 14033, a web server 14034, user data 14035, and APP data pose input/output) 13040, a USB interface 13050, a USB 14036, among others. In one or more embodiments, processor interface 13051, a SPI (serial peripheral interconnect) inter 14010 may execute one or more of OS 14030, applications face 13060, a SPI interface 13061, an IC (inter-integrated APPS 14031-14033, and web server 14034 and/or utilized circuit) interface 13070, an IC interface 13071, a UART one or more of user data 14035, and APP data 14036 to interface 13080, a UART interface 13081, a network interface implement one or more of an exemplary method, a process, an 13090, a network interface 13091, a wireless interface 13100, exemplary method element, a process element, a portion of an and a wireless interface 13101 may be coupled to processor exemplary method element, and a portion of a process ele 13010. In one or more embodiments, one or more other ment, described herein. devices and/or systems may be coupled to processor 13010 0147 As shown, processing unit 14010 may be coupled to via one or more of components 13040-13101. In one a memory 14021, a GPIO interface 14040, a USB interface example, device 10010 may be or include a SoC (system on 14050, one or more SPI interfaces 14060 and 14061, one or chip) that includes one or more of components 13040-13101, more IC interfaces 14070 and 14071, one or more UARTs and one or more other devices and/or systems may be coupled 14080 and 14081, one or more network interfaces 14090 and to processor 13010 via one or more of components 13040 14091, and one or more wireless interfaces 14100 and 14101, 13101. In a second example, device 10010 may be or include among others. As illustrated, one or more buttons 14400 a microcontroller (e.g., a MCU) that includes one or more of 14402 may be coupled to GPIO interface 14040. In one or components 13040-13101, and one or more other devices more embodiments, processing unit 14010 may receive user and/or systems may be coupled to processor 13010 via one or input via one or more buttons. As shown, a display 14370 may more of components 13040-13101. In another example, be coupled to SPI interface 14060. In one or more embodi device 10010 may be or include an application(s) processor ments, processing unit 14010 may provide output via a dis that includes one or more of components 13040-13101, and play. one or more other devices and/or systems may be coupled to 0148 Turning now to FIG. 15, an exemplary device is processor 13010 via one or more of components 13040 illustrated, according to one or more embodiments. As 13101. shown, device 10012 may include one or more memories 0143. As shown, memory 13020 may include one or more 15020 and 15021 coupled to a processing unit 15010. As of an operating system (OS) 13030, applications (APPs) illustrated, memory 15020 may include one or more of an OS 13031-13033, a web server 13034, user data 13035, and 15030, APPs 15031-15033, user data 15035, and APP data application (APP) data 13036, among others. In one or more 15036, among others. In one or more embodiments, processor embodiments, processor 13010 may execute one or more of 15010 may execute one or more of OS 15030, and applica OS 13030, applications APPs 13031-13033, and web server tions APPs 15031-15033, and/or utilized one or more of user 13034 and/or utilized one or more of user data 13035, and data 15035, and APP data 15036 to implement one or more of APP data 13036 to implement one or more of an exemplary an exemplary method, a process, an exemplary method ele method, a process, an exemplary method element, a process ment, a process element, a portion of an exemplary method element, a portion of an exemplary method element, and a element, and a portion of a process element, described herein. portion of a process element, described herein. As shown, processor 15010 may be coupled to one or more of 0144. In one or more embodiments, an OS may include a a GPIO interface 15040 and a network interface 15090, realtime OS (RTOS). For example, the RTOS may include among others. FreeRTOS, OpenRTOS, SafeRTOS, uC/OS-II, uC/OS-III, 0149. As illustrated, processing unit 15010 may be NuttX, SYS/BIOS, QNX, VxWorks, LynxOS OSE, Atom coupled to a serial interface 15210, and serial interface 15210 US 2015/0260527 A1 Sep. 17, 2015

may include one or more of one or more UARTs 15080 and waypoints. In a second example, APP data may include con 15081, one or more of IC interfaces 15070 and 15071, one or figuration information that may allow position device 15310 more SPI interfaces 15060 and 15061, and one or more USB to determine a position. In another example, one or more of interfaces 15050 and 15051, among others. As shown, serial OS 15430 and one or more of APPs 15431-15433 may interface 15210 may be coupled to one or more of a position include instructions that are executable by processor 15410 to device 15310 and a wireless interface 15100, among others. implement one or more processes, methods, and/or systems 0150 Turning now to FIG. 16, an exemplary device is described herein. illustrated, according to one or more embodiments. As (O155 As illustrated, position device 15310 may include a shown, device 10014 may include one or more memories serial interface 15440 coupled to processor 15410. As shown, 16020 and 16021 coupled to a processing unit 16010. As serial interface may include one or more of a USB interface illustrated, memory 16020 may include one or more of an OS 15450, a SPI interface 15460, an IC interface 15470, a 16030, APPs 16031-16033, user data 16035, and APP data UART interface 15480, and a CAN interface 15490, among 16036, among others. In one or more embodiments, processor others. As shown, position device 15310 may include one or 16010 may execute one or more of OS 16030, and APPs more of a wireless interface 15400 and a network interface 16031-16033, and/or utilized one or more of user data 16035, 15490. In one or more embodiments, position device 15310 and APP data 16036 to implement one or more of an exem may communicate with one or more other devices via one or plary method, a process, an exemplary method element, a more of wireless interface 15400, serial interface 15440, and process element, a portion of an exemplary method element, network interface 15490, among others. and a portion of a process element, described herein. As 0156. As shown, an antenna 15495 may be coupled to shown, processor 16010 may be coupled to one or more of a processing unit 15410 via an analog to digital converter GPIO interface 16040 and a network interface 16090, among (ADC) 15494. In one or more embodiments, position device others. 15310 may determine a position based on a location of 0151. As illustrated, processing unit 16010 may be antenna 15495. In one example, antenna 15495 may be a coupled to a serial interface 16210, and serial interface 16210 passive antenna. In another example, antenna 15495 may be may include one or more of one or more UARTs 16080 and an active antenna. For instance, antenna 15495 may include 16081, one or more of IC interfaces 16070 and 16071, one or one or more active electronic components (e.g., one or more more SPI interfaces 16060 and 16061, and one or more USB transistors) and/or one or more active electronic circuits (e.g., interfaces 16050 and 16051, among others. As shown, serial one or more of an amplifier and an impedance matching interface 16210 may be coupled to one or more of a heading circuit, among others). In one or more embodiments, position device 16310 and a wireless interface 16100, among others. device 15310 may include antenna 15495, as shown in FIG. 0152 Turning now to FIG. 17, an exemplary device is 18B. illustrated, according to one or more embodiments. As (O157. As illustrated, a clock 15498 may be coupled to shown, device 10013 may include one or more memories processing unit 15410. In one or more embodiments, clock 17020 and 17021 coupled to a processing unit 17010. As 15498 may be or may not be synchronized with one or more illustrated, memory 17020 may include one or more of an OS clocks of respective one or more satellites, pseudolites, and/or 17030, APPs 17031-17033, user data 17035, and APP data ground stations. In one example, a bias error (e.g., a consis 17036, among others. In one or more embodiments, processor tent error, repeatable error, etc.) and/or a constant offset may 17010 may execute one or more of OS 17030, and APPs be associated with clock 15498 and a system time (e.g., a 17031-17033, and/or utilized one or more of user data 17035, global positioning system time). In another example, one or and APP data 17036 to implement one or more of an exem more clocks of respective one or more of satellites, pseudo plary method, a process, an exemplary method element, a lites, and/or ground stations may be offset from the system process element, a portion of an exemplary method element, time. In one or more embodiments, clock 15498 may include and a portion of a process element, described herein. As an oscillator that may be utilized in generating time informa shown, processor 17010 may be coupled to one or more of a tion and/or timing information. In one example, clock 15498 GPIO interface 17040 and a network interface 17090, among may include a ceramic oscillator. In another example, clock others. As illustrated, GPIO interface 17040 may be coupled 15498 may include a quartz oscillator. In one or more to one or more of an audio output device 17360 and an audio embodiments, clock 15498 may be or include anatomic clock input device 17370, among others. that may be utilized in generating time information and/or 0153. As shown, processing unit 17010 may be coupled to timing information. For example, clock 15498 may be or a serial interface 17210, and serial interface 17210 may include a chip-scale atomic clock. include one or more of one or more UARTs 17080 and 17081, 0158. In one or more embodiments, time information and/ one or more of IC interfaces 17070 and 17071, one or more or timing information from clock 15498 may be utilizing in SPI interfaces 17060 and 17061, and one or more USB inter determining a position of antenna 15495. For example, a faces 17050 and 17051, among others. As illustrated, serial pseudo range from antenna 15495 to a satellite, pseudolite, or interface 17210 may be coupled to one or more of a heading ground station may be determined utilizing clock 15498 device 17310 and a wireless interface 17100, among others. which may be or may not by synchronized with a clock of the 0154 Turning now to FIG. 18A, a position device is illus satellite, pseudolite, or ground station. For instance, the trated, according to one or more embodiments. As shown, pseudo range may be determined utilizing first time informa position device 15310 may include one or more memories tion from the satellite, pseudolite, or ground station and sec 15420 and 15421 coupled to a processor 15410. As illus ond time information from clock 15498 which may be or may trated, memory 15420 may include one or more of an OS not be synchronized with the clock of the satellite, pseudolite, 15430, user data 15435, APP data 15436, and one or more or ground station. APPs 15431-15433, among others. In one example, user data 0159. In one or more embodiments, position device 15310 15435 may include information associated with one or more may determine a position of antenna 15495 via receiving US 2015/0260527 A1 Sep. 17, 2015 multiple signals, via antenna 15495, from respective multiple a rate at least twice a chipping rate (e.g., a digital clock rate, satellite(s), pseudolite(s), and/or ground station(s). In one a digital clock frequency, etc.) of the BOC(X(m,n) code. example, position device 15310 may determine a position of 0164. In another example, the signal from the satellite, antenna 15495 via receiving at least three signals from pseudolite, or ground station may include a PRN code, the respective at least three satellites, pseudolites, and/or ground signal from the satellite, pseudolite, or ground station may be stations. In another example, position device 15310 may down convened to an intermediate frequency signal, and determine a position of antenna 15495 via receiving at least ADC 15494 may sample the intermediate frequency signal at four signals from respective at least four satellites, pseudo a rate at least twice a chipping rate (e.g., a digital clock rate, lites, and/or ground stations. For instance, the at least four a digital clock frequency, etc.) of the PRN code. In one signals from respective at least four satellites, pseudolite, instance, the chipping rate may be 1.023 MHz for a L1 C/A and/or ground stations may be utilized in populating infor code. In another instance, the chipping rate may be 10.23 mation associated with four equations of four unknowns (e.g., MHz for a L1 and L2 P(Y) code. In one or more embodi x, y, and Z of antenna 15495 and a time offset), and pro ments, oversampling may reduce a receiver sensitivity to an cessor 15410 may execute instructions from a memory (e.g., analog to digital conversion, which may reduce a number of memory 15420, memory 15421, etc.) to compute the four bits required for an analog to digital conversion. unknowns that are associated with and/or that include the 0.165. In one or more embodiments, processing unit 15410 position of antenna 15495. may perform one or more DSP functions. In one example, 0160. In one or more embodiments, signals from multiple processing unit 15410 may execute instructions from a satellites, pseudolites, and/or ground stations may include a memory to perform one or more DSP functions. In another direct sequence spread spectrum (DSSS) modulation that example, processing unit 15410 may include a digital signal may provide a structure for transmission and/or reception processing unit that may perform one or more DSP functions. ranging signals and/or navigation data. In one example, the In one or more embodiments, processing unit 15410 may signals from multiple of Satellite(s), pseudolite(s), and/or receive samples from ADC 15494 and may process the ground station(s) may include ranging signals that may samples. In one example, multiple digital signal processing include PRN (pseudorandom noise) codes that may binary channels may process multiple codes from respective mul phase shift key (BPSK) one or more carrier frequencies of the tiple satellites, pseudolites, and/or ground stations. For signals from multiple satellites, pseudolites, and/or ground instance, N (e.g., a positive integer greater than one) digital stations. In one instance, a carrier frequency and/or center signal processing channels may process N codes from respec frequency may include 1176.45 MHz (e.g., L5). In a second tive N satellites, pseudolites, and/or ground stations. In instance, a carrier frequency and/or center frequency may another example, the digital signal processing unit may include 1227.6 MHz (e.g., L2). In another instance, a carrier include N (e.g., a positive integer greater than one) digital frequency and/or center frequency may include 1575.42 MHz signal processing channels that may process N codes from (e.g., L1). In another example, the signals from multiple of respective N satellites, pseudolites, and/or ground stations. satellite(s), pseudolite(s), and/or ground station(s) may (0166 In one or more embodiments, each channel of the include ranging signals that may include M-codes that may multiple digital signal processing channels may compute include and/or utilize a binary offset carrier that may be code measurements, carrier-phase measurements, and/or referred to as BOC(m,n) codes. For instance, M-codes may navigation data demodulation. For example, each channel of include BOC(10.5) codes. the multiple digital signal processing channels may include 0161 In one or more embodiments, utilizing BCX(m,n) code and/or carrier tracking loops to compute the code mea codes may include modulating a signal, where a modulated Surements, the carrier-phase measurements, and/or the navi signal divides signal power, mainly, between two spectral gation data demodulation. In one or more embodiments, each lobes symmetrically about a center frequency. In one channel of the multiple digital signal processing channels example, a center frequency may include 1176.45 MHZ (e.g., may correspond to and/or may be associated with one or more L5). In a second example, a center frequency may include types of satellite-to-antenna, pseudolite-to-antenna, or 1227.6 MHz (e.g., L2). In another example, a center fre ground station-to-antenna measurements. For example, the quency may include 1575.42 MHZ (e.g., L1). one or more types measurements may include one or more of 0162. In one or more embodiments, a signal received from a pseudo range, a delta range (e.g., a delta pseudo range), and a satellite, pseudolite, or ground station may include one or a Doppler shift, among others. more of navigation data and one or more ranging codes, 0167. In one or more embodiments, processing unit 15410 among others. For example, the signal received from the may compute a position of antenna 15495 from the N digital satellite, pseudolite, or ground station that includes the one or signal processing channels. For example, N may be four, and more of the navigation data and the one or more ranging codes processing unit 15410 may compute a solution to four equa may include a spread spectrum format. For instance, the tions associated with four unknowns to compute the position spread spectrum format may include a CDMA (code division of antenna 15495. For instance, the four unknowns may multiple access) format. include x, y, and Z (of a Cartesian coordinate system) 0163. In one or more embodiments, ADC 15494 may corresponding to the position of antenna 15495 and a time sample the signal from the satellite, pseudolite, or ground offset, and each of the four equations may be populated with station and may transform the signal from the satellite or corresponding information from, or derived from, a respec ground station to a digital signal that may be processed by tive one of the four digital signal processing channels. processing unit 15410. In one example, the signal from the 0.168. In one or more embodiments, one or more signals satellite or ground station may include a BOC(m,n) code, the from a satellite, pseudolite, or ground station may include a signal from the satellite, pseudolite, or ground station may be unique ranging code. For example, a first ranging code from down converted to an intermediate frequency signal, and a first satellite, pseudolite, or ground Station may be different ADC 15494 may sample the intermediate frequency signal at from a second ranging code from a second satellite, pseudo US 2015/0260527 A1 Sep. 17, 2015

lite, or ground station, different from the first satellite, Taylor series expansion of pseudolite, or ground station. For instance, the first ranging (x,-X.) +(y-y)+ (Z-Z.) +ct. code and the second range code may include and/or be asso 0172. In one or more embodiments, position device 15310 ciated with low cross-correlation properties. may determine a position of antenna 15495 and a time offset 0169. In one or more embodiments, one or more signals based on at least three positions of at least three different from a satellite, pseudolite, or ground station may include satellites, pseudolites, and/or ground stations. For example, a ephemeris information that may be utilized by position device pseudorange for an ith satellite may be expressed as pseudo 15310 in determining a position of the satellite, pseudolite, or range, IIs, al+ct, wheres, is a position of the ith satellite, a ground station. For example, the one or more signals from the is a position of antenna 15495, c is a speed of light (e.g., an satellite, pseudolite, or ground station may include one or assumed or an approximate propagation speed of the one or more of a reference time of ephemeris, a square root of a more signals from the ith satellite), and t, is an advance of semimajor axis of an orbit, an eccentricity of an orbit, an clock 15498 with respect to the system time (i.e., global inclination angle, a longitude of an ascending node (e.g., at a position system time). In one or more embodiments, pseudo weekly epoch), an argument of a perigee at the reference time range, may be computed ie: 1... M for some Me3, and the of ephemeris, a mean anomaly at the reference time of position of antenna 15495 may be a position associated with ephemeris, a rate of change of the inclination angle, a rate of a radius of uncertainty. In one example, clock 15498 may be change of longitude of the ascending node, a mean motion at least as accurate a clock on one of the three satellites. For correction, an amplitude of sine correction to an argument of instance, clock 15498 may be at least as accurate an atomic latitude, an amplitude of cosine correction to the argument of clock. In another example, a height of antenna 15495 may be latitude, an amplitude of sine correction to an orbital radius, available (e.g., known) and may be utilized in computing an amplitude of cosine correction to the orbital radius, an multiple peudoranges. amplitude of sine correction to the inclination angle, and an 0173. In one or more embodiments, position device 15310 amplitude of cosine correction to the inclination angle, may determine a position of antenna 15495 and a time offset among others. based on multiple positions of multiple different satellites, pseudolites, and/or ground stations. For example, a pseudor (0170 For instance, position device 15310 may utilize the ange for an ith satellite may be expressed as pseudorange, ephemeris information to determine a position (e.g., x, y, Z. s-a+ct; where s, is a position of the ith satellite, a is a in a Cartesian coordinate system) of the satellite, pseudolite, position of antenna 15495, c is a speed of light (e.g., an or ground station. In one or more embodiments, position assumed or an approximate propagation speed of the one or device 15310 may transform the one or more signals (e.g., more signals from the ith satellite), and t, is an advance of analog signals) from the satellite, pseudolite, or ground sta clock 15498 with respect to the system time (e.g., global tion into the ephemeris information to determine a position position system time). In one or more embodiments, a Kal (e.g., x, y, Z, in a Cartesian coordinate system) of the man filtering system, method and/or process may be utilized satellite, pseudolite, or ground station. In one or more in computing the multiple peudoranges. For example, a Kal embodiments, x, y, z in a Cartesian coordinate system may man filtering system, method and/or process may be utilized be associated with an Earth-centered Earth-fixed (ECEF) in computing one or more of position data, Velocity data, and coordinate system. For example, the ECEF coordinate system time data, among others. In one instance, the multiple pseu rotates with Earth. For instance, a latitude, a longitude, and a doranges may include three or more pseudoranges. In another height (e.g., a distance from a center of Earth, a distance instance, the multiple pseudoranges may include four or more above a surface of Earth, etc.) may rotate with Earth. pseudoranges. 0171 In one or more embodiments, position device 15310 0.174. In one or more embodiments, a Kalman filtering may determine a position of antenna 15495 and a time offset system, method and/or process may be utilized in integrating based on at least four positions of at least four different data from multiple sensors. For example, a Kalman filtering satellites, pseudolites, and/or ground stations. For example, a system, method and/or process may include a statistical fil pseudorange for an ith satellite may be expressed as pseudo tering system, method and/or process that combines a range, IIs, al+ct, wheres, a position of the ith satellite, a is dynamic model of a system with one or more statistical a position of antenna 15495, c is a speed of light (e.g., an behaviors of errors associated with the system. For instance, assumed or an approximate propagation speed of the one or a Kalman filtering system, method and/or process may man more signals from the ith satellite), and t, is an advance of age and/or endure one or more of GPS signal interruption, clock 15498 with respect to the system time (i.e., global magnetic anomalies, and sensor irregularities, among others, position system time). In one or more embodiments, pseudo to minimize one or more degradations of one or more accu range may be computed ie: 1... M for some Me4, and the racies. position of antenna 15495 may be a position associated with (0175. In one or more embodiments, position device 15310 a radius of uncertainty. For example, computing the position may provide the position of antenna 15495 to another device. of antenna 15495 may minimize the radius of uncertainty For example, position device 15310 may provide the position and/or reduce an approximation of a position of antenna ofantenna 15495 to another device via at least one of wireless 15495. For instance, computing the position of antenna interface 15400, network interface 15490, and serial interface 15495 may utilize a least squares fit method and/or process. In 15440 one or more embodiments, s-a+ct, may be approximated 0176). In one or more embodiments, a position may be by a Taylor series expansion in computing the position of determined based on positions of multiple ground stations antenna 15495. For example, the Taylor series expansion of and/or pseudolites wirelessly communicating or being s-a+ct, may produce linear equations that may be utilized capable of wirelessly communicating with a position device. in a least squares fit method and/or process. For instance, the In one example, a position of a device may be determined via Taylor series expansion of Is-a+ct, may be or include a multilateration which is a navigation technique that may uti US 2015/0260527 A1 Sep. 17, 2015

lize measurements of differences in distances to two or more 0181. In one or more embodiments, a MFS may transform multiple ground stations and/or pseudolites, at previously magnetic field magnitudes into one or more analog signals determined or known locations, that broadcast one or more (e.g., one or more Voltage signals, one or more current signals, signals at previously determined or known times. In a second etc.), and ADIX19510 may transform the one or more analog example, a position of a device may be determined via trilat signals associated with the magnetic field magnitudes into eration which is a navigation technique that may utilize dis digital data that may be utilized by processing unit 19010. For tances or absolute measurements of time-of-flight from three example, a MFS may include one or more of a magnetometer, or more ground stations and/or pseudolites. In another a Saturable core magnetometer, a fluxgate magnetometer, a example, a position of a device may be determined via trian Hall effect sensor, a magneto-resistive sensor, and a magneto gulation which is a navigation technique that may utilize inductive sensor, among others, and ADC 19510 may trans measurements of absolute angles. form the one or more analog signals, from the MFS, associ (0177. As illustrated in FIG. 18B, position device 15310 ated with the magnetic field magnitudes into digital data that may include antenna 15495. As shown in FIG. 18A, antenna may be utilized by processing unit 19010. 15495 may be external to and coupled to position device 0182. In one or more embodiments, a MFS may be asso 15310. In one or more embodiments, position device 15310 ciated with an axis of measurement, and the MFS may trans may utilize and may be coupled to two or more antennas. For form magnetic ticld magnitudes associated with the axis of example, position device 15310 may utilize and may be measurement into one or more signals (e.g., Voltages, cur coupled to two or more antennas such as two or more of rents, machine-readable signals, computer-readable signals, antennas 15495-15497 as illustrated in FIG. 18C. In one or etc.). For example, a measurement of a magnetic field mag more embodiments, position device 15310 may utilize two or nitude may be or include a function of an angle between the more antennas to determine one or more of instantaneous magnetic field and the axis of measurement associated with heading information and yaw information, among others. For the MFS. For instance, magnetic field magnitude may be example, each of the two or more antennas may be located at proportional to a trigonometric function (e.g., sine, cosine, least one meter from another of the two or more antennas. tangent, arcsine, arccosine, arctangent, etc.) of an angle 0.178 Turning now to FIG. 19, a bearing device is illus between the magnetic field and the axis of measurement trated, according to one or more embodiments. As shown, associated with the MFS (e.g., an angle between one or more bearing device 5110 may include one or more memories lines of flux of the magnetic field and the axis of measurement 19020 and 19021 coupled to a processing unit 19010. As associated with the MFS). illustrated, memory 19020 may include one or more of an OS 0183. In one or more embodiments, axes of MFSs 19520 19030, APP data 19036, and one or more APPs 19031-19033, 19522 may correspond with respective three orthogonal axes among others. In one example, APP data 1903.6 may include of bearing device 5110. For example, an axis of MFS 19520 information associated with an angle of declination, soft iron may correspond to the left and right of the page that includes offset information, hard iron offset information, etc. In a FIG. 19 (e.g., a x-axis), an axis of MFS 19521 may corre second example, APP data may include configuration infor spond to the bottom and top of the page that includes FIG. 19 mation that may allow bearing device 5110 to determine a (e.g., a y-axis), and an axis of MFS 19522 may correspond to bearing, as described herein. In another example, one or more a line out of the page that includes FIG. 19 (e.g., a Z-axis). of OS 19030 and one or more of APPs 19031-19033 may 0.184 In one or more embodiments, measuring magnetic include instructions that are executable by processing unit field magnitudes along three orthogonal axes may be utilized 19010 to implement one or more processes, methods, and/or in computing more readings when bearing device 5110 is systems described herein. tilted or is not orthogonal to a line from an origin (e.g., a 0179. As illustrated, bearing device 5110 may include a center of sphere 6000, a center of Earth, etc.) to bearing serial interface 19210 coupled to processing unit 19010. As device 5110. For example, measuring magnetic field magni shown, serial interface 19210 may include one or more of a tudes along three orthogonal axes and determining one or USB interface 19050, a SPI interface 19060, an IC interface more tilt angles of bearing device 5110 (e.g., one or more 19070, a UART interface 19080, and a CAN interface 19090, angles of pitch of bearing device 5110, one or more angles of among others. As shown, bearing device 5110 may include roll of bearing device 5110, etc.) may permit more accurate one or more of a wireless interface 19000 and a network computations of bearings than measuring magnetic field interface 19091. In one or more embodiments, bearing device magnitudes along two orthogonal axes when bearing device 5110 may communicate with one or more other devices via 5110 is tilted or is not orthogonal to a line from an origin (e.g., one or more of wireless interface 19190, serial interface a center of sphere 6000, a center of Earth, etc.) to bearing 19210, and network interface 19091, among others. device 5110. 0180. As shown, one or more of magnetic field sensors 0185. In one or more embodiments, computing one or (MFSs) 19520-19522 may be coupled to processing unit more tilt angles may include receiving data from an acceler 19010 via an ADC 19510. In one or more embodiments, a ometer. As illustrated, bearing device 5110 may include an magnet field sensor (MFS) (e.g., a MFS device) may trans accelerometer 19540 coupled to processing unit 19010. For form a magnetic field into Voltages, currents, and/or numbers. example, accelerometer 19540 may include a micro electro For example, the MFS may transform magnetic field magni mechanical system (MEMS) that may transform one or more tudes into Voltages, currents, and/or numbers. For instance, changes of one or more angles of pitch, roll, and yaw into the MFS may transform magnetic field magnitudes into one Voltages, currents, numbers, and/or machine-readable (e.g., or more machine-readable (e.g., computer-readable) signals. computer-readable) signals. For instance, accelerometer In one or more embodiments, the magnetic field that is trans 1954.0 may be associated with axes 20110-20130, as illus formed into one or more of Voltages, currents, numbers, and trated in FIG. 20. In one or more embodiments, computing machine-readable (e.g., computer-readable) signals, among one or more tilt angles may include receiving data from a others, may be a magnetic field of a planet (e.g., an Earth). gyroscope. As shown in FIG. 19, bearing device 5110 may US 2015/0260527 A1 Sep. 17, 2015 include a gyroscope 19530 coupled to processing unit 19010. embodiments, regulator 21620 may regulate one or more of For example, gyroscope 19530 may include a MEMS that one or more Voltages and one or more currents. In one or more may transform one or more changes of one or more angles of embodiments, power from regulator 21620 may be transmit pitch, roll, and yaw into Voltages, currents, numbers, and/or ted to one or more devices described herein via a transmission machine-readable (e.g., computer-readable) signals. For line 21630. In one or more embodiments, a transmission line instance, gyroscope 19530 may be associated with axes may include and/or be associated with an electrical ground 20010-20030, as illustrated in FIG. 20. and/or an electrical reference. 0186. In one or more embodiments, an accelerometer 0189 Turning now to FIG. 22, an exemplary power sys device (e.g., accelerometer 19540) may transform accelera tem is illustrated, according to one or more embodiments. As tions along an axis into Voltages, currents, and/or numbers. In shown, a power supply 22600 may include one or more of one example, an accelerometer device may transform one or power supplies 22602 and 22604. As illustrated, power sup more rates of change in Velocity into Voltages, currents, and/ ply 22602 may include a regulator 22620 which may be or numbers. For instance, an accelerometer device may tran coupled to a power source 22610 and a wireless power trans Stform one or more rates of change in Velocity into one or mitter 22640. In one or more embodiments, power source more machine-readable (e.g., computer-readable) signals. In 22610 may supply one or more electrical currents at one or another example, an accelerometer device may transform one more Voltages. In one example, power source 22610 may or more phenomena of weight (e.g., one or more forces of include a battery. In a second example, power source 22610 gravity upon an object associated with a mass) associated may include a photovoltaic cell (e.g., a solar cell). In a third with a test mass at rest in a frame of reference of the acceler example, power source 22610 may include a fuel cell. In ometer device into Voltages, currents, and/or numbers. In one another example, power source 22610 may include a genera instance, the accelerometer device may transform one or tor. In one or more embodiments, regulator 22620 may regu more phenomena of weight associated with a test mass at rest late one or more of one or more Voltages and one or more in a frame of reference of the accelerometer device into one or CurrentS. more machine-readable (e.g., computer-readable) signals. In 0190. In one or more embodiments, wireless power trans another instance, the accelerometer device may include a mitter 22640 may transmit one or more power electromag MEMS that may transform accelerations along an axis into netic signals 22650 to power supply 22604. As shown, power Voltages, currents, numbers, and/or machine-readable (e.g., supply 22604 may include a wireless power receiver 22660 computer-readable) signals. that may receive the one or more power electromagnetic 0187. In one or more embodiments, the accelerometer signals 22650. In one or more embodiments, power from device may transform one or more phenomena of weight wireless power receiver 226.60 may be transmitted to one or associated with a test mass at restina frame of reference of the more devices described herein via a transmission line 22630. accelerometer device and associated with an axis of the accel erometer device into one or more machine-readable (e.g., 0191 Turning now to FIG. 23, a mobile device is illus computer-readable) signals. For example, determining a tilt trated, according to one or more embodiments. As shown, or difference in angle between a first axis and the axis asso device 23017 may include a power supply 23.600 that may be ciated with the accelerometer device may include determin coupled to a power source 23610. In one or more embodi ing a difference between a first acceleration and a second ments, power source 23610 may supply one or more electrical acceleration. For instance, the first acceleration may be deter currents at one or more Voltages. In one example, power mined when the axis associated with the accelerometer device source 23610 may include a battery. In a second example, corresponds to and/or is aligned with a vector from an origin power source 23610 may include a photovoltaic cell (e.g., a (e.g., an center of a sphere, a center of mass of a planet, etc.), solar cell). In a third example, power source 23610 may and the second acceleration the second acceleration may be include a fuel cell. In another example, power source 23610 determined when the axis associated with the accelerometer may include a generator. device does not correspond to and/or is not aligned with a 0.192 In one or more embodiments, power supply 23,600 vector from the origin. In one or more embodiments, a dif may include one or more structures and/or functionalities ference between the first acceleration and the second accel described with reference to power supply 21600. In one or eration may be utilized in determining an angle between the more embodiments, power from power supply 23.600 may be axis associated with the accelerometer device and a vector transmitted to one or more components of device 23017 via a from the origin. For example, the difference between the first transmission line 23630. In one or more embodiments, one or acceleration and the second acceleration may be utilized in more other devices described herein may include one or struc determining an angle of tilt (e.g., angle of pitch and/or angle tures and/or functionalities as those described with reference of roll) of the accelerometer device and/or a structure that is to device 23017. coupled to the accelerometer device. 0193 Turning now to FIG. 24, a mobile device is illus 0188 Turning now to FIG. 21, an exemplary power sys trated, according to one or more embodiments. As shown, tem is illustrated, according to one or more embodiments. As device 24011 may include a power supply 24600 and a power shown, a power supply 21600 may include a regulator 21620 source 24610. As illustrated, power supply 24600 may be which may be coupled to a power source 21610. In one or coupled to power source 24610. In one or more embodiments, more embodiments, power source 21610 may supply one or power supply 24600 may include one or more structures more electrical currents at one or more Voltages. In one and/or functionalities described with reference to power Sup example, power source 21610 may include a battery. In a ply 21600. In one or more embodiments, power source 24610 second example, power source 21610 may include a photo may supply one or more electrical currents at one or more Voltaic cell (e.g., a Solar cell). In a third example, power Voltages. In one example, power source 22610 may include a source 21610 may include a fuel cell. In another example, battery. In a second example, power source 24610 may power source 21610 may include a generator. In one or more include a photovoltaic cell (e.g., a Solar cell). In a third US 2015/0260527 A1 Sep. 17, 2015

example, power source 24610 may include a fuel cell. In by via a portion of a user 27510. In one or more embodiments, another example, power source 24610 may include a genera device 27310 may include one or more structures and/or tOr functionalities of one or more devices described herein. 0194 In one or more embodiments, power from power 0200 Turning now to FIG.27C, exemplary mobile device supply 24600 may be transmitted to one or more components is illustrated, according to one or more embodiments. As of device 24011. In one or more embodiments, one or more shown in FIG. 27C, a device 27610 may include a display other devices described herein may include one or structures 27710. In one or more embodiments, device 27610 may and/or functionalities as those described with reference to include one or more structures and/or functionalities of one or device 24011 via a transmission line 24630. more devices described herein. In one or more embodiments, (0195 Turning now to FIG. 25, a mobile device is illus device 27610 may be or include one or more of a wireless trated, according to one or more embodiments. As shown, telephone (e.g., a cellular telephone, a satellite telephone, device 25012 may include a power supply 25600 that may be etc.), a personal digital assistant, a digital music player, a coupled to a power source 25610. In one or more embodi palm computing device, and a tablet computing device, ments, power source 25610 may supply one or more electrical among others. currents at one or more Voltages. In one example, power 0201 Turning now to FIG. 28A, an exemplary method of source 25610 may include a battery. In a second example, determining a plane that includes a determined position and a power source 25610 may include a photovoltaic cell (e.g., a pole is illustrated, according to one or more embodiments. At solar cell). In a third example, power source 25610 may 28010, a position may be determined. In one example, posi include a fuel cell. In another example, power source 25610 tion 6010 (as illustrated in FIG. 6A) may be determined. In a may include a generator. second example, position 6015 (as illustrated in FIG. 6B) may 0196. In one or more embodiments, power supply 25600 be determined. In a third example, position 6017 (as illus may include one or more structures and/or functionalities trated in FIG. 6C) may be determined. In a fourth example, described with reference to power supply 21600. In one or position 9010 (as illustrated in FIG.9A) may be determined. more embodiments, power from power supply 25600 may be In a fifth example, position 9015 (as illustrated in FIG. 9B) transmitted to one or more components of device 25012 via a may be determined. In another example, position 9017 (as transmission line 25630. In one or more embodiments, one or illustrated in FIG. 9C) may be determined. more other devices described herein may include one or struc 0202 In one or more embodiments, a plane may be asso tures and/or functionalities as those described with reference ciated with, may correspond to, and/or may be described by a to device 25012. vector that is normal to (e.g., perpendicular to) the plane. For 0.197 Turning now to FIG. 26, mobile device and a power example, a plane may be described as ax+by+c'Z0, and a Supply are illustrated, according to one or more embodi vector that is normal to (e.g., perpendicular to) the plane may ments. As shown, power Supply 26602 may include a regula be (a,b,c). tor 26620 which may be coupled to a power source 26610 and 0203 At 28020, a vector, based on the position, may be a wireless power transmitter 22640. In one or more embodi computed. For example, the vector may be computed via a ments, power source 22610 may supply one or more electrical vector cross product of a vector corresponding to the deter currents at one or more Voltages. In one example, power mined position and a vector corresponding to a pole (e.g., a source 26610 may include a battery. In a second example, north pole, a South pole, etc.). In one or more embodiments, power Source 26610 may include a photovoltaic cell (e.g., a the computed vector is normal to a plane that includes the solar cell). In a third example, power source 26610 may determined position and the pole, and the computed vector include a fuel cell. In another example, power source 26610 may be utilized to describe the plane that includes the deter may include a generator. In one or more embodiments, regu mined position and the pole. lator 26620 may regulate one or more of one or more voltages 0204 Turning now to FIG. 28B, an exemplary method of and one or more currents. determining a plane that includes a determined position, 0198 In one or more embodiments, wireless power trans according to one or more embodiments. At 28050, a position mitter 26640 may transmit one or more power electromag may be determined. In one example, position 6010 (as illus netic signals 26650 to power supply 26604. As illustrated, trated in FIG. 6A) may be determined. In a second example, device 26013 may include a power supply 26604 which may position 6015 (as illustrated in FIG. 6B) may be determined. include a wireless power receiver. As shown, power Supply In a third example, position 6017 (as illustrated in FIG. 6C) 26604 may include a wireless power receiver 26.660 that may may be determined. In a fourth example, position 9010 (as receive the one or more power electromagnetic signals 26650. illustrated in FIG.9A) may be determined. In a fifth example, In one or more embodiments, power from wireless power position 9015 (as illustrated in FIG.9B) may be determined. receiver 26.660 may be transmitted to one or more compo In another example, position 9017 (as illustrated in FIG. 9C) nents of device 26013 via a transmission line 26630. In one or may be determined. more embodiments, one or more other devices described 0205 At 28060, a vector corresponding to and/or associ herein may include one or structures and/or functionalities as ated with the position may be altered. In one example, the those described with reference to device 26013. position may include a spherical coordinate form that may be (0199 Turning now to FIGS. 27A and 27B, exemplary utilized for the vector corresponding to and/or associated wearable devices are illustrated, according to one or more with the position. For instance, a position device may provide embodiments. As illustrated in FIG.27A, a device 27010 may the position in a spherical coordinate form (e.g., latitude and include a display 27110 and may be worn by via a portion of longitude) that may be utilized for the vector corresponding to a user 27210. In one or more embodiments, device 27010 may and/or associated with the position. In another example, the include one or more structures and/or functionalities of one or position may be converted to a spherical coordinate form that more devices described herein. As shown in FIG. 27B, a may be utilized for the vector corresponding to and/or asso device 27310 may include a display 27410 and may be worn ciated with the position. For instance, the position may US 2015/0260527 A1 Sep. 17, 2015

include a Cartesian coordinate form and may be converted into a spherical coordinate form that may be utilized for the vector corresponding to and/or associated with the position. In one or more embodiments, altering the vector correspond ing to and/or associated with the position may include setting In one or more embodiments, adding or Subtracting ninety a component of the vector. For example, the vector corre degrees or sponding to and/or associated with the position may include (p,0.(p), and the p component may be set to (p, 0–3, 3).

2 radians to the 0 component of the altered vector may produce a vector that is normal the vector corresponding to and/or associated with the position and that is included in a plane that producing includes equator 6110 of sphere 6000. For example, at least one of (p. 9, ). (p, 0+ 2. ..) and (p. 9-3, ..) 0206. At 28070, a vector normal to the altered vector cor responding to and/or associated with the position may be may be utilized to describe a plane that includes the deter determined. In one example, a vector normal to the altered mined position and a pole of sphere 6000. For instance, the at vector corresponding to and/or associated with the position least one of may be determined via adding ninety degrees or by (p, 0+ 2. ..) and (p. 9-3, ..)

may be converted into a Cartesian coordinate system, where the at least one of radians to the 0 component of the altered vector. For instance, adding ninety degrees or by (p, 0+ 2. 3) and (p,0- 2. S),

converted into a Cartesian coordinate system, may be utilized to describe a plane that includes the determined position and radians to the 0 component of the altered vector may produce a pole of sphere 6000. 0207 Turning now to FIG. 29, an exemplary method of determining a position of an object is illustrated, according to (p,0+ 2. ). one or more embodiments. At 29010, a first bearing to an object may be determined. In one or more embodiments, user 5010 may align bearing device 5110 with the object. For example, user 5010, at a first position (e.g., position 6010), In another example, a vector normal to the altered vector may align bearing device 5110 with object 3210. In one or corresponding to and/or associated with the position may be more embodiments, bearing device 5110 may determine a determined via Subtracting ninety degrees or by first angle of the object, with respect to a magnetic pole (e.g., a magnetic north pole). In one example, the first angle may be utilized as the first bearing. In another example, the first bearing may be based on the first angle, determined via the bearing device, and an angle of declination. For instance, the first bearing may be computed as a Sum of the first angle, radians from the 0 component of the altered vector. For determined via the bearing device, and the angle of declina instance, Subtracting ninety degrees or tion. (0208. At 29020, a first position may be determined. For example, position device 15310 may determine the first posi tion (e.g., position 6010). In one or more embodiments, the first position corresponds to the first bearing. In one example, the first bearing to the object and the first position may be determined simultaneously. In a second example, the first radians from the 0 component of the altered vector may bearing to the object and the first position may be determined produce concurrently. For instance, at least one portion of determining US 2015/0260527 A1 Sep. 17, 2015 the first bearing to the object and at least one portion of (e.g., a magnetic north pole) may be utilized in computing a determining the first position may occur during an amount of bearing Ll that is referenced to a geographic pole (e.g., a time transpiring. In another example, the first bearing to the geographic north pole Such as pole 6120). object and the first position may be determined serially such 0213. At 29050, a second position may be determined. For that an amount of time transpiring does not adversely affect example, position device 15310 may determine the second an accuracy of determining the position of the object. For position (e.g., position 9010). In one or more embodiments, instance, determining the first position may be determined the second position corresponds to the second bearing. In one within a foot or two of determining the first bearing. In one example, the second bearing to the object and the second example, a system that determines the position of the object position may be determined simultaneously. In a second may be moving. For instance, the system that determines the example, the second bearing to the object and the second position of the object may be moving at a first speed. In position may be determined concurrently. For instance, at another example, a system that determines the position of the least one portion of determining the second bearing to the object may be stationary. object and at least one portion of determining the second 0209. At 29030, a first vector that is normal to an origin, position may occur during an amount of time transpiring. In the object, and the first position may be determined. For another example, the second bearing to the object and the example, a vector 30110, as illustrated in FIG. 30A, may be second position may be determined serially such that an determined as the first vector. For instance, the origin, the amount of time transpiring does not adversely affect an accu object (e.g., at position 6210), and the first position (e.g., racy of determining the position of the object. For instance, position 6010) may be a basis for a plane 30010, which is determining the second position may be determined within a illustrated in FIG.30A as an intersection with sphere 6000. In foot or two of determining the second bearing. In one one or more embodiments, determining the first vector may example, a system that determines the position of the object include utilizing the first bearing. For example, plane 30010 may be moving. In another example, a system that determines may intersect surface of sphere 6000 at a great circle 30215. the position of the object may be stationary. as illustrated in FIG. 30B. 0214. At 29060, a second vector that is normal to the 0210. As further illustrated in FIG.30B, great circle30215 origin, the object, and the second position may be determined. may be at an angle LL to pole 6120. In one or more embodi For example, a vector 31110, as illustrated in FIG.31A, may ments, angle LL may be the first bearing. In one or more be determined as the second vector. For instance, the origin, embodiments, angle L. may be based on the first bearing and the object, and the second position may be a basis for a plane an angle of declination. For example, a declination angle 31010, which is illustrated in FIG.31A as an intersection with (e.g., an offset angle) may be added or Subtracted to the first sphere 6000. In one or more embodiments, determining the bearing in determining. In one or more embodiments, the second vector may include utilizing the second bearing. For declination angle (e.g., the offset angle) may be based on a example, plane 31010 may intersect surface of sphere 6000 at position on a planet (e.g., Earth). For example, an angular a great circle 31215, as illustrated in FIG. 31B. As further difference (e.g., a declination angle) may exist between a illustrated in FIG.31B, great circle 31215 may be at an angle magnetic pole (e.g., a magnetic north pole) and a geographic L to pole 6120. In one or more embodiments, angle 912 (e.g., pole (e.g., a geographic north pole Such as pole 6120) depend 12 as illustrated in FIG. 31B) may be the second bearing. In ing on a position on the planet (e.g., Earth). For instance, one or more embodiments, angle 2 may be based on the adding or subtracting (e.g., adding a negative number) the second bearing. For example, an offset angle (e.g., a declina angular difference (e.g., the declination angle) to or from the tion angle) may be added or Subtracted to the second bearing first bearing based on a magnetic pole (e.g., a magnetic north in determining LL. pole) may be utilized in computing a bearing LL (e.g., LL as 0215 Referring now to FIG. 29, at 29070, a third vector illustrated in FIG.30B) that is referenced to a geographic pole that is normal to the first vector and the second vector may be (e.g., a geographic north pole Such as pole 6120). determined. In one or more embodiments, determining the 0211. In one or more embodiments, a declination angle third vector may include determining an intersection of may vary over an amount of time transpiring. For example, a planes 30010 and 31010. For example, FIG. 32A illustrates first declination angle corresponding to a position on a planet the intersection of planes 30010 and 31010. In one or more (e.g., Earth) on a first date may be different from a second embodiments, determining the intersection of planes 30010 declination angle corresponding to the position on the planet and 31010 may include determining a vector cross product of on a second date, different from the first date. the first vector and the second vector. For example, determin 0212 Referring now to FIG. 29, at 29040, a second bear ing the third vector may include computing a vector cross ing to an object may be determined. In one or more embodi product of the first vector (e.g., vector 30.110) and the second ments, user 5010 may align bearing device 5110 with the vector (e.g., vector 31110). object. For example, user 5010, at a second position (e.g., 0216. At 29080, a position of the object may be deter position 9010), may align bearing device 5110 with object mined. In one or more embodiments, determining the posi 3210. In one or more embodiments, bearing device 5110 may tion of the object may include determining an intersection of determine a second angle of the object, with respect to a plane 30010, plane 31010, and sphere 6000, as illustrated in magnetic pole (e.g., a magnetic north pole). In one example, FIG. 32A. For example, position 6210 may be determined the second angle may be utilized as the second bearing. In utilizing the third vector (e.g., a vector 32620 as illustrated in another example, the second bearing may be based on the FIG. 32B). For instance, position 6210 may be determined second angle and an angle of declination. In one instance, the from an intersection of sphere 6000 and the third vector. In second bearing may be computed as a sum of the secondangle one or more embodiments, the third vector may be scaled to and the angle of declination. In another instance, adding or a radius of sphere 6000, a radius of Earth, or a radius of Earth Subtracting (e.g., adding a negative number) the declination plus or minus an altitude. For example, the position of the angle to or from the second bearing based on a magnetic pole object (e.g., object 6210) may be determined by scaling the US 2015/0260527 A1 Sep. 17, 2015

third vector to a radius of sphere 6000, a radius of Earth, or to be or include a basis for a plane 36010, which is illustrated as a radius of Earth plus or minus an altitude. For instance, an intersection with sphere 6000 in FIG. 36. vector 32620 (e.g., the third vector) may be scaled to a radius 0223) In one or more embodiments, determining the plane of sphere 6000, as illustrated in FIG.32C as a vector 32630. (e.g., plane 36010) may include computing a vector cross In one or more embodiments, a radius of sphere 6000 may be product of a first vector associated with the first position (e.g., scaled to a radius of Earth or a radius of Earth plus or minus position 6210) and a second vector associated with the second an altitude. position (e.g., position 6220). For example, the vector cross 0217. In one or more embodiments, the position of the product of the first vector associated with the first position and object may be determined to be the third vector or at least a the second vector associated with the second position may be portion of the third vector. For example, the third vector may or include a vector 36110. For instance, vector 36110 may be be a vector in a spherical coordinate system, and the position normal to plane 36010. of the object may be determined to be or to include the angular 0224. In one or more embodiments, determining the plane portions of the third vector. For instance, as illustrated in FIG. (e.g., plane 36010) may include utilizing the first position 32C, the position of the object (e.g., object 6210) may be (e.g., position 6210), the second position (e.g., position determined to be or to include a first angle, 0, to a first 6220), and an origin (e.g., the origin of sphere 6000). In one reference direction (e.g., a positive X-axis or axis 32610), and example, position 6210, position 6220, and the origin of a second angle, p, to a second reference direction (e.g., a sphere 6000 may form a basis for plane 36010. In a second positive Z-axis or axis 32614). FIG. 32C also illustrates a example, plane 36010 may be determined such that plane positive y-axis or axis 32612. 36010 includes position 6210, position 6220, and the origin 0218. In one or more embodiments, the method illustrated of sphere 6000. in FIG. 29 may be repeated in determining one or more 0225 Turning now to FIG. 37, an exemplary method of positions of respective one or more objects. In one example, determining a distance is illustrated, according to one or more the method illustrated in FIG.29 may be repeated to compute embodiments. At 37010, a position may be determined. For position 6220 of a second object (e.g., object 3220). In a example, position device 15310 may determine the position second example, the method illustrated in FIG. 29 may be (e.g., a position of positions 35410-35430 illustrated in FIG. repeated to compute a position 35810 (illustrated in FIG. 35) 35). In one example, a system that determines the position of of a third object (e.g., a windward mark, a point of interest, the object may be moving. For instance, position device etc.). In a third example, the method illustrated in FIG. 29 15310 may be moving. In another example, a system that may be repeated to compute a position 35820 (illustrated in determines the position of the object may be stationary. For FIG. 35) of a fourth object (e.g., a leeward mark, a building, instance, position device 15310 may be stationary. In one or a tower, a structure, etc.). more embodiments, being stationary may include not chang 0219. In a fourth example, the method illustrated in FIG. ing a position, within a coordinate system, within an amount 29 may be utilized to compute position 6215 utilizing a first of time transpiring. For example, being stationary may position of position 6015 and a second position of position include not changing a position, within an ECEF coordinate 9015, as illustrated in FIGS. 6B and 9B, respectively. In system, within an amount of time transpiring. another example, the method illustrated in FIG. 29 may be utilized to compute position 6217 utilizing a first position of 0226. At 37020, a distance from the position to a great are position 6017 and a second position of position 9017, as may be determined. For example, a distance from a position illustrated in FIGS. 6C and 9C, respectively. of positions 354.10-35430 to great arc35310, as illustrated in FIG. 35, may be determined. In one or more embodiments, 0220 Turning now to FIG. 33, an exemplary method of great arc 35310 may be or include starting line 3310 and/or a determining a great are is illustrated, according to one or more finish line. embodiments. At 33010, a first position of a first object may be determined. For example, as illustrated in FIG.35, the first 0227 Turning now to FIG. 38, an exemplary method of position may be or include position 6210. At 33020, a second determining a distance to a plane is illustrated, according to position of a second object may be determined. For example, one or more embodiments. At 38010, a position may be as illustrated in FIG. 35, the second position may be or determined. For example, position device 15310 may deter include position 6220. mine the position (e.g., a position of positions 36410-36430 0221. At 33030, a great are bounded by the first position illustrated in FIG. 36). In one example, a system that deter and the second position may be determined. For example, as mines the position of the object may be moving. In another illustrated in FIG.35, a great arc 35310 bounded by position example, a system that determines the position of the object 6210 and position 6220 may be determined. In one or more may be stationary. embodiments, great arc 35310 may be or include a portion of 0228. At 38020, a distance from the position to a plane a great circle that includes positions 6210 and 6220, where may be determined. For example, a distance from a position positions 6210 and 6220 may be boundaries of the portion of of positions 36410-36430 to plane 36010, as illustrated in a great circle that includes positions 6210 and 6220. FIG. 36, may be determined. In one or more embodiments, 0222 Turning now to FIG. 34, an exemplary method of plane 36010 may include starting line 3310 and/or a finish determining a plane is illustrated, according to one or more line. embodiments. In one or more embodiments, method ele 0229. In one or more embodiments, a distance from the ments 34010 and 34020 may be performed with respect to position to the plane may be determined by projecting a method elements 33010 and 33020, respectively. At 34030, a vector from an origin (e.g., the origin of sphere 6000) to the plane may be determined, utilizing the first position and the position (e.g., a position of positions 36410-36430) onto the second position. For example, an origin (e.g., an origin of plane (e.g., plane 36010). For example, projecting the vector sphere 6000), the first position, and the second position may onto the plane may include determining a vector dot product US 2015/0260527 A1 Sep. 17, 2015

(e.g., an inner product) of the vector, from the origin to the 0234. At 39040, a third result of a sine function of the position, and vector 36110 (e.g., a vector that may be utilized result determined at 39030 may be determined. For example, to describe plane 36110). determining tile third result of tile sine function of the second 0230. In one or more embodiments, vector 36110 may not result, determined at 39030, may include computing a result be a unit vector, and projecting the vector onto the plane may of the sine function of the second result, determined at 39030. include determining a magnitude of vector 36110. In one For instance, example, the vector dot product of the vector, from the origin to the position, and vector 36110 may be divided by the magnitude of vector 36110. In another example, the vector - Position dot product of the vector, from the origin to the position, and 2 ld vector 36110 may be multiplied by a reciprocal of the mag nitude of vector 36110. may be computed as the third result. 0231. In one or more embodiments, the distance from the position to the plane may be sufficient to determine a distance 0235. At 39050, a fourth result of the third result multi from the position to starting line 3310, a finish line, and/or plied by the first result may be determined. For example, great arc 35310. For example, plane 36010 may include start determining the fourth result may include computing the third ing line 3310 (as illustrated in FIG. 3), the finish line, and/or result multiplied by the first result. For instance, the fourth great arc 35310 (as illustrated in FIG. 35). In one instance, a result may be determined by computing difference of the distance from the position (e.g., a position of positions 36410-36430) to plane 36010 and a measure of a great arc (of sphere 6000) from the position to plane 36010 tan(iii). sin:7 Position). may be negligible. For example, the difference that may be negligible may be less than or equal to a radius of uncertainty of position device 15310. In one or more embodiments, if 0236. At 39060, a fifth result of an inverse tangent function difference is negligible, less computations may be performed, of the fourth result may be determined. For example, deter and/or a processor of low computing power processor (e.g., a mining the fifth result may include computing an inverse processor that does not include a floating point unit) may be tangent function of the fourth result. For instance, the fifth utilized in determining a distance from the position to starting result may be determined by computing line 3310, the finish line, and/or great are 35310. 0232 Turning now to FIG. 39A, an exemplary method of determining, utilizing a first bearing from a first position to an tan (tan(pl.) sin - Position )). object at a second position, a first great circle intercept is illustrated, according to one or more embodiments. At 39010, a first bearing from a first position to an object may be deter 0237. At 39070, a sixth result of the fifth result subtracted mined. For example, the first bearing may be angle L. For from Position may be determined, where Position is the 0 instance, angle L. may be computing is a same or similar component of the first position expressed in a spherical coor fashion as described above. For example, LL may be based on dinate system. For example, determining the sixth result of a declination angle. the fifth result subtracted from Position may include com 0233. At 39020, a first result of a tangent function of L, puting may be determined. For example, determining the first result of a tangent function of LL may include computing a tangent function of LL (e.g., tan(L)). At 39030, a second result of -l ... , 7. Position subtracted from Position - tan (tan(u?); sin() Position). 0238. At 39090, a first angle of the great circle intercept may be established. For example, the first angle of the great circle intercept may be established as the sixth result. For may be determined, where Position is the p component of instance, the first angle of the great circle intercept may be set the first position expressed in a spherical coordinate system. to the sixth result (e.g., For example, determining the second result of Position, Sub tracted from GreatCircle intercept = Positiona - tan' (tan(us) sing Position).

0239. At 39080, a magnitude of the great circle intercept may be established. In one example, the magnitude of the may include computing a result of great circle intercept may be established as a radius of a sphere or a radius of Earth. For instance, the magnitude of the great circle intercept may be set to the radius of the sphere (e.g., sphere 6000) or the radius of Earth. In another example, 2 Position. the magnitude of the great circle intercept may be established as a unit value. For instance, the magnitude of the great circle intercept may be set to one. US 2015/0260527 A1 Sep. 17, 2015

0240. In one or more embodiments, setting the magnitude 0245 At 39130, a second result of Position-subtracted of the great circle intercept to one (e.g., unity) may simplify from (e.g., reduce) and/or eliminate one or more computations. For example, the magnitude of the great circle intercept may be utilized in one or more computations Subsequent to determin ing and/or computing the magnitude of the great circle inter cept, and at least one of the Subsequent one or more compu tations may be simplified (e.g., reduced) and/or eliminated. may be determined, where Position is the p component of the second position expressed in a spherical coordinate sys 0241. At 39090, a second angle of the great circle intercept tem. For example, determining the second result of may be established. For example, the second angle of the Position-subtracted from great circle intercept may be established as an angle of a plane, that includes the great circle, with respect to a positive Z-axis or axis 6614, as illustrated in FIG. 6G. For instance, the great circle may include and/or be equator or great circle 6110, and the secondangle of the great circle intercept may be established as and/or set to may include computing a result of

-2 - - O.S.iiiOii.2d

At 39140, a third result of a sine function of the result deter 0242. In one or more embodiments, the method illustrated mined at 39130 may be determined. For example, determin in FIG. 39A may be associated with a spherical right triangle ing the third result of the sine function of the second result, illustrated in FIG. 40 that provides further details or a mag determined at 39130, may include computing a result of the nified view of a portion of FIG.30B. For example, the spheri sine function of the second result, determined at 39130. For cal right triangle may include sides 40510-40530 and may instance, include angles C, B, and L. For instance, angle B may include a measure of 90 degrees or sin? 2 Position 2)

may be computed as the third result. 0246. At 39150, a fourth result of the third result multi plied by the first result may be determined. For example, determining the fourth result may include computing the third radians, angle L, may correspond with the description above, result multiplied by the first result. For instance, the fourth and (O may be a third angle of the spherical right triangle. In result may be determined by computing one or more embodiments, the first position, as described above, may be or include position 6010, the position of the object may be or include position 6210, and the great circle tan(pt): sing7 Position2). intercept may be or include position 40450. For example, the great circle, as described above may be or include great circle or equator 6110, and the great circle intercept may be or At 39160, a fifth result of an inverse tangent function of the include an equator intercept that is or includes position fourth result may be determined. For example, determining the fifth result may include computing an inverse tangent 40450. In one or more embodiments, great circle intercept function of the fourth result. For instance, the fifth result may 40450 and position 6010 may establish and/or lie on a great be determined by computing circle 30215, as illustrated in FIG. 40. 0243 Turning now to FIG. 39B, an exemplary method of determining, utilizing a second bearing from a second posi tan (tan(u2) sin Position2). tion to an object at a second position, a second great circle intercept is illustrated, according to one or more embodi 0247. At 39170, a sixth result of the fifth result subtracted ments. At 39110, a second bearing from a second position to from Position may be determined, where Positionis the 0 an object may be determined. For example, the second bear component of the first position expressed in a spherical coor ing may be angle Ll2. For instance, angle L2 may be computing dinate system. For example, determining the sixth result of is a same or similar fashion as described herein. For example, the fifth result subtracted from Position may include com a L. may be based on a declination angle. puting 0244. At 39120, a first result of a tangent function of may be determined. For example, determining the first result of a tangent function of may include computing a tangent Position 2 - tan' (tan(H2) sin() Position2). function of LL (e.g., tan(LL)). US 2015/0260527 A1 Sep. 17, 2015 20

0248. At 39190, a first angle of the great circle intercept 0253 Turning now to FIG. 39C, an exemplary method of may be established. For example, the first angle of the great determining a vector that is normal to a first position, an circle intercept may be established as the sixth result. For origin, and a second position of a remote object is illustrated, instance, the first angle of the great circle intercept may be set according to one or more embodiments. At 39210, a great to the sixth result (e.g., circle intercept may be determined utilizing apole of a sphere and a first position. In one or more embodiments, the great circle intercept may include an intersection of a first great circle, that includes the pole and the first position, and an GreatCircle Intercept2 = Position 29 - tan (tan(H2) sing Position2). equator of the sphere (e.g., a second great circle). 0254. At 39220, a first vector normal to the origin, the 0249. At 39180, a magnitude of the great circle intercept pole, and the great circle intercept may be determined. In one may be established. In one example, the magnitude of the example, determining the first vector may include computing great circle intercept may be established as a radius of a a vector cross product of a vector from the origin to the first sphere or a radius of Earth. For instance, the magnitude of the position and a vector from the origin to the pole. In a second great circle intercept may be set to the radius of the sphere example, determining the first vector may include computing (e.g., sphere 6000) or the radius of Earth. In another example, a vector cross product of a vector from the origin to the the magnitude of the great circle intercept may be established equator intercept and a vector from the origin to the first as a unit value. For instance, the magnitude of the great circle position. In another example, determining the first vector may intercept may be set to one. include computing a vector cross product of a vector from the 0250 In one or more embodiments, setting the magnitude origin to the equator intercept and a vector from the origin to of the great circle intercept to one may simplify (e.g., reduce) the pole. and/or eliminate one or more computations. For example, the (0255. At 39230, an axis of rotation may be determined magnitude of the great circle intercept may be utilized in one utilizing the origin and the first position. For example, deter or more computations Subsequent to determining and/or com mining axis of rotation may include computing a vector from puting the magnitude of the great circle intercept, and at least the origin to the first position. At 39240, a second vector may one of the Subsequent one or more computations may be be determined via a rotation, by a bearing angle to the remote simplified (e.g., reduced) and/or eliminated. object, of the first vector about the axis of rotation. In one or 0251. At 39190, a second angle of the great circle intercept more embodiments, the methods illustrated in FIGS. 42 and may be established. For example, the second angle of the 44 may be utilized to compute the second vector via a rota great circle intercept may be established as an angle of a tion, by the bearing angle to the remote object, of the first plane, that includes the great circle, with respect to a positive vector about the axis of rotation. In one or more embodi Z-axis or axis 6614, as illustrated in FIG. 6G. For instance, the ments, the method illustrated in FIG. 39C may be utilized in great circle may include and/or be equator or great circle a rotation of a plane about an axis or a vector. 6110, and the secondangle of the great circle intercept may be 0256 Turning now to FIG. 42, an exemplary method of established as and/or set to determining, utilizing a bearing from a first position to an object at a second position, a plane that includes the first position, an origin, and the second position is illustrated, according to one or more embodiments. At 42010, a first quaternion may be computed, utilizing the first position (e.g., position 6010). In one or more embodiments, a quaternion 0252. In one or more embodiments, the method illustrated may include a form and/or representation Such as q S+Xi+y+ in FIG. 39B may be associated with a spherical right triangle zk that may obey rules such as i-ji=k*-ijk=-1, ij=k, jki, illustrated in FIG. 41 that provides further details or a mag kij. ji=-k, k=-i, and ik -, where S, X, y, and Z may be nified view of a portion of FIG.31B. For example, the spheri numbers (e.g., real numbers). In one example, quaternions cal right triangle may include sides 41510-41530 and may may be or include a division ring. In another example, quater include angles C2, f2., L. For instance, angle f2 may include nions may be or include hypercomplex numbers. a measure of 90 degrees or 0257. In one or more embodiments, a quaternion q may include a form and/or representation such as q s.a. where S eRandaeR. For example, q=s+xi+yj+zks,a)=s+ai+aj+ ak. In one or more embodiments, a first quaternion may be computed, utilizing the first position, such that radians, angle L. may correspond with the description above, and C may be a third angle of the spherical right triangle. In a =cos(), sin(p) one or more embodiments, the second position, as described above, may be or include position 9010, the position of the object may be or include position 6210, and the great circle where 0 may be the bearing from the first position to the intercept may be or include position 41450. For example, the object at the second position and P is a vector associated with great circle, as described above may be or include great circle the first position. In one or more embodiments, P. may be or equator 6110, and the great circle intercept may be or normalized and/or scaled such that IP =1. include an equator intercept that is or includes position 0258. In one or more embodiments, 0 may be or include 41450. In one or more embodiments, great circle intercept the bearing from the first position to the object at the second 41450 and position 9010 may establish and/or lie on a great position adjusted by an angle of declination (e.g., a number). circle 31215, as illustrated in FIG. 41. For example, 0 may be or include the bearing from the first US 2015/0260527 A1 Sep. 17, 2015 position to the object at the second position Such that the angle 0261. At 42040, a second quaternion may be computed, of declination is added to or subtracted from the bearing from utilizing the vector normal to the origin, the first position, and the first position to the object at the second position. In one at least one of the pole and the equator intercept. In one or instance. 0-1. In another instance, 0. more embodiments, the second quaternion may be computed, 0259. At 42020, an equator intercept may be computed, utilizing the vector normal to the origin, the first position, and utilizing the first position. In one or more embodiments, the the equator intercept, such that q=0.v, where V represents first position may be expressed and/or represented in a spheri the vector normal to the origin, the first position, and the cal coordinate system such that the first position is associated equatorintercept. In one example, V may beaunit vector such with and/or includes (Position Positionio Position), and that v=1. For instance, V may be normalized and/or scaled the equator intercept may be computed via setting Position such that v=1. tO 0262 At 42050, a third quaternion may be computed based on the first position. In one or more embodiments, the third quaternion may be computed, based on the first position, such that

Such that the equator intercept is a =cos(), -sin(e) where 0 may be the bearing from the first position to the (Position, Positiong, 3). object at the second position and P is a vector associated with the first position. For example, 0 may be or include the bear ing from the first position to the object at the second position 0260. At 42030, a first vector normal to the origin, the first such that the angle of declination is added to or subtracted position, and the equator intercept may be computed, utiliz from the bearing from the first position to the object at the ing the equator intercept. In one example, computing the first second position. In one instance. 0-1. In another instance, vector normal to the first position and the equator intercept 0-l. In one or more embodiments, computing the third may include computing a vector cross product of a first vector quaternion, based on the first position, may include comput associated with the first position and a second vector associ ing an inverse of the first quaternion. For example, q, q', ated with the equator intercept. In another example, comput where ing the first vector normal to the first position and the equator intercept may include adding or subtracting

s: a' = e 2

where q is a conjugate of q, and where q is a magnitude radians to or from the theta-component of the equator inter of qi. For instance, computing ld may include computing cept. In one instance, the first vector normal to the first posi s+ax+a+a12. tion and the equator intercept may be 0263. In one or more embodiments, the first quaternion may be a unit normal quaternion (i.e., q =1), and the con jugate of the first quaternion may be the inverse of the first quaternion. For example, q1*-q', and qs=q* (e.g., qs may (Position, Position g + 2. 3). be a conjugate of q). 0264. At 42060, a fourth quaternion may be computed, utilizing the first quaternion and the second quaternion. In one In another instance, the first vector normal to the first position or more embodiments, the tburth quaternion may be deter and the equator intercept may be mined via quaternion multiplication. For example, qaqq Isil wheresalsal-Iss-a as a+s2a+ax a 2. (Position, Positiong - 2. ). 0265 At 42070, a fifth quaternion may be computed, ulti lizing the fourth quaternion and the third quaternion. In one or more embodiments, the fifth quaternion may be determined In one or more embodiments, the first vector normal to the Via quaternion multiplication. For example, qs=qaqs, first position and the equator intercept may include and/or be assas-Sass-a assas-s-at-axal, where aa is an associated with a plane formed by the origin, the first position, inner product of vectors aanda, and where axa is a vector and the equator intercept. In one or more embodiments, the cross product of vectors a and a. In one or more embodi first vector normal to the first position and the equator inter ments, method elements 42060 and 42070 describe multiply cept may include and/or be associated a vector that is normal ing three quaternions such as qqq (qq)q. In one or more to the first position, an origin, and a pole (e.g., a geographic embodiments, quaternion multiplication may include an pole, pole 6120, pole 6130, etc.). For example, the first vector associative property Such as qi qaqs (qiq2)qs q(qqs), and normal to the first position and the equator intercept may the method described with reference to FIG. 42 may be modi computed via a vector cross product of a vector associated fied in accordance with the associative property of quaternion with the first position and the pole. multiplication. US 2015/0260527 A1 Sep. 17, 2015 22

0266. At 42080, a second vector may be determined, ulti with and/or includes the first position by the bearing (e.g., LL) lizing the fifth quaternion. In one or more embodiments, the from the first position to the object at the second position. For fifth quaternion may be a “pure' quaternion Such that qs=0, instance, as illustrated in FIG. 31C, the second plane may as, and the second vector may be or includeas. In one or more include the origin of sphere 6000, position 9010, and at least embodiments, the second vector may be associated with a one of an equator intercept 31310 and a pole (e.g., pole 6120, plane. For example, the second vector may be associated with pole 6130, etc.), and may be rotated by angle Labout an axis plane 30010 illustrated in FIG.30A. For instance, the second from the origin to position 9010 to compute plane 31010, vector may be or include vector 30110 illustrated in FIG. illustrated in FIG. 31A, which includes the origin, the first 30A. position, and the second position (e.g., the position of the 0267. In one or more embodiments, the method illustrated remote object). in FIG.42 may be utilized in a computation of a rotated vector from a first vector rotated about a second vector oran axis via 0271 In one or more embodiments, a plane may be computing a quaternion rotation qpq, where q and p are rotated, by an angle, about an axis or a vector. For example, quaternions. For example, computing a quaternion rotation the method illustrated in FIG. 42 may be utilized in a rotation, may include computing qpq'. by a bearing, of a plane about an axis or a vector. 0268. In one instance, (0272. In one instance, plane 30005 (illustrated in FIG. 30C) that includes the origin, position 6010, and at least one of an equator intercept and a pole (e.g., pole 6120, pole 6130, q =cos(), sin(s) etc.) may be represented by and/or associated with vector 30105 which may be rotated about a vector from the origin to position 6010 (or a vector from the origin to position 6010 and v is a first vector or the axis (e.g., a normalized vector of divided by a non-Zero Scalar Such as a magnitude of the vector a vector from an origin to the first position), where 0 may be from the origin to position 6010) to compute vector 30110 or include the bearing from the first position to the object at (illustrated in FIG. 30A) that represents and/or is associated the second position. In a second instance, P-0.v.), wherev, with plane 30010. In another instance, plane 31005 (illus is a normalized vector that is normal to (e.g., perpendicular to) trated in FIG. 31C) that includes the origin, position 9010, the position, the origin, and the equator intercept and/or a and at least one of the equator intercept and a pole (e.g., pole pole. In another instance, 6120, pole 6130, etc.) may be represented by and/or associ ated with vector 31105 which may be rotated about a vector from the origin to position 9010 (or a vector from the origin to -1 - 2 s: position 9010 divided by a non-zero scalar) to compute vector i |al? 31110 (illustrated in FIG.31A) that represents and/or is asso ciated with plane 31010. In one or more embodiments, a computation of qpq pro 0273 Turning now to FIG. 43, an exemplary method of duces a "pure” quaternion such as qpq=0.v.). computing a product of two quaternions is illustrated, accord 0269. In one or more embodiments, method described ing to one or more embodiments. In one or more embodi with reference to FIG. 42 may provide a functionality that ments, a quaternion product of qi q2, where q-sail and rotates a plane that includes the origin, the first position, and qsa), may be computed utilizing multiple dot products at least on of the equator intercept and a pole (e.g., pole 6120, (e.g., inner products). For example, qqa-sals, pole 6130, etc.) about an axis that is associated with, parallel al-SS2-a as a+S2a+axa, which may be expressed as to, and/or includes the first position by the bearing from the first position to the object at the second position, adjusted by an angle of declination (e.g., a number) if the angle of decli S1 - Cly - Cly -(1z S2 nation is non-Zero. In one example, a first plane that includes Cix S Olz dily a2X W = W the origin, a first position (e.g., position 6010 of FIG. 30B), aly az is -ax lay "''' and at least one of an equator intercept and a pole (e.g., pole dZ dy Cix Sl d2Z 6120, pole 6130, etc.) may be rotated about an axis that is associated with, parallel to, and/or includes the first position by the bearing (e.g., LL) from the first position to the object at 0274. At 43010, a dot product (e.g., an inner product) of a the second position. For instance, as illustrated in FIG. 30C, first row of M and vector V may be computed. For the first plane may include the origin of sphere 6000, position example, (S1-ax-ay-a2)(S2,a2a2a22) may be com 6010, and at least one of an equator intercept 30310 and a pole puted as a first element of V. At 43020, a dot product (e.g., (e.g., pole 6120, pole 6130, etc.), and may be rotated by angle an inner product) of a second row of M and vector V may Labout an axis from the origin to position 6010 to compute be computed. For example, (ax.S.-a, -a2)(S2.ax,a2, plane 30010, illustrated in FIG. 30A, which includes the a22) may be computed as a second element of Vs. At 43030, origin, the first position, and the second position (e.g., the a dot product (e.g., an inner product) of a third row of M and position of the remote object). In one or more embodiments, vector V may be computed. For example, (a,a2,.S.-a,) the axis from the origin to position 6010 may be represented ‘(s.a.a.a.a.22) may be computed as a third element of Vs. by a unit vector. At 43040, a dot product (e.g., an inner product) of a fourth row 0270. In another example, a second plane that includes the of M and vector V may be computed. For example, (alz origin, a first position (e.g., position 9010 of FIG.31B), and at a.aix.S) (S2,a2,..,a2a22) may be computed as a fourth ele least one of an equator intercept and a pole (e.g., pole 6120, ment of Vs. In one or more embodiments, the method illus pole 6130, etc.) may be rotated about an axis that is associated trated in FIG. 43 computes US 2015/0260527 A1 Sep. 17, 2015 23

rotation is not clockwise (e.g., counterclockwise), a sixth vector may be determined, at 44110, via computing a sum of the third vector and the fourth vector and computing a differ ent between the sum and the fifth vector. If the rotation is clockwise, a sixth vector may be determined, at 44120, via computing a Sum of the third vector, the fourth vector, and the fifth vector. 0275 Turning now to FIG. 44, an exemplary method of 0281. In one or more embodiments, a plane may be computing, utilizing a bearing from a first position to an rotated, by an angle, about an axis or a vector. For example, object at a second position, a plane that includes the first the method illustrated in FIG. 44 may be utilized in a rotation, position, an origin, and the second position is illustrated, by a bearing, of a plane about an axis or a vector. In one according to one or more embodiments. At 44010, a cosine of instance, plane 30005, illustrated in FIG. 30C, that includes an angle (e.g., 0) may be determined, utilizing the bearing the origin, position 6010, and at least one of the equator from a first position an object at a second position. In one or intercept and a pole (e.g., pole 6120) may be represented by more embodiments, the angle may be or include the bearing and/or associated with vector 30105 which may be rotated from the first position to the object at the second position about a vector from the origin to position 6010 (or a vector adjusted by an angle of declination (e.g., a number). from the origin to position 6010 divided by a non-zero scalar) 0276. At 44020, a difference between one and the cosine to compute vector 30110, illustrated in FIG.30A, that repre of the angle may be computed. At 44030, a first vector may be sents and/or is associated with plane 30010. computed, utilizing an origin and the first position. For (0282. In another instance, plane 31005, illustrated in FIG. example, computing the first vector may include determining 31C, that includes the origin, position 9010, and at least one a vector from the origin to the first position. At 44040, a of the equator intercept and a pole (e.g., pole 6120) may be second vector that is normal to the first vector and at least one represented by and/or associated with vector 31105 which of a pole (e.g., pole 6120, pole 6130, etc.) and an equator may be rotated about a vector from the origin to position 9010 intercept may be computed. In one example, the method (or a vector from the origin to position 9010 divided by a illustrated in FIG. 28A may be utilized to compute the second non-zero scalar) to compute vector 31110, illustrated in FIG. vector. In another example, the method illustrated in FIG. 31A, that represents and/or is associated with plane 31010. 28B may be utilized to compute the second vector. 0283. In one or more embodiments, the method illustrated (0277. At 44050, a dot product (e.g., an inner product) of in FIG. 44 may be utilized in a computation of a rotated vector the first vector and the second vector may be computed. At from a first vector rotated about a second vector oran axis. For 44060, a third vector may be computed via the difference example, the method illustrated in FIG. 44 may be utilized in between one and the cosine of the angle (e.g., as computed at an implementation of a rotated vector from a first vector 44020), the dot product of the first vector and the second rotated about a second vector or an axis. For example, the vector (e.g., as computed at 44040), and the first vector. In one method illustrated in FIG. 44 may be utilized in an imple or more embodiments, a product of the difference between mentation of one and the cosine of the angle and the dot product of the first 0284) v. v cos (0)+(v.xv) sin (0)+v(v. vector and the second vector may be computed via multiply v)(1-cos(0)), where v is the first vector, v is the second ing the difference between one and the cosine of the angle and vector or the axis, and 0 is the bearing to the remote object. In the dot product of the first vector and the second vector, and one instance, 0=L at position 6010, as illustrated in FIG.30B, the third vector may be computed via multiplying the first which may be utilized to compute vector 30110 as illustrated vector and the product of the difference between one and the in FIG. 30A. In another instance, 0–1 at position 9010, as cosine of the angle and the dot product of the first vector and illustrated in FIG. 31B, which may be utilized to compute the second vector. vector 31110 as illustrated in FIG. 31A. (0278. At 44070, a fourth vector may be computed via the 0285 Turning now to FIG. 45, an exemplary method of second vector and the cosine of the angle. For example, com determining, utilizing a bearing from a first position to an puting the fourth Vector, via the second vector and the cosine object at a second position, a plane that includes the first of the angle, may include computing a product of the second position, the second position, and an origin is illustrated, vector and the cosine of the angle via multiplying the cosine according to one or more embodiments. At 45010, a cosine of of the angle to produce the fourth vector. an angle (e.g., 0) may be determined, utilizing the bearing 0279. At 44080, a sine of the angle may be determined. For from the first position to the object at the second position. For example, determining the sine of the angle may include com example, determining the cosine of the angle may include puting the sine of the angle. At 44090, a fifth vector may be computing the cosine of the angle. In one or more embodi determined via the sine of the angle and a cross product of the ments, the angle may be or include the bearing from the first first vector and the second vector. For example, determining position to the object at the second position adjusted by an the fifth vector, via the sine of the angle and the cross product angle of declination (e.g., a number). For example, the angle of the first vector and the second vector may include comput may be or include the bearing from the first position to the ing the cross product of the first vector and the second vector object at the second position Such that the angle of declination and computing a product of the sine of the angle and the cross is added to or subtracted from the bearing from the first product of the first vector and the second vector via multiply position to the object at the second position. In one instance, ing the angle and the cross product of the first vector and the 0–L. In another instance, 0-l. second vector. 0286. At 45020, a difference between one and the cosine 0280 At 44100, it may be determined if the rotation is of the angle may be determined. For example, determining clockwise. In one or more embodiments, the rotation may be the difference between one and the cosine of the angle may with respect to the first vector as an axis of rotation. If the include computing the difference between one and the cosine US 2015/0260527 A1 Sep. 17, 2015 24 of the angle. At 45030, a first matrix may be determined. In 0290. At 45080, a fifth matrix may be determined. For one or more embodiments, determining the plane that example, determining the fifth matrix (Ms) may include com includes the first position and the second position may puting a multiplicative product of the result of method ele include rotating, by the bearing, a first vector about a second ment 45070 and the fourth matrix. For example, vector or an axis associated with the second vector. For example, v (the first vector) may be rotated, by 0, about v. (the second vector). For instance. v may be associated with a plane that includes the first position, and the origin and/or may be utilized to describe and/or reference a plane that includes the first position and the origin. In one or more embodiments, the first matrix (M) may be populated with components of the second vector. For example, 0291. At 45090, a sixth matrix may be determined. For example, determining the sixth matrix (M) may include computing a matrix Sum of the second matrix, the third matrix, and the fifth matrix. For example, MM+M+Ms. At 45100, a third vector may be determined. For example, determining the third vector may include computing a prod uct of the sixth matrix and the first vector. For instance, v M.V. In one or more embodiments, Ms may be a rotation matrix that rotates a vector, v about the first position (or a 0287. At 45040, a second matrix (M) may be determined. vector associated with the first position such as v) by 0. In For example, determining the second matrix may include one example, 0–L. In another example, 0–L. computing a multiplicative product of the result of method 0292. In one or more embodiments.v., may describe and/ element 45020 and the first matrix. For example, or be associated with the plane that includes the first position, the second position, and the origin and/or may be utilized to describe and/or reference the plane that includes the first position, the second position, and the origin. In one or more embodiments, a plane may be rotated, by an angle, about an axis or a vector. For example, the method illustrated in FIG. 45 may be utilized in a rotation, by a bearing, of a plane about an axis or a vector. 0288. At 45050, a third matrix may be determined. In one 0293. In one instance, plane 30005, illustrated in FIG. or more embodiments, the third matrix (M) may be popu 30A, that includes the origin, position 6010, and at least one lated with components of the cosine of the bearing. For of the equator intercept and a pole (e.g., pole 6120) may be example, represented by and/or associated with vector 30105 (e.g., v) which may be rotated about a vector (e.g., v.) from the origin to position 6010 (or a vector from the origin to position 6010 cos(8) O O divided by a non-zero scalar) to compute vector 30110 (e.g., v), illustrated in FIG. 30A, that represents and/or is associ - O cos(8) O | ated with plane 30010. In another instance, plane 31005, O O cos(8) illustrated in FIG. 31C, that includes the origin, position 9010, and at least one of the equator intercept and a pole (e.g., 0289. At 45060, a fourth matrix may be determined. In one pole 6120) may be represented by and/or associated with or more embodiments, the fourth matrix (M) may be popu vector 31105 (e.g., v) which may be rotated about a vector lated with components of the second vector. For example, (e.g., v.) from the origin to position 9010 (or a vector from the origin to position 9010 divided by a non-zero scalar) to com pute vector 31110 (e.g., v), illustrated in FIG. 31A, that represents and/or is associated with plane 31010. 0294 Turning now to FIG. 46, an exemplary method of determining a position relative to one or more great circles is illustrated, according to one or more embodiments. At 4.6010, a first plane may be determined utilizing a first position and a At 45070, a sine of an angle (e.g., 0) may be determined, second position. For example as illustrated in FIG.35, a first utilizing the bearing from the first position to the object at the vector from the origin of sphere 6000 to position 6210 (e.g., second position. For example, determining the sine of the the first position) may be computed, a second vector from the angle may include computing the sine of the angle. In one or origin of sphere 6000 to position 6220 (e.g., the second posi more embodiments, the angle may be or include the bearing tion) may be computed, and a third vector may be computed from the first position to the object at the second position from a vector cross product of the second vector and the first adjusted by an angle of declination (e.g., a number). For vector. For instance, the third vector may be associated with example, the angle may be or include the bearing from the and/or may be utilized to describe the first plane. In one or first position to the object at the second position such that the more embodiments, the first plane may include great arc angle of declination is added to or Subtracted from the bearing 35310. from the first position to the object at the second position. In 0295. At 4.6020, a second plane may be determined utiliz one instance. 0-L. In another instance. 0-1. ing a first position and a first equator intercept. For example, US 2015/0260527 A1 Sep. 17, 2015

a fourth vector from the origin of sphere 6000 to the first indicate that position35420 is east (e.g., if pole 6120 is a north equator intercept may be computed, and a fifth vector may be pole) of great circle35520. For instance, if position 35420 is computed from a vector cross product of the first vector and east of great circle35520, a shortest distance to the start line the fourth vector. For instance, the fifth vector may be asso may include a distance to position 6210. ciated with and/or may be utilized to describe the second 0301 Turning now to FIG. 47, an exemplary method of plane. In one or more embodiments, the second plane may determining a position may be determined from two planes include a great circle35520. determined via least squares is illustrated, according to one or 0296. At 46030, a third plane may be determined utilizing more embodiments. At 47010, multiple data points, of a first a second position and a second equator intercept. For set of data points, on or proximate to a first great circle may be example, a sixth vector from the origin of sphere 6000 to the acquired. For example, the first set of data points may be second equator intercept may be computed, and a seventh acquired via a position device traveling on or proximate to vector may be computed from a vector cross product of the great circle 35520 (illustrated in FIG. 35). At 47020, a first sixth vector and the second vector. For instance, the seventh plane may be computed utilizing the first set of data points. In vector may be associated with and/or may be utilized to one or more embodiments, a least Squares method, process, describe the third plane. In one or more embodiments, the and/or system may be utilized in computing the first plane third plane may include a great circle35510. from the first set of data points. 0297. At 46040, a side of a great circle may be determined 0302 At 47030, multiple data points, of a second set of from a user position and a vector associated with and/or data points, on or proximate to a second great circle may be utilized to describe a plane that includes the great circle. In acquired. For example, the second set of data points may be one example, the user position may be or include a position acquired via a position device traveling on or proximate to a 35410, and an eighth vector may be computed from the origin great circle that includes great arc 35310 (illustrated in FIG. of sphere 6000 to position 35410. For instance, a dot product 35). At 47020, a second plane may be computed utilizing the (e.g., an inner product) of the eighth vector and the vector second set of data points. In one or more embodiments, a least associated with and/or utilized to describe the plane that squares method, process, and/or system may be utilized in includes the great circle. If the dot product of the eighth vector computing the second plane from the second set of data and the vector associated with and/or utilized to describe the points. plane that includes the great circle is a positive number, posi 0303 At 47040, an intersection of the first plane, the sec tion35410 is to a first side of the great circle. If the dot product ond plane, and a sphere associated with the first great circle of the eighth vector and the vector associated with and/or and the second great circle may be computed. For example, utilized to describe the plane that includes the great circle is a the first plane may be associated with and/or described be a negative number, position 35410 is to a second side of the first vector, and the second plane may be associated with great circle. If the dot product of the eighth vector and the and/or described be a second vector. In one or more embodi vector associated with and/or utilized to describe the plane ments, computing the intersection of the first plane, the sec that includes the great circle is Zero, position 35410 is on the ond plane, and the sphere associated with the first great circle great circle. and the second great circle may include computing a cross 0298. In one or more embodiments, method element product of the first vector and the second vector and may 46040 may be repeated with one or more of great circles include computing an intersection of the cross product of the and/or respective one or more vectors associated with and/or first vector and the second vector with the sphere. For utilized to describe respective one or more planes that include example, computing the intersection of the first plane, the respective great circles and/or one or more user positions second plane, and the sphere associated with the first great (e.g., one or more positions 35420-35440). For example, circle and the second great circle may produce position 6210. determining a user position with respect to one or more sides 0304 Turning now to FIG. 48, an exemplary method of of great circles may determine a position relative to a startline determining a bearing to a remote object is illustrated, accord and/or a starting area. For instance, great are 35310 may be or ing to one or more embodiments. At 48010, a first position include a start line (e.g., start line 3310 of FIG. 3), and pole may be determined. In one example, determining the first 6120 may be on a course side of the start line. position may include receiving first position information 0299. In one example, a computation of a dot product of from a position device. In another example, determining the the eighth vector (e.g., associated with position 35410) and first position may include a position device computing the the third vector may produce a negative number which may first position. indicate that position 35410 is not on the course side of the 0305 At 48020, a second position may be determined. In start line. In a second example, a ninth vector may be com one example, determining the second position may include puted from the origin of sphere 6000 to position 35420, and a receiving second position information from a position device. computation of a dot product of the ninth vector (e.g., asso In another example, determining the second position may ciated with position 35420) and the third vector may produce include a position device computing the second position. a negative number which may indicate that position 35420 is 0306 In one or more embodiments, a first position, a sec not on the course side of the start line. In a third example, a ond position, and a position of a remote object may lie on a tenth vector may be computed from the origin of sphere 6000 great circle. In one example, as illustrated in FIG. 49, a first to position 35430, and a computation of a dot product of the position 49010, a second position 49020, and position 6210 tenth vector (e.g., associated with position 35430) and the of a remote object may lie on a great circle 49210. In another third vector may produce a positive number which may indi example, a first position 49110, a second position 49120, and cate that position 35430 is on the course side of the start line. position 6210 of the remote object may lie on a great circle 0300. In another example, a computation of a dot product 49220. In one or more embodiments, the first position and the of the ninth vector (e.g., associated with position 35420) and second position may be interchanged, and a bearing may be the fifth vector may produce a positive number which may adjusted by one hundred and eighty degrees or tradians. US 2015/0260527 A1 Sep. 17, 2015 26

0307. In one or more embodiments, the first position and method illustrated in FIG. 48 (utilizing positions 49010 and the second position may be represented via spherical coordi 49020) may be utilized with either position 49010 or position nates. At 48030, a first result may be computed via an angular 49020 and a second bearing determined via the method illus difference. For example, the first position may be represented trated in FIG. 48 (utilizing positions 49110 and 49120) may via (p,0.cp), the second position may be represented via be utilized with either position 49110 or position 49120 to (p.0.cp), and the angular difference may be 0-0. At determine position 6210. 48040, a second result may be computed via a sine of the first result. For example, computing the second result may include 0313. In one or more embodiments, the method illustrated computing sin (0-0). At 48050, a third result may be com in FIG. 48 may be utilized in configuring and/or calibrating a puted via computing a sine of p. For instance, computing the digital compass. For example, a digital compass reading may third result may include computing sin (cp). At 48060, a be acquired at a first position of a system, traversing a portion fourth result may be computed via a product of the second of a great circle, and at, or after, a second position of the great result and the fourth result. For example, the fourth result may circle a bearing may be computed and may be compared with include computing sin (0-0) sin (cp). the digital compass reading and/or utilized to configure and/ 0308. At 48070, a fifth result may be computed via com or calibrate the digital compass and/or utilized as an offset for puting a sine of (p. For example, computing the fifth result further digital compass readings. may include computing sin (cp). At 48080, a sixth result may 0314 Turning now to FIG. 50, an exemplary method of be computed via computing a cosine of p2. For example, determining, utilizing a bearing, a distance along a first great computing the sixth result may include computing cos (cp). circle from a position to a second great circle is illustrated, At 48090, a seventh result may be computed via a product of according to one or more embodiments. At 50010, a position the fifth result and the sixth result. For example, the seventh may be determined. In one example, the position may be result may include computing sin (cp)cos (cp). received from a position device. In another example, the 0309 At 48100, an eighth result may be computed via position may be computed via a position device. At 50020, a computing a cosine of 0. For example, computing the eighth bearing to the second great circle may be determined. In one result may include computing cos (cp). At 48110, a ninth example, the bearing may be received from a bearing device. result may be computed via computing a sine of (p. For In a second example, the bearing may be computed via a example, computing the ninth result may include computing bearing device. In a third example, the bearing may be sin (cp). At 48120, a tenth result may be computed via com received from a heading device. In another example, the puting an angular difference. For example, computing the bearing may be computed via a heading device. In one or angular difference may be computed via computing 0-0. In more embodiments, a heading of a vehicle and/or vessel may one or more embodiments, computing a result may duplicate be utilized as the bearing determined at 50020. computing resources, and another computation that may 0315. At 50030, a plane that includes the position, an duplicate a previous computation may retrieve a previous origin, and a pole (e.g., a geographic pole, pole 6120, pole result from a memory as computing the result. For example, 6130, etc.) may be computed. In one or more embodiments, computing the tenth result may include retrieving the first computing the plane that includes the position, the origin, and result from a memory. At 48130, an eleventh result may be the pole may utilize one or more portions of one or more computed via computing a cosine of the angular difference. methods, processes, and/or systems described herein. At For example, computing the eleventh result may include com 50040, a rotation of the plane, about the position, by the puting cos (0-0). bearing may be computed. In one or more embodiments, 0310. At 48140, a twelfth result may be computed via a computing the rotation of the plane, about the position, by the product of the eighth result, the ninth result, and the eleventh bearing may utilize one or more portions of one or more result. For example, computing the twelfth result may include methods, processes, and/or systems described herein. computing cos (cp)sin (cp) cos (0-0). At 48150, a thir teenth result may be computed via a difference of the seventh 0316. In one or more embodiments, the second great circle result and the twelfth result. For example, the thirteenth result may be described via at least two positions. For example, the may include computing sin(p) cos (gp2)-cos(p)sin (gp2) cos second great circle may be described via positions 6210 and (0-0). 6220. For instance, the second great circle may be described 0311. At 48160, a complex number may be created from as an intersection of a surface of a sphere (e.g., sphere 6000) the fourth result and the thirteenth result. For example, ZX and a plane that includes the at least two positions and an iy, where x is the thirteenth result, i-V-1, and y is the fourth origin of the sphere. In one or more embodiments, the plane result. At 48170, an argument (e.g., a phase) of the complex that includes the at least two positions may be described by number may be computed. For example, arg(z) may be com and/or associated with a vector that is a cross product of two puted. For instance, arg(z) may be a phase of X--iy. In one or vectors respectively associated with the at least two positions. more embodiments, the phase (e.g., arg(z)) is the bearing to 0317. At 50050, an intersection of the plane, rotated about the remote object. In one or more embodiments, the phase of the position by the bearing, and the plane that includes the at X+ly may be less than Zero, and the phase may be adjusted via least two positions and the origin may be computed. For computing an addition of three hundred and sixty degrees or example, a first vector may be associated with the rotated 27 tradians to the phase. In one example, the bearing to the plane, about the position, by the bearing, and a second vector object may be arg(z)+360, if the phase is less than Zero. In may be associated with the plane that includes the at least two another example, the bearing to the object may be arg(Z)+2t, positions and the origin. For instance, the intersection of the if the phase is less than Zero. rotated plane, about the position, by the bearing and the plane 0312. In one or more embodiments, the method illustrated that includes the at least two positions and the origin may be in FIG. 48 may be utilized in determining a position of a computed via computing a cross product of the first vector remote object. For example, a first bearing determined via the and the second vector. In one or more embodiments, the cross US 2015/0260527 A1 Sep. 17, 2015 27 product of the first vector and the second vector may produce may be utilized in computing if the vehicle and/or the vessel a third vector that may be scaled via a radius (e.g., a radius of shall intersect and/or intercept the portion of the great circle a planet) and/or an altitude. (e.g., the starting line) at an amount of time transpiring (e.g., 0318. At 50060, a distance along the first great circle from when a countdown finishes). the position to the second great circle may be computed 0323. In one or more embodiments, a vehicle and/or a utilizing the position and the third vector. In one or more vessel may change one or more positions, headings, and/or embodiments, the third vector may be associated with a posi Velocities during an amount of time transpiring. For example, tion on the second great circle. For example, the distance a sailboat may change one or more positions, headings, and/ along the first great circle from the position to the second or Velocities during a countdown to a start of a sailboat race. great circle may be computed utilizing the position and the Accordingly, it may be necessary to utilize a computing position on the second great circle. device to perform multiple computations, described herein, to 0319. In one or more embodiments, the position may be achieve an outcome that would be favorable to a crew of the associated with a fourth Vector, and the distance along the first sailboat, according to one or more embodiments. For great circle from the position to the second great circle may be example, a member of the crew of the sailboat may not have computed via computing a multiplicative product of a radius time to perform repeated calculations during a last thirty (e.g., a radius of a planet) and/or an altitude and an arccosine seconds of a start sequence of a sailboat race. of an inner product (e.g., a dot product) of the third vector and 0324 Turning now to FIG. 51, an exemplary method of the fourth vector. For example, the distance along the first determining a distance along a first great circle from a posi great circle from the position to the second great circle may be tion to a second great circle is illustrated, according to one or computed via computing R-cos' (vs. v.), where R is a radius more embodiments. At 51010, a position may be determined. (e.g., a radius of a planet) and/or an altitude. For instance, the In one example, the position may be received from a position third vector and the fourth vector may be unit vectors. In one device. In another example, the position may be computed via or more embodiments, the third vector and the fourth vector a position device. may be converted from a spherical coordinate system to a 0325 At 51020, a plane that includes at least two positions Cartesian coordinate system to compute the distance along and an origin may be computed. In one or more embodiments, the first great circle from the position to the second great the second great circle may be described via at least two circle. positions. For example, the second great circle may be 0320 In one or more embodiments, the method illustrated described via positions 6210 and 6220. For instance, the in FIG. 50 may be utilized a number of times within an second great circle may be described as an intersection of a amount of time transpiring. For example, the method illus surface of a sphere (e.g., sphere 6000) and a plane that trated in FIG.50 may be utilized a number of times during a includes the at least two positions and an origin of the sphere. start sequence of a sailboat race. For instance, as time tran In one or more embodiments, computing the plane that spires (e.g., a countdown to a start of a sailboat race), the includes at least two positions include computing a cross method illustrated in FIG. 50 may be utilized a number of product of two vectors respectively associated with the at times to compute a distance to a starting line (e.g., great circle least two positions. For example, a vector associated with the portion 35310 as illustrated in FIG. 35) as the time transpires. cross product, oftwo vectors respectively associated with the 0321. In one or more embodiments, a position of an at least two positions, may be utilized to describe the com antenna of a position device may be taken into account when puted plane. computing a distant to an object and/or a starting line. For 0326. At 51030, a distance along a first great circle from example, the position of the antenna of the position device the position to a second great circle may be computed utiliz may be at the back or Stern of a vessel, and a length of the ing the position and the vector that may be utilized to describe vessel may be subtracted from the distant to the object and/or the plane. For example, a first vector may be associated with the starting line. the position, and a second vector may be the vector utilized to 0322. In one or more embodiments, a velocity of a vehicle describe the plane. For instance, the distance along the first and/or a vessel may be determined, the method illustrated in great circle from the position to the second great circle may be FIG. 50 may be utilized to determine a distance from a posi computed via computing R-cos' (viv), where R is a radius tion of the vehicle and/or the vessel, and an amount of time for (e.g., a radius of a planet) and/or an altitude. In one or more the vehicle and/or the vessel to intersect and/or intercept a embodiments, the first vector and the second vector may be portion of a great circle (e.g., a starting line) may be com unit vectors. In one or more embodiments, this computation puted. In one instance, computing an amount of time for the may be utilized to compute a shortest distance, on a surface of vehicle and/or the vessel to intersect and/or intercept a portion a sphere (e.g., along the first great circle), from the position to of a great circle (e.g., a starting line) may be utilized in a great circle (e.g., the second great circle). For example, this computing if the vehicle and/or the vessel shall intersect computation may be utilized to compute a shortest distance and/or intercept the portion of the great circle (e.g., the start from a position to a starting line, such as arc 35310 as illus ing line) before an amount of time transpires (e.g., before a trated FIG.35. For instance, this computation may be utilized countdown finishes). In a second instance, computing an to compute a shortest distance from one or more of positions amount of time for the vehicle and/or the vessel to intersect 35430, 35810, 35440, 35410, and 35820, among others to a and/or intercept a portion of a great circle (e.g., a starting line) starting line, such as arc 35310 as illustrated FIG. 35. may be utilized in computing if the vehicle and/or the vessel 0327. In one or more embodiments, the method illustrated shall intersect and/or intercept the portion of the great circle in FIG. 51 may be utilized a number of times within an (e.g., the starting line) after an amount of time transpires (e.g., amount of time transpiring. For example, the method illus after a countdown finishes). In another instance, computing trated in FIG. 51 may be utilized a number of times during a an amount of time for the vehicle and/or the vessel to intersect start sequence of a sailboat race. For instance, as time tran and/or intercept a portion of a great circle (e.g., a starting line) spires (e.g., a countdown to a start of a sailboat race), the US 2015/0260527 A1 Sep. 17, 2015 28 method illustrated in FIG. 51 may be utilized a number of 0332. As shown in FIG. 53, a sight 53110 may be utilized times to compute a distance to a starting line (e.g., great circle to determine a first bearing to a remote object (e.g., an exit portion 35310 as illustrated in FIG. 35) as the time transpires. ramp shown in FIG. 53). In one or more embodiments, user 0328. In one or more embodiments, a velocity of a vehicle input may be received that may align a sight 53110 with the and/or a vessel may be determined, the method illustrated in remote object. In one or more embodiments, one or more FIG. 51 may be utilized to determine a distance from a posi methods and/or processes may be utilized to determine a tion of the vehicle and/or the vessel, and an amount of time for position of the remote object via an image. For example, one the vehicle and/or the vessel to intersect and/or intercept a or more methods and/or processes associated with computer portion of a great circle (e.g., a starting line) may be com vision may be utilized to determine the remote object via the puted. In one instance, computing an amount of time for the image. For instance, sight 53110 may not be present when one vehicle and/or the vessel to intersect and/or intercept a portion or more methods and/or processes associated with computer of a great circle (e.g., a starting line) may be utilized in vision may be utilized to determine the remote object via the computing if the vehicle and/or the vessel shall intersect image. In one or more embodiments, a first offset may be and/or intercept the portion of the great circle (e.g., the start computed from a position of the remote object within image ing line) before an amount of time transpires (e.g., before a 53010, and aheading of vehicle 52010 and the first offset may countdown finishes). In a second instance, computing an be utilized to determine the first bearing. amount of time for the vehicle and/or the vessel to intersect 0333. In another example, as shown in FIG. 54, an image and/or intercept a portion of a great circle (e.g., a starting line) 54010 may be acquired via camera 52110, and a second may be utilized in computing if the vehicle and/or the vessel position may be determined where vehicle 52010 or camera shall intersect and/or intercept the portion of the great circle 52110 was when image 54010 was acquired. As shown in (e.g., the starting line) after an amount of time transpires (e.g., FIG. 54, a sight 54110 may be utilized to determine a second after a countdown finishes). In another instance, computing bearing to the remote object (e.g., the exit ramp shown in FIG. an amount of time for the vehicle and/or the vessel to intersect 54). In one or more embodiments, user input may be received and/or intercept a portion of a great circle (e.g., a starting line) that may align a sight 54110 with the remote object. In one or may be utilized in computing if the vehicle and/or the vessel more embodiments, one or more methods and/or processes shall intersect and/or intercept the portion of the great circle may be utilized to a position of determine the remote object (e.g., the starting line) at an amount of time transpiring (e.g., via an image. For example, one or more methods and/or when a countdown finishes). processes associated with computer vision may be utilized to 0329. In one or more embodiments, a vehicle and/or a determine the remote object via the image. For instance, sight vessel may change one or more positions, headings, and/or 54110 may not be present when one or more methods and/or Velocities during an amount of time transpiring. For example, processes associated with computer vision may be utilized to a sailboat may change one or more positions, headings, and/ determine the remote object via the image. In one or more or Velocities during a countdown to a start of a sailboat race. embodiments, a second offset may be computed from a posi Accordingly, it may be necessary to utilize a computing tion of the remote object within image 54010, and a heading of vehicle 52010 and the first offset may be utilized to deter device to perform multiple computations, described herein, to mine the second bearing. In one or more embodiments, the achieve an outcome that would be favorable to a crew of the first position (e.g., of camera 52110 or vehicle 52010), the sailboat, according to one or more embodiments. For first bearing to the remote object as determined via image example, a member of the crew of the sailboat may not have 53010, the second position (e.g., of camera 52110 or vehicle time to perform repeated calculations during a last thirty 52010), and the second bearing to the remote object as deter seconds of a start sequence of a sailboat race. mined via image 54010 may be utilized in computing a posi 0330 Turning now to FIGS. 52A and 52B, one or more tion of the remote object. cameras are illustrated, according to one or more embodi 0334. In one or more embodiments, two or more of cam ments. As illustrated in FIG. 52A, a vehicle 52010 may be eras 52110-52117 may be utilized in determining a position associated with one or more cameras 52110-52117. In one or of a remote object. In one example, as shown in FIG.55, an more embodiments, one or more cameras 52110-52117 may image 55010 may be acquired via camera 52111, and a first be mounted within and/or on vehicle 52010. As shown, position may be determined where vehicle 52010 or camera arrows from cameras 52110-52117 may indicate a center of 52111 was when image 55010 was acquired. As shown in view of a respective camera. As illustrated in FIG. 52B, FIG.55, a sight 55110 may be utilized to determine a first device 27610 may include and/or be coupled to camera bearing to a remote object (e.g., a house or a garage of a house 52110. In one or more embodiments, a camera (e.g., a camera shown in FIG. 55). In one or more embodiments, user input of cameras 52110-52117) may include one or more image may be received that may align a sight 55110 with the remote sensors that transforms light (e.g., light reflected off one or object. In one or more embodiments, one or more methods more objects) into one or more machine-readable (e.g., com and/or processes may be utilized to determine a position of puter-readable) signals. the remote object via an image. For example, one or more 0331. In one example, as shown in FIG. 53, an image methods and/or processes associated with computer vision 53010 may be acquired via camera 52110, and a first position may be utilized to determine the remote object via the image. may be determined where vehicle 52010 or camera 52110 For instance, sight 55110 may not be present when one or was when image 53010 was acquired. In one or more embodi more methods and/or processes associated with computer ments, one or more of cameras 52110-52117 may acquire still vision may be utilized to determine the remote object via the images. In one or more embodiments, one or more of cameras image. In one or more embodiments, a first offset may be 52110-52117 may acquire motion pictures and/or videos. In computed from a position of the remote object within image one or more embodiments, one or more still images may be 55010, and aheading of vehicle 52010 and the first offset may acquired from a video and/or a motion picture. be utilized to determine the first bearing. US 2015/0260527 A1 Sep. 17, 2015 29

0335. In a second example, as shown in FIG. 56, an image magnetic north pole, a magnetic South pole, pole 6120, pole 56010 may be acquired via camera 52112, and a second 6130, etc.). For instance, the heading may include a direction position may be determined where vehicle 52010 or camera (e.g., an angular difference), with respect to a pole, that a 52112 was when image 56010 was acquired. As shown in vehicle or vessel is traveling. FIG. 56, a sight 56110 may be utilized to determine a second 0339. At 58030, a first image may be acquired. In one or bearing to a remote object (e.g., the house or the garage of the more embodiments, the first image may be acquired via an house shown in FIG. 56). In one or more embodiments, user image sensor. In one example, the image sensor may include input may be received that may align a sight 56110 with the a camera (e.g., a camera of cameras 52110-52117). In another remote object. In one or more embodiments, one or more example, a camera (e.g., a camera of cameras 52110-52117) methods and/or processes may be utilized to determine a may include the image sensor. In one or more embodiments, position of the remote object via an image. For example, one an image sensor may transform light (e.g., light reflected off or more methods and/or processes associated with computer objects) into a machine-readable (e.g., computer-readable) vision may be utilized to determine the remote object via the signals and/or data. image. For instance, sight 56110 may not be present when one (0340. At 58040, a position of the remote object within the or more methods and/or processes associated with computer first image may be determined. In one or more embodiments, vision may be utilized to determine the remote object via the the first image may be displayed to a user, and determining the image. In one or more embodiments, a second offset may be position of the remote object within the first image may computed from a position of the remote object within image include receiving user input, where the user input indicates 56010, and a heading of vehicle 52010 and the second offset the position of the remote object within the first image. In one may be utilized to determine the second bearing. or more embodiments, determining the position of the remote 0336. In another example, as shown in FIG. 57, an image object within the first image utilizing user input may include 57010 may be acquired via camera 52113, and a third position computing a position within the first image that may be may be determined where vehicle 52010 or camera 52112 expressed in pixels. In one or more embodiments, determin was when image 57010 was acquired. As shown in FIG. 57, a ing the position of the remote object within the first image sight 57110 may be utilized to determine a second bearing to may include computing the position of the remote object a remote object (e.g., the house or the garage of the house within the first image via a computer imaging process (e.g., a shown in FIG. 57). In one or more embodiments, user input computer vision process). For example, a computer vision may be received that may align a sight 57110 with the remote imaging process may be utilized in determining the position object. In one or more embodiments, one or more methods of the remote object within the first image. In one or more and/or processes may be utilized to determine a position of embodiments, determining the position of the remote object the remote object via an image. For example, one or more within the first image utilizing a computer imaging process methods and/or processes associated with computer vision may include computing a position within the first image that may be utilized to determine the remote object via the image. may be expressed in pixels. For instance, sight 57110 may not be present when one or (0341. At 58050, a first bearing to the remote object may be more methods and/or processes associated with computer computed. In one or more embodiments, computing the first vision may be utilized to determine the remote object via the bearing to the remote object may include utilizing the first image. In one or more embodiments, a third offset may be heading and the position of the remote object within the first computed from a position of the remote object within image image. In one or more embodiments, computing the first 57010, and a heading of vehicle 52010 and the third offset bearing to the remote object may include utilizing the first may be utilized to determine the third bearing. heading, the position of the remote object within the first 0337. In one or more embodiments, a first data set may image, and an offset. In one example, the offset may include include the first position (e.g., of camera 52111 or vehicle a declination angle. In another example, the offset may 52010), and the first bearing to the remote object as deter include a mounting angle of the image sensor. For instance, mined via image 55010; a second data set may include the offsets may include Zero degrees, forty-five degrees, ninety second position (e.g., of camera 52112 or vehicle 52010), and degrees, one hundred and thirty-five degrees, one hundred the second bearing to the remote object as determined via and eighty degrees, two hundred and twenty-five degrees, two image 56010; and a third data set may include the third hundred and seventy degrees, and three hundred and fifteen position (e.g., of camera 52113 or vehicle 52010), and the degrees for cameras 52110-52117, respectively. third bearing to the remote object as determined via image 0342. In one or more embodiments, utilizing the position 57010. In one or more embodiments, at least two of the first of the remote object within the first image may include uti data set, the second data set, and the third data set may be lizing a function of pixels to angles and/or a mapping of pixels utilized to compute the position of the remote object. to angles. In one example, the function of pixels to angles 0338 Turning now to FIG. 58, an exemplary method of and/or the mapping of pixels to angle may include one hun computing, utilizing one or more image sensors, a position of dred pixels, in a horizontal or X-axis direction, to the right of a remote object from two positions is illustrated, according to center of the first image may provide an angle of positive ten one or more embodiments. At 58010, a first position may be degrees. In another example, the function of pixels to angles determined. At 58020, a first heading may be determined. In and/or the mapping of pixels to angles may include one hun one example, the first heading may include a first heading of dred pixels, in a horizontal or x-axis direction, to the left of a vehicle. In another example, the first heading may include a center of the first image may provide an angle of negative ten first heading of a vessel. In one or more embodiments, a degrees. heading device or a bearing device may be utilized in deter 0343 At 58060, a second position may be determined. At mining a heading. For example, a heading may include a 58070, a second heading may be determined. In one example, direction (e.g., an angular difference), with respect to a pole the second heading may include a second heading of a (e.g., a geographic north pole, a geographic South pole, a vehicle. In another example, the first heading may include a US 2015/0260527 A1 Sep. 17, 2015 30 second heading of a vessel. At 58080, a second image may be 0348 Turning now to FIG. 59, an exemplary method of acquired. In one or more embodiments, the second image determining a position of a remote object via utilizing mul may be acquired via an image sensor. In one example, the tiple devices at multiple positions is illustrated, according to image sensor may include a camera (e.g., a camera of cameras one or more embodiments. At 59010, a first position may be 52110-52117). In another example, a camera (e.g., a camera determined via a first device. In one or more embodiments, of cameras 52110-52117) may include the image sensor. In the first device may be operated by a first user. At 59020, a first one or more embodiments, an image sensor may transform bearing, at the first position, to a remote object may be deter light (e.g., light reflected off objects) into a machine-readable mined via a second device. At 59030, a second position, (e.g., computer-readable) signals and/or data. different from the first position, may be determined via a third (0344). At 58090, a position of the remote object within the device. In one or more embodiments, the third device may be second image may be determined. In one or more embodi operated by a second user. For example, the second user may ments, the second image may be displayed to a user, and be differ from the first user. At 59040, a second bearing, at the determining the position of the remote object within the sec second position, to the remote object may be determined via ond image may include receiving user input, where the user a fourth device. input indicates the position of the remote object within the (0349. At 59050, position information and bearing infor second image. In one or more embodiments, determining the mation may be provided to a fifth device. In one or more position of the remote object within the second image utiliz embodiments, the first device may provide the first position ing user input may include computing a position within the and the first bearing to the fifth device. In one or more second image that may be expressed in pixels. In one or more embodiments, the third device may provide the second posi embodiments, determining the position of the remote object tion and the second bearing to the fifth device. In one or more within the second image may include computing the position embodiments, the position information and the bearing infor of the remote object within the second image via a computer mation may be provided to the fifth device in one or more of imaging process (e.g., a computer vision process). For a wired and wireless fashion. In one example, the position example, a computer vision imaging process may be utilized information and the bearing information may be provided to in determining the position of the remote object within the the fifth device via one or more of WiFi signals, cellular second image. In one or more embodiments, determining the telecommunications signals, satellite telecommunications position of the remote object within the second image utiliz signals, Bluetooth communication signals, and a wireless ing a computer imaging process may include computing a network, among others. In a second example, the position position within the second image that may be expressed in information and the bearing information may be provided to pixels. the fifth device via one or more of a wired network, a wired telecommunications network, coaxial cable, twisted pair 0345. At 58100, a second bearing to the remote object may cable, and fiber optic cable, among others. In one or more be computed. In one or more embodiments, computing the embodiments, the position information and the bearing infor second bearing to the remote object may include utilizing the mation may be provided to the fifth device via a network second heading and the position of the remote object within 64110, as described with reference to FIG. 64. the second image. In one or more embodiments, computing 0350. At 59060, the position information and the bearing the second bearing to the remote object may include utilizing information may be received via the fifth device. In one or the second heading, the position of the remote object within more embodiments, the fifth device may receive the position the second image, and an offset. In one example, the offset information from the first device. In one or more embodi may include a declination angle. In another example, the ments, the fifth device may receive the position information offset may include a mounting angle of the image sensor. For from the third device. In one or more embodiments, the first instance, offsets may include Zero degrees, forty-five degrees, device may be or include the second device. In one or more ninety degrees, one hundred and thirty-five degrees, one hun embodiments, the third device may be or include the fourth dred and eighty degrees, two hundred and twenty-five device. In one or more embodiments, the fifth device may be degrees, two hundred and seventy degrees, and three hundred or include one or more of the first device, the second device, and fifteen degrees for cameras 52110-52117, respectively. the third device, and the fourth device. At 59070, a position of 0346. In one or more embodiments, utilizing the position the remote object may be computed, via the fifth device, via of the remote object within the second image may include the first position, the first bearing, the second position, and the utilizing a function of pixels to angles and/or a mapping of second bearing. pixels to angles. In one example, the function of pixels to 0351 Turning now to exemplary FIGS. 60 and 61, a user angles and/or the mapping of pixels to angles may include sighting a remote object via device 27610 is illustrated, fifty-seven pixels, in a horizontal or X-axis direction, to the according to one or more embodiments. As shown in FIG. 60, right of center of the second image may provide an angle of user 5010, at a first position, may orient device 27610 to positive eight degrees. In another example, the function of establish a sight line 3410 to a remote object 60010. As pixels to angles and/or the mapping of pixels to angles may illustrated in FIG. 61, user 5010, at a second position (differ include fifty-two, in a horizontal or x-axis direction, to the left ent from the first position), may orient device 27610 to estab of center of the first image may provide an angle of negative lish a sight line 7410 to remote object 60010. In one or more eight degrees. embodiments, user 5010 and device 27610 may be moving at (0347. At 58110, a position of the remote object may be a first speed at the first position and may be moving at a computed based on the first position, the first bearing, the second speed at the second position. In one example, the second position, and the second bearing. In one or more second speed may be different from the first speed. In another embodiments, computing the position of the remote object, at example, the second speed may be the first speed. 58100, may include utilizing one or more methods, processes, 0352 Turning now to FIG. 65, an exemplary method of and/or systems described herein. determining a position of a remote object and providing the US 2015/0260527 A1 Sep. 17, 2015

position to a user via the map is illustrated, according to one provider, a street, a cafe, a coffee shop, a bar, a hotel, an or more embodiments. At 65010, a first position may be airport, a place to rent a vehicle (e.g., a car, a van, a bike, a determined. For example, a first position of device 27610, as sailboat, etc.), a convenient store, a library, a department illustrated in FIG. 60, may be determined via device 27610. store, a clothing store, aboutique, a concert, and a concert At 65020, a first bearing to a remote object (e.g., object 60010 hall, among others. In a second example, the information as shown in FIG. 60) may be determined. For example, device based on the position of the remote object may include turn 27610 may determine the first bearing to the remote object. by-turn directions to the position of the remote object. In For instance, the bearing to the remote object may be associ another example, the information based on the position of the ated with sight line 3410. remote object may include advertising and/or promotion 0353 At 65030, a second position may be determined. For information associated with one or more of a restaurant, a example, a second position of device 27610, as illustrated in museum, a store, a goods provider, a service provider, a street, FIG. 61, may be determined via device 27610. At 65040, a a cafe, a coffee shop, a bar, a hotel, an airport, a place to rent second bearing to the remote object (e.g., object 60010 as a vehicle (e.g., a car, a van, a bike, a motor cycle, a motor shown in FIG. 61) may be determined. For example, device Scooter, a canoe, a sailboat, a motorboat, etc.), a convenient 27610 may determine the second bearing to the remote store, a library, a department store, a clothing store, a bou object. For instance, the bearing to the remote object may be tique, a concert, and a concert hall, among others. In one or associated with sight line 7410. At 65050, a position of the more embodiments, information 63110 may include one or remote object may be computed via the first position, the first more of text, a graphic, a picture, a sound, Sounds, a song, a bearing, the second position, and the second bearing. For motion picture, a video, and a message, among others. example, device 27610 may compute the position of the 0359. In one or more embodiments, the position of the remote object via the first position, the first bearing, the sec remote object may be provided to one or more of a mapping ond position, and the second bearing. service computing device, an information service computing 0354) At 65060, the position of the remote object may be device, an advertising service computing device, and a pro provided to the user via a map. For example, device 27610 motion service computing device, among others. For may provide the position of the remote object to the user via example, device 27610 may be coupled to a network 64110, a map 62010, as illustrated in FIG. 62A. For instance, the as illustrated in FIG. 64, and may provide the position of the position of the remote object (e.g., The University of Texas remote object to one or more of a mapping service computing Tower) may be provided to the user via an icon 62110 via map device 64010, an information service computing device 62010, as shown in FIG. 62A. 64020, a promotion service computing device 64030, and an 0355. In one or more embodiments, the position of the advertising service computing device 64040, among others, remote object may be an estimated position. In one example, via network 64110. For instance, one or more of mapping the first position and the second position may be associated service computing device 64010, information service com with, respectively, a first radius of uncertainty and a second puting device 64020, promotion service computing device radius of uncertainty. In another example, a digital compass 64030, and advertising service computing device 64040 may may be associated with a resolution of one degree and/or with be coupled to network 64110. an uncertainty of plus or minus one half of a degree. For 0360. In one or more embodiments, network 64110 may instance, the position (e.g., the estimated position) of the be or include a communications network. In one example, remote object may be provided to the user via an icon 62210 network 64110 may be or include multiple networks and/or via map 62010, as shown in FIG. 62B. In one or more embodi may be coupled to one or more other networks. In one or more ments, an error of an estimated position may increase as the embodiments, network 64110 may be, include, or form part distance from the first or second positions to the remote object of a wide area network. For example, the wide area network increases. For example, the estimated position of the remote may include one or more of a private wide area network, a object, as shown in FIG. 62B via icon 62210, may be due to corporate wide area network, and a public wide area network, the distance from the first or second positions to the remote among others. For instance, the public wide area network may object was several miles. be, include, or form part of an Internet. In one or more 0356. In one or more embodiments, the map may be pro embodiments, network 64110 may be, include, or form part vided to the user via a display. For example, map 62010 may of a wireless network. In one or more embodiments, network be provided to the user via display 63010, as illustrated in 64110 may be, include, or form part of a wired (e.g., via FIG. 63. For instance, display 63010 (as shown in FIG. 63) cables including metal, cables including optical fibers, etc.) may be or include display 27710 (of FIG. 27C) of device network. 2761O. 0361. In one or more embodiments, network 64110 may 0357 At 65070 (of FIG. 65), information based on the be or include a telecommunications network and/or a tele position of the remote object may be provided to the user. For phone network. In one example, network 64110 may be or example, information 63110 may be provided to the user via include a wired telephone network. In a second example, display 63010, as illustrated in FIG. 63. network 64110 may be or include a wireless telephone net 0358. In one or more embodiments, device 27610 may work (e.g., a satellite telephone network, a cellular telephone include a mapping database that may be utilized to provide network, etc.). In a third example, network 64110 may be or the position of the remote object to the user. In one or more include a public switched telephone network. In a fourth embodiments, device 27610 may include an information example, network 64110 may be or include a packet switched database that may be utilized to provide, to the user, the telephone network. In another example, network 64110 may information based on the position of the remote object. In one be or include a wired telephone network. example, the information based on the position of the remote 0362. In one or more embodiments, device 27610 may object may include information associated with one or more receive one or more of mapping information via mapping of a restaurant, a museum, a store, a goods provider, a service service computing device 64010, information via informa US 2015/0260527 A1 Sep. 17, 2015 32 tion service computing device 64020, promotion information device, and/or a system may be or include an electronic sys via promotion service computing device 64030, and adver tem. In one or more embodiments, a computer, a computing tising information via advertising service computing device device, and/or a computer system may be broadly character 64040. For example, one or more of the mapping information, ized to include any device that includes a processing unit or the information, the promotion information, the advertising processor that executes instructions from a memory. For information may be provided to the user via information example, a processor (e.g., a central processing unit or CPU) 63110 via display 63010, as illustrated in FIG. 63. may execute instructions from a memory that stores the 0363 Turning now to FIG. 66, an exemplary display that instructions which may include one or more software pro displays information is illustrated, according to one or more grams in accordance with one or more of processes, methods, embodiments. As illustrated, display 63010 may display and/or flowcharts described herein. In one instance, the pro information via information display areas 66010-66040. As cessing unit and the memory, that stores the instructions shown, display 63010 may display input areas 66110-66140, which may include one or more software programs in accor where a user may input information. In one or more embodi dance with one or more of processes, methods, and/or flow ments, the user may actuate submit button or icon 66210, charts described herein, may form one or more means for one when information is to be transferred. In one example, the or more functionalities described with references to one or information may be transferred to a storage and/or a memory. more of processes, methods, and/or flowcharts described In another example, the information may be transferred to a herein. In another instance, at least one of an ASIC and a computing device. For instance, the information may be FPGA may be configured in accordance with one or more of transferred to device 10010. processes, methods, and/or flowcharts described herein, may 0364. In one or more embodiments, the information may form one or more means for one or more functionalities be transferred to web server 13034 of device 10010. For described with references to one or more of processes, meth example, display 63010 may display information via infor ods, and/or flowcharts described herein. mation display areas 66010–66040 and/or input areas 66110 0369. In one or more embodiments, one or more of the 66140 in accordance with a web page from web server 13034. method elements described herein and/or one or more por In one or more embodiments, the information may be trans tions of an implementation of an exemplary method element ferred to APP 13031 of device 10010. For example, display may be repeated, may be performed in varying orders, may be 63010 may display information via information display areas performed concurrently with one or more of the other method 66010-66040 and/or input areas 66110-66140 in accordance elements and/or one or more portions of an implementation of With APP 13031. an exemplary method element, or may be omitted, according 0365. In one or more embodiments, wireless interface to one or more embodiments. For example, one or more 13100 of device 10010 may include, be, or form part of a methods may be repeated in computing multiple rotations, via wireless access point (e.g., a WiFi access point). For example, multiple angles, about multiple positions. device 27610 may include display 63010, and device 27610 0370. In one or more embodiments, “determining may be may communicate with device 10010 via the wireless access “computing. For example, a system and/or a device may point. perform “determining via “computing. For instance, “com 0366. In one or more embodiments, a system and/or a puting may include a processing unit executing instructions device may be moving at a first speed at a first position and from a memory. In one or more embodiments, a position may may be moving at a second speed at a second position when mean position information and/or location information. For utilizing one or more methods and/or processes described example, a position may mean position information and/or herein. In one example, the second speed may be different location information with reference to a coordinate system. from the first speed. In another example, the second speed 0371. In one or more embodiments, concurrently may may be the first speed. mean simultaneously. In one or more embodiments, concur 0367. In one or more embodiments, the term “memory” rently may mean apparently simultaneously according to may mean a “memory device', a “memory medium', and/or Some metric. For example, two tasks (e.g., two processes, two "tangible computer readable storage medium'. In one threads, etc.) may be context switched such that such that they example, one or more of a “memory device', a “memory appear to be simultaneous to a human. In one instance, a first medium', and a "tangible computer readable storage task of the two tasks may include a first method element medium may include Volatile storage such as random access and/or a first portion of a first method element. In a second memory (RAM), DRAM, Rambus RAM. SRAM, EDO instance, a second task of the two tasks may include a second RAM, etc. In another example, one or more of a “memory method element and/or a first portion of a second method device', a “memory medium', and a "tangible computer element. In another instance, a second task of the two tasks readable storage medium may include nonvolatile storage may include the first method element and/or a second portion such as an EEPROM, an EPROM, flash memory, FRAM of the first method element. Further, one or more of the system (ferroelectric random access memory), a DVD-ROM, a CD elements described herein may be omitted and additional ROM, a floppy disk, a magnetic tape, NVRAM, a magnetic system elements may be added as desired, according to one or media (e.g., a hard drive), optical storage, etc. In one or more more embodiments. Moreover, Supplementary, additional, embodiments, a memory medium may include one or more and/or duplicated method elements may be instantiated and/ Volatile storages and/or one or more nonvolatile storages. or performed as desired, according to one or more embodi 0368. In one or more embodiments, a system may include mentS. one or more devices. In one or more embodiments, a system 0372. One or more modifications and/or alternatives of the may include one or more components of a device. In one or embodiments described herein may be apparent to those more embodiments, a device may include one or more micro skilled in the art in view of this description. Hence, descrip controllers and/or applications processors. In one or more tions of the embodiments, described herein, are to be taken embodiments, a device may be or include an electronic and/or construed as illustrative and/or exemplary only and are US 2015/0260527 A1 Sep. 17, 2015

for the purpose of teaching those skilled in the art the general device, the circuit, the system that stores instructions execut manner of carrying out the embodiments describer herein. In able via the processing unit, or the other component is not one or more embodiments, one or more materials and/or currently in operation. elements may be swapped or substituted for those illustrated 0377. In one or more embodiments, enumerations (e.g., and described herein. In one or more embodiments, one or first, second, third, etc.) may be utilized, herein, to identify more parts, methods, and/or processes may be reversed, and/ two or more elements, where the enumerations do not apply or certain one or more features of the described one or more and/or necessitate an ordering (e.g., spatial, temporal, logical, embodiments may be utilized independently, as would be step-wise, etc.). In one example, enumerations may be uti apparent to one skilled in the art after having the benefit of this lized, herein, to differentiate two or more elements. For description. instance, a first element and a second element may be utilized 0373. In one or more embodiments, a measure or a metric to describe different elements. In another example, enumera may include units of a coordinate system. In one example, the tions may be utilized, herein, to identify same elements. For coordinate system may include a spherical coordinate sys instance, a first element and a second element may be utilized tem. For instance, first units of the coordinate system may to describe a same element. In one or more embodiments, include radians for measures of phi and theta, and second terms are used in this disclosure in a singular fashion shall be units of the coordinate system may include inches, feet, miles, deemed to include the plural when applicable, and when used kilometers, meters, centimeters, millimeters, nautical miles, herein in the plural to include the singular when applicable. nautical minutes, nautical seconds, etc. for rho. In another I claim: example, the coordinate system may include a Cartesian 1. A system, comprising: coordinate system. For instance, units of the Cartesian coor a position device; dinate system may include inches, feet, miles, kilometers, a processor; meters, centimeters, millimeters, nautical miles, nautical at least one camera; and minutes, nautical seconds, etc. In one or more embodiments, utilizing a pole (e.g., a geographic pole, a pole of a sphere, a a memory device, wherein the memory device stores pole of an ellipsoid, a pole of a geoid, etc.) may be associated instructions that are executable by the processor, with a vector. For example, the vector may be, include, and/or wherein the position device: utilized as (0,0,1) or (0,0,-1) as express via a Cartesian coor receives multiple location signals, via at least one dinate system. For instance, including a pole in a computation antenna coupled to the position device; and may include utilizing the vector (e.g., (0,0,1) or (0,0,-1) as determines a first position and a second position, differ express via a Cartesian coordinate system) as the pole. ent from the first position, via computing the first position, based on a first location of the at least one 0374. In one or more embodiments, a function may be antenna and the multiple location signals, and com implemented and/or approximated via a Taylor series. In one puting the second position, based on a second location example, one or more trigonometric functions (e.g., sine, of the at least one antenna and the multiple location cosine, tangent, arcsine, arccosine, arctangent, etc.) may be signals, wherein the second location of the at least one implemented, estimated, and/or approximated via Taylor antenna is different from the first location of the at series. In another example, a square root function may be least one antenna; implemented and/or approximated via a Taylor series. In one wherein the at least one camera: or more embodiments, a sine function and/or a cosine func tion may be computed via a Cordic method and/or process. acquires a first image that includes a first remote object For example, a processing unit (e.g., a microcontroller, an image of a remote object and that corresponds to the ASIC, a FPGA, an application processor, etc.) may not first position; and include a floating point unit, and the processing unit that may acquires a second image that includes a second remote not include a floating point unit may compute a sine function object image of the remote object and that corre and/or a cosine function may be computed via a Cordic sponds to the second position; and method and/or process. wherein, as the processor executes the instructions, the 0375. In one or more embodiments, each of the terms processor: “comprise' and “include” is open-ended. For instance, each determines a first image position of the first remote of these terms does not foreclose additional structure, ele object image of the remote object included by the first ments, and/or steps. In one or more embodiments, the term image: “based on' is utilized to describe one or more factors that determines a first bearing to the remote object at a affect a determination. This term may not foreclose additional remote object position, different from the first posi factors that may affect a determination and/or a computation. tion and different from the second position, based on In one instance, a determination and/or a computation may be the first image position; solely based on those factors, or in another instance, a deter determines a second image position of the second mination and/or a computation may be based, at least in part, remote object image of the remote object included by on those factors. the second image; 0376. In one or more embodiments, “configured to may determines a second bearing to the remote object at the be utilized to describe that a device, a circuit, a system that remote object position based on the second image stores instructions executable via a processing unit, or other position; component may perform one or more tasks. In one or more computes a first rotation, by the first bearing, of a first embodiments, a device, a circuit, a system that stores instruc vector associated with the first position; tions executable via a processing unit, or other component computes a second rotation, by the second bearing, of a may be said to be configured to perform a task when the second vector associated with the second position; US 2015/0260527 A1 Sep. 17, 2015 34

computes the remote object position based on the first wherein the intersection of the first plane and the second rotation, by the first bearing, of the first vector and the plane indicates the remote object position. second rotation, by the second bearing, of the second 11. The system of claim 1, wherein the processor further: Vector. computes, utilizing the first position, a first plane, wherein 2. The system of claim 1, wherein the processor further the first plane is normal to the first vector and the first provides, via a display, information based on the remote plane initially includes the first position, a geographic object position. pole, and an origin; and 3. The system of claim 1, wherein the processor further: computes, utilizing the second position, a second plane, receives first user input that indicates the first image posi wherein the second plane is normal to the second vector tion of the first remote object image of the remote object and the second plane initially includes the second posi included by the first image; and tion, the geographic pole, and the origin; receives second user input that indicates the second image wherein when the processor computes the first rotation, by position of the second remote object image of the remote the first bearing, of the first vector associated with the object included by the second image. first position, the processor computes a rotation of the 4. The system of claim 3, wherein the processor further first plane about the first position by the first bearing displays, via a display, the first image and the second image. Such that the first plane no longer includes the geo 5. The system of claim 1, graphic pole and includes the first position, the origin, wherein the first image position of the first remote object and the remote object position; image of the remote object included by the first image is wherein when the processor computes the second rotation, based on a first number of pixels; by the second bearing, of the second vector associated wherein the second image position of the second remote with the second position, the processor computes a rota object image of the remote object included by the second tion of the second plane about the second position by the image is based on a second number pixels; second bearing Such that the second plane no longer wherein when the processor determines the first bearing to includes the geographic pole and includes the second the remote object at the remote object position, the pro position, the origin, and the remote object position; and cessor utilizes the first number of pixels; and wherein when the processor computes the remote object wherein when the processor determines the second bearing position based on the first rotation, by the first bearing, of to the remote object at the remote object position via the the first vector and the second rotation, by the second second image position, the processor utilizes the second bearing, of the second vector, the processor computes an number of pixels. intersection of the first plane and the second plane. 6. The system of claim 5, 12. The system of claim 1, wherein when the processor determines the first bearing to wherein when the processor computes the first rotation, by the remote object at the remote object position, utilizing the first bearing, of the first vector associated with the the first number of pixels, the processor utilizes at least first position, the processor: one of a first function of number of pixels to angles and computes a first quaternion, utilizing the first position a first mapping of number of pixels to angles; and and the first bearing; wherein when the processor determines the second bearing computes a second quaternion, utilizing the first vector; to the remote object at the remote object position via the computes an inverse of the first quaternion as a third second image position, utilizing the second number of quaternion; and pixels, the processor utilizes at least one of a second computes a first quaternion multiplication of the first function of number of pixels to angles and a second quaternion, the second quaternion, and the third mapping of number of pixels to angles. quaternion; and 7. The system of claim 5, wherein the second number of wherein when the processor computes the second rotation, pixels equals the first number of pixels. by the second bearing, of the second vector associated 8. The system of claim 5, wherein the at least one of the with the second position, the processor: second function of number of pixels to angles and the second mapping of number of pixels to angles is the at least one of the computes a fourth quaternion, utilizing the second posi first function of number of pixels to angles and the first tion and the second bearing; number of mapping of pixels to angles. computes a fifth quaternion, utilizing the second vector; 9. The system of claim 1, wherein the at least one camera computes an inverse of the fourth quaternion as a sixth further acquires at least one of a motion picture and a video quaternion; and that includes the first image and the second image. computes a second quaternion multiplication of the 10. The system of claim 1, fourth quaternion, the fifth quaternion, and the sixth wherein when the processor computes the remote object quaternion. position based on the first rotation, by the first bearing, of 13. The system of claim 1, the first vector and the second rotation, by the second wherein the first rotation, by the first bearing, of the first bearing, of the second vector, the processor computes an vector is associated with a third vector; intersection of a first plane and a second plane, different wherein the second rotation, by the second bearing, of the from the first plane; second vector is associated with a fourth vector, and wherein the first plane includes the first position and the wherein when the processor computes the remote object remote object position; position based on the first rotation, by the first bearing, of wherein the second plane includes the second position and the first vector and the second rotation, by the second the remote object position; and bearing, of the second vector, the processor computes a US 2015/0260527 A1 Sep. 17, 2015

cross product of the third vector and the fourth vector, wherein when the processor determines the second bearing wherein the cross product indicates the remote object to the remote object at the remote object position based position. on the second image position, the processor determines 14. The system of claim 13, wherein the processor further: the second bearing to the remote object at the remote computes, utilizing the first position, the first vector normal object position further based on the second heading via to the first position, an origin, and a geographic pole; and the second machine readable signal. computes, utilizing the second position, the second vector 20. The system of claim 19, normal to the second position, the origin, and the geo wherein the electronic heading device includes a plurality graphic pole; of magnetic field sensor devices; wherein when the processor computes the first rotation, by wherein the electronic heading device computes the first the first bearing, of the first vector associated with the heading via the first transform of the magnetic field and first position, the processor computes a first transform of the first orientation of the electronic heading device the first vector into the third vector, wherein the proces within the magnetic field into the first machine readable sor computes the first rotation of the first vector about the signal via the plurality of magnetic field sensor devices; first position by the first bearing; and and wherein when the processor computes the second rotation, wherein the electronic heading device computes the sec by the second bearing, of the second vector associated ond heading via the second transform of the magnetic with the second position, the processor computes a sec field and the second orientation of the electronic heading ond transform of the second vector into the fourth vector, device within the magnetic field into the second machine wherein the processor computes the second rotation of readable signal via the plurality of magnetic field sensor the second vector about the second position by the sec devices. ond bearing. 21. The system of claim 20, wherein the plurality of mag 15. The system of claim 1, further comprising: netic field sensor devices includes a plurality of magnetom an electronic heading device; eters. wherein the electronic heading device computes a first heading: 22. The system of claim 1, wherein when the position device determines the first position and the second position, wherein the electronic heading device computes a second different from the first position, via computing the first posi heading: tion, based on the first location of the at least one antenna and wherein when the processor determines the first bearing to the multiple location signals, computing the second position, the remote object at the remote object position based on based on the second location of the at least one antenna and the first image position, the processor determines the the multiple location signals, the position device: first bearing to the remote object at the remote object computes the first position while the at least one antenna is position further based on the first heading; and moving at a first speed; and wherein when the processor determines the second bearing to the remote object at the remote object position based computes the second position while the at least one antenna on the second image position, the processor determines is moving at a second speed. the second bearing to the remote object at the remote 23. The system of claim 22, wherein the second speed is the object position further based on the second heading. first speed. 16. The system of claim 15, wherein the second heading is 24. The system of claim 1, the first heading. wherein the position device further provides the first posi 17. The system of claim 15, wherein the position device tion and the second position to the processor; includes the electronic heading device. wherein the at least one camera further provides the first 18. The system of claim 17, wherein the position device image and the second image to the processor, and includes a global position system (GPS) receiver device that wherein the processor further: computes the first heading and computes the second heading. receives the first position and the second position from 19. The system of claim 1, further comprising: the position device; and an electronic heading device; receives the first image and the second image from the at wherein the electronic heading device computes a first least one camera. heading via a first transform of a magnetic field and a first orientation of the electronic bearing device within 25. The system of claim 1, the magnetic field into a first machine readable signal wherein the processor further receives multiple data sets; based on the first heading; wherein a first data set of the multiple data sets includes the wherein the electronic heading device computes a second first image and the first position; and heading via a second transform of the magnetic field and wherein a second data set of the multiple data sets includes a second orientation of the electronic bearing device the second image and the second position. within the magnetic field into a second machine readable 26. The system of claim 1, wherein the position device signal based on the second heading: includes a global position system (GPS) receiver device. wherein when the processor determines the first bearing to the remote object at the remote object position based on 27. The system of claim 1, further comprising: the first image position, the processor determines the the display; first bearing to the remote object at the remote object wherein the display is coupled to the processor; and position further based on the first heading via the first wherein the display displays the information based on the machine readable signal; and remote object position. US 2015/0260527 A1 Sep. 17, 2015 36

28. The system of claim 1, further comprising: the processor determining a first bearing to the remote the at least one antenna. object at a remote object position, different from the first 29. The system of claim 1, position and different from the second position, based on wherein when the processor determines the first bearing to the first image position; the remote object at the remote object position, different the processor determining a second image position of the from the first position and different from the second second remote object image of the remote object position, based on the first image position, the processor included by the second image: performs at least one of adding a declination angle and the processor determining a second bearing to the remote Subtracting the declination angle; and object at the remote object position based on the second wherein when the processor determines the second bearing image position; to the remote object at the remote object position based the processor computing a first rotation, by the first bear on the second image position, the processor performs at ing, of a first vector associated with the first position; least one of adding the declination angle and subtracting the processor computing a second rotation, by the second the declination angle. bearing, of a second vector associated with the second 30. The system of claim 1, position; and wherein the at least one camera includes at least two cam the processor computing the remote object position based eras; on the first rotation, by the first bearing, of the first vector wherein when the at least one camera acquires the first and the second rotation, by the second bearing, of the image that includes the first remote object image of the second vector. remote object and that corresponds to the first position, 35. The method of claim 34, further comprising: a first camera of the at least two cameras acquires the the processor providing, via a display, information based first image that includes the first remote object image of on the remote object position. the remote object and that corresponds to the first posi 36. The method of claim 34, further comprising: tion; and the processor receiving first user input that indicates the wherein when the at least one camera acquires the second first image position of the first remote object image of image that includes the second remote object image of the remote object included by the first image; and the remote object and that corresponds to the second the processor receiving second user input that indicates the position, a second camera of the at least two cameras second image position of the second remote object acquires the second image that includes the second image of the remote object included by the second remote object image of the remote object and that cor image. responds to the second position. 37. The method of claim 36, further comprising: 31. The system of claim 30, wherein a first center of view the processor providing, via a display, the first image and of the first camera is different from a second center of view of the second image. the second camera. 38. The method of claim 36, 32. The system of claim 1, wherein the first image position of the first remote object wherein the at least one camera acquires the first image that image of the remote object included by the first image is includes the first remote object image and that corre based on a first number of pixels; sponds to the first position while moving at a first speed; wherein the second image position of the second remote and object image of the remote object included by the second wherein the at least one camera acquires the second image image is based on a second number of pixels; that includes the second remote object image and that wherein the processor determining the first bearing to the corresponds to the second position while moving at a remote object at the remote object position, different second speed. from the first position and different from the second position, based on the first image position includes uti 33. The system of claim32, wherein the second speed is the lizing the first number of pixels; and first speed. wherein the processor determining the second bearing to 34. A method, comprising: the remote object at the remote object position based on a position device, coupled to at least one antenna, receiving the second image position includes utilizing the second multiple location signals via the at least one antenna; number of pixels. the position device computing a first position and a second 39. The method of claim 38, position, different from the first position, based on the wherein the processor determining the first bearing to the multiple location signals and a first location of the at remote object at the remote object position, different least one antenna and a second location, different from from the first position and different from the second the first location, of the at least one antenna; position, based on the first image position further at least one camera acquiring a first image that includes a includes utilizing at least one of a first function of num first remote object image of a remote object and that ber of pixels to angles and a first mapping of number of corresponds to the first position; pixels to angles; and the at least one camera acquiring a second image that wherein the processor determining the second bearing to includes a second remote object image of the remote the remote object at the remote object position based on object and that corresponds to the second position; the second image position further includes utilizing at a processor determining a first image position of the first least one of a second function of number of pixels to remote object image of the remote object included by the angles and a second mapping of number of pixels to first image: angles.