GS 609 Surveying with Satellites

Homework No. 3

GS 609 Surveying with Satellites Winter Quarter, 2000 February 15, 2001 Due: March 1, 2001

Given RINEX observation and navigation data files for a stationary GPS receiver with unknown location, perform the following:

1. Linearize the pseudorange observation equation and compute the partial derivatives using satellite coordinates from (2) below (note that the approximate coordinates of the GPS antenna are given in the RINEX observation header file).

2. Compute the satellites’ positions at the epoch of observation, based on RINEX navigation data, using the algorithm that you developed for Lab #2. The file can be downloaded on the class web (http://geodesy.eng.ohio- state.edu/course/gs609/).

3. Use pseudorange data given in the RINEX observation file to compute 3D Cartesian coordinates of the location of the GPS antenna and the receiver clock correction (based on RINEX navigation data compute and apply the satellite clock correction first; neglect all other unknowns in the equation). What is the minimum number of observations that you need to obtain the solution? Perform the minimum-constellation solution based on P-code ranges.

4. Use pseudorange data given in the RINEX observation file to compute 3D Cartesian coordinates of the location of the GPS antenna and the receiver clock correction (based on RINEX navigation data compute and apply the satellite clock correction first; neglect all other unknowns in the equation). Obtain separate solutions from P-code and C/A code observable, respectively. This time, use all the satellite observation data provided to get solution. Compare the results and discuss.

5. Compare the results from (3) and (4) above. Discuss.

2 6. Prove the relationship: t=k/f from the enclosed handout (distributed in class

earlier), where t is the ionospheric delay of the signal, k is a constant and f is the signal frequency. Hint: start from the relationship between time, velocity and distance, and find the change in time as a function of varying velocity; assume fixed travel distance.

1/3 Navigation File (Lab301.99n)

2 NAVIGATION DATA RINEX VERSION / TYPE GPS Data Logger GRDL 22-Mar-1999 12:01 PGM / RUN BY / DATE COMMENT END OF HEADER 2 99 3 22 18 0 0.0 -.387239269912D-04 -.443378667114D-11 .000000000000D+00 .860000000000D+02 .641250000000D+02 .486698844389D-08 -.232240216658D+01 .310130417347D-05 .185836175224D-01 .107176601887D-04 .515368502235D+04 .151200000000D+06 .195577740669D-06 .116264416932D+01 -.115483999252D-06 .936313573653D+00 .155625000000D+03 -.221862730186D+01 -.795747431789D-08 .101789954246D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 -.232830643654D-08 .860000000000D+02 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 7 99 3 22 18 0 0.0 .813954044133D-03 .147792889038D-11 .000000000000D+00 .170000000000D+03 .603750000000D+02 .481091467962D-08 .272033290081D+01 .302121043205D-05 .102233515354D-01 .410713255405D-05 .515360291672D+04 .151200000000D+06 -.447034835815D-07 .225165927234D+01 -.165775418282D-06 .955617560370D+00 .294500000000D+03 -.216826844627D+01 -.827677333226D-08 .539308178636D-10 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 -.931322574615D-09 .682000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 13 99 3 22 17 59 44.0 -.690338201821D-04 -.210320649785D-10 .000000000000D+00 .000000000000D+00 .275000000000D+01 .470412451710D-08 -.162968136300D+01 .251457095146D-06 .212027202360D-02 .709854066372D-05 .515377128983D+04 .151184000000D+06 -.745058059692D-08 -.874646144797D+00 .149011611938D-07 .961259925683D+00 .243750000000D+03 -.109490109393D+01 -.815426822943D-08 .333228166005D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 .558793544769D-08 .256000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 15 99 3 22 18 0 0.0 .664619728923D-03 .397903932026D-11 .000000000000D+00 .213000000000D+03 -.826875000000D+02 .416767360033D-08 -.539578337546D+00 -.423565506935D-05 .714090676047D-02 .632181763649D-05 .515359841728D+04 .151200000000D+06 -.521540641785D-07 -.290786742981D+01 .689178705215D-07 .983325919289D+00 .267781250000D+03 .151707954902D+01 -.821319925557D-08 -.277868717205D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .200000000000D+01 .000000000000D+00 -.931322574615D-09 .725000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 19 99 3 22 17 59 44.0 -.122420489788D-03 -.420641299570D-11 .000000000000D+00 .138000000000D+03 -.230312500000D+02 .554451666566D-08 -.111179038367D-01 -.119209289551D-05 .478158739861D-02 .786408782005D-05 .515360654449D+04 .151184000000D+06 .651925802231D-07 .107957328490D+00 .242143869400D-07 .927524976258D+00 .209281250000D+03 -.278069029823D+01 -.858785771874D-08 -.283583240952D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 -.325962901115D-08 .138000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 26 99 3 22 18 0 0.0 .357320066541D-03 .470663508167D-10 .000000000000D+00 .128000000000D+03 .225000000000D+01 .477769901034D-08 .241671187380D+01 .175088644028D-06 .111072373111D-01 .674650073051D-05 .515358551025D+04 .151200000000D+06 -.169500708580D-06 -.868448606462D+00 .210478901863D-06 .960262099982D+00 .249031250000D+03 -.103266892749D+00 -.818176937496D-08 .240009997380D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 .000000000000D+00 .384000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 27 99 3 22 17 59 44.0 .148387625813D-04 .113686837722D-11 .000000000000D+00 .660000000000D+02 -.188750000000D+02 .522878922863D-08 -.530517243864D+00 -.964850187302D-06 .133102550171D-01 .775977969170D-05 .515368167686D+04 .151184000000D+06 .281259417534D-06 .143695736910D+00 -.111758708954D-07 .941077547360D+00 .216000000000D+03 -.294706393665D+01 -.848785355317D-08 -.260725145963D-09 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 .465661287308D-09 .660000000000D+02 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00 31 99 3 22 18 0 0.0 .154948793352D-04 .568434188608D-12 .000000000000D+00 .165000000000D+03 .688437500000D+02 .504806741513D-08 .152727803811D+01 .359117984772D-05 .886761641596D-02 .414252281189D-05 .515370834351D+04 .151200000000D+06 -.167638063431D-06 .225269650320D+01 .502914190292D-07 .955064555392D+00 .299562500000D+03 .778139664206D+00 -.863857411700D-08 .564309220030D-10 .000000000000D+00 .100200000000D+04 .000000000000D+00 .700000000000D+01 .000000000000D+00 .139698386192D-08 .165000000000D+03 .147630000000D+06 .000000000000D+00 .000000000000D+00 .000000000000D+00

2/3 Observation File (Lab301.99o)

2 OBSERVATION DATA G (GPS) RINEX VERSION / TYPE GPS Data Logger GRDL 22-Mar-1999 12:01 PGM / RUN BY / DATE holl COMMENT topex1 COMMENT COMMENT NOS MARKER NAME 7031 D 1977 MARKER NUMBER dmm NOS OBSERVER / AGENCY UZ01286 ASHTECH Z-SURVEYOR UE00 REC # / TYPE / VERS CD16199 ashtech chokering ANT # / TYPE 310880.617 -4679087.195 4308925.762 APPROX POSITION XYZ 2.0 0 0 ANTENNA: DELTA H/E/N 1 1 WAVELENGTH FACT L1/2 5 C1 L1 L2 P1 P2 # / TYPES OF OBSERV 1 INTERVAL 1999 3 22 17 1 22 TIME OF FIRST OBS 1999 3 22 21 51 5 TIME OF LAST OBS END OF HEADER 99 3 22 17 1 22.0000000 0 6 15 31 27 26 7 13 21594940.921 11609407.06401 9047549.64101 21594939.245 21594947.336 22563844.186 13226364.74301 10294014.15201 22563842.766 22563850.920 20261148.335 12073632.93801 9406275.67801 20261147.263 20261152.933 24634912.090 -789202.16501 -615223.99801 24634912.480 24634921.398 23260563.863 11270500.28501 8787740.46301 23260562.980 23260573.029 23494472.305 13044704.23601 10154322.73801 23494471.963 23494481.281