electronics

Article Positioning Using IRIDIUM Signals of Opportunity in Weak Signal Environment

Zizhong Tan, Honglei Qin, Li Cong * and Chao Zhao School of Electronic and Information , Beihang University (BUAA), Beijing 100191, China; [email protected] (Z.T.); [email protected] (H.Q.); [email protected] (C.Z.) * Correspondence: [email protected]; Tel.: +86-1381-0629-638

 Received: 9 December 2019; Accepted: 25 December 2019; Published: 27 December 2019 

Abstract: In order to get rid of the dependence of the navigation and positioning system on the global navigation satellite system (GNSS), , , satellite, and other signals of opportunity (SOPs) can be used to achieve receiver positioning. The space-based SOPs based on offer better coverage and availability than ground-based SOPs. Based on the related research of Iridium SOPs positioning in the open environment, this paper mainly focuses on the occluded environment and studies the Iridium SOPs positioning technique in weak signal environment. A new quadratic square accumulating instantaneous Doppler estimation algorithm (QSA-IDE) is proposed after analysing the and signal characteristics of the Iridium satellite. The new method can improve the ability of the Iridium weak signal Doppler estimation. The theoretical analysis and positioning results based on real signal data show that the positioning based on Iridium SOPs can be realized in a weak signal environment. The research broadens the applicable environment of the Iridium SOPs positioning, thereby improving the availability and continuity of its positioning.

Keywords: signals of opportunity positioning; Iridium; weak signal; instantaneous Doppler

1. Introduction The new methods for receiver positioning based on abundant and various signals have emerged in recent years. This new positioning technique is termed opportunistic navigation (OpNav) [1,2] and collaborative opportunistic navigation (COpNav) [3]. The navigation via signals of opportunity (NAVSOP) program made by the UK defense firm BAE Systems in 2012 is the typical system. The US Defense Advanced Research Projects Agency (DARPA) also presents a new program, all source positioning and navigation (ASPN), to research the correlation technique. These systems treat the same signals used by mobile phones, TVs, and other radio systems as the radiation sources instead of navigation satellite signals to realize receiver positioning. It can get rid of dependence on the Global Navigation Satellite System (GNSS), or as a new method for overcoming the situation that GNSS does not work. Space-based low orbit (LEO) signals, as the new SOPs, have some important advantages in terms of more availability and better coverage than for ground-based SOPs. Plentiful non-GNSS satellites are operational today; IRIDIUM [4], GLOBALSATR [5], and [6] are typical representatives. The related institutions plan to launch a large number of satellites [7]. The Iridium SOPs positioning can still provide location services when GNSS does not work due to interference and other effects. It also can be treated as a full standalone backup of the GNSS. The Iridium signals are generally stronger than the GNSS satellite signals. However, it also encounters signal attenuation caused by interference and signal occlusion. In a weak signal environment, the traditional method of positioning based on Iridium satellite SOPs may fail to capture the signals. As a result, the receiver cannot offer a location service since failing to get the positioning observation

Electronics 2020, 9, 37; doi:10.3390/electronics9010037 www.mdpi.com/journal/electronics Electronics 2020, 9, 37 2 of 18 information. This situation limits the field of application of this technology. Therefore, this paper mainly studies the method of positioning using Iridium satellite SOPs in weak signal environment. Before realizing receiver positioning based on Iridium satellite SOPs, we need to measure the positioning observation information, Doppler-shift. Therefore, the difficulty of positioning using Iridium satellite SOPs in weak signal environment lies in accuracy estimation of signal Doppler-shift. The main reason is that Iridium satellite SOPs have a partially known characterization, which means the Doppler-shift estimation in weak signal environment only bases on the limited information. On the other hand, unlike traditional GNSS signals, Iridium satellite transmits discontinuous time-division signals, which will also affect the design of the Doppler-shift estimation in weak signal environment. The early work of our team researches on the concept of positioning based on the Iridium satellite SOPs and the tests and demonstrations of positioning based on Iridium satellite SOPs in open sky were presented [8]. Based on the previous work, this paper mainly studies the Iridium satellite SOPs positioning technology under the condition of weak signal in the occluded environment. In Section2, the Iridium satellite orbit and Iridium signal characteristics are discussed. It can provide a basis for the acquisition of positioning observation information in weak signal environment. In Section3, a new algorithm of quadratic square accumulating instantaneous Doppler estimation (QSA-IDE) is proposed and its mathematical model is given. In Section4, we describe the principle of the positioning using Iridium satellite SOPs in weak environment. Experimental results based on real Iridium signals are described in Section5. Finally, the discussion and conclusions are presented in Sections6 and7.

2. Iridium Satellite Orbit and Signal Characteristics The number of visible satellites for receiver and positioning measurements are related to the constellation distribution (Iridium satellite orbit) and Iridium signal characteristics, respectively. This section mainly analyzes the Iridium constellation structure and the signal characteristics. It can provide the basis for the Iridium satellite SOPs positioning in weak signal environment. The concept of Iridium satellite system is first proposed by Bary Bertiger in 1987. The Iridium system, with its constellation of 66 low Earth orbit (LEO) satellites, is a satellite-based, personal , providing voice and data services to virtually any destination on earth [9]. The generation Iridium satellites are almost out of use, expect two satellites are on standby. Iridium Satellite LLC in 2007 announced to launch IRIDIUM NEXT, a second-generation satellite, consisting of 66 active satellites which are used to take the place of the generation Iridium satellites, with another nine in-orbit spares and six on-ground spares. Today, 75 IRIDIUM NEXT satellites are in-orbit operational in six orbital planes, each with an inclination angle of 86.6 degrees to the equatorial plane. The orbit altitude of 70 satellites is 625 km, while the other five satellite orbit altitudes is 720 km. All the satellites have an orbital period of 97 min. At least one satellite can be seen in low latitudes anytime and anywhere. The Iridium system uses a combination of space division multiple access (SDMA), time division multiple access (TDMA), and frequency division multiple access (FDMA) [10]. The adjacent 12 of the 48 spot beams on each satellite are grouped into a set, to share the total user downlink frequency band based on SDMA and FDMA. For every spot beam, channels are implemented using a TDMA architecture based on time division duplex (TDD) using a time frame. The user uplink and downlink are in different time slots of the same frame of the same TDMA carrier. The frequency accesses are divided into the duplex channel band and the simplex channel band which are used as the traffic channel and signaling channel, respectively. Every time the frame also consists of a simplex part and duplex part. As a result, the simplex signal and duplex signal are in different time slots and different frequency bands. The Iridium frequency allocation and frame structure are shown in Figure1. Electronics 2020, 9, 37 3 of 18 Electronics 2020, 9, x FOR PEER REVIEW 3 of 18

FigureFigure 1. 1. IridiumIridium frequency frequency allocation allocation and and frame frame structure. structure.

TheThe system usesuses L-bandL-band frequencies of of 1616 1616 to to 1626.5 1626.5 MHz MHz for thefor userthe user link. link. The frequencyThe frequency band bandshared shared by duplex by duplex channels channels is from is 1616.0–1626.0 from 1616.0 MHz.–1626.0 The MHz. 10 MHz The band10 MHz is organized band is organized into sub-bands, into sub-bands,each of which each contains of which eight contains frequency eight accesses. frequency Each accesses. sub-band Each occupies sub-band 333.333 occupies kHz (333.3338 * 41.667 kHz kHz (8 , *and 41.667 the kHz, guard and band the isguard 10.17 band kHz). is The10.17 Iridium kHz). The is capable Iridium of is operatingcapable of with operating up to with 30 sub-bands, up to 30 sub-bands,containing acontaining total of 240 a total frequency of 240 access. frequency A 12-frequency access. A 12-frequency (12 * 41.667 kHz,(12 * and41.667 the kHz, work and band the is work31.50 kHz)band accessis 31.50 band kHz) is access reserved band for is the reserved simplex for (ring the alert simplex and messaging)(ring alert and channels. messaging) These channels. channels Theseare located channels in a globallyare located allocated in a globally 500 kHz bandallocated between 500 kHz 1626.0 band and 1626.5between MHz. 1626.0 The and simplex 1626.5 channels MHz. Theof every simplex beam channels have 12 of frequency every beam accesses have and 12 frequency 240 frequency accesses accesses and of240 duplex frequency channels accesses that areof duplexdivided channels into 12 spot that beams are divided equally into [11 ].12 As spot a result, beams every equally spot [11]. beam As has a result, 32 frequency every accesses.spot beam Every has 32spot frequency beam has accesses. 80 duplex Every channels spot beam since everyhas 80 frequency duplex channels access is since with every four duplex frequency frequency access accesses is with fourby TDD. duplex Every frequency satellite canaccesses at most by get TDD. 3840 Every duplex satellite frequency can accesses at most (4.8 get Kbps) 3840 sinceduplex every frequency satellite accesseshas 48 beams. (4.8 Kbps) since every satellite has 48 beams. TheThe TDMA frameframe isis in in total total 90 90 ms ms long. long. It consistsIt consists of a of 20.32 a 20.32 ms downlink ms downlink timeslot timeslot which which shares sharessimplex simplex frequency frequency band, followed band, followed by four 8.28by four ms duplex8.28 ms uplink duplex timeslots uplink timeslots and four duplexand four downlink duplex downlinktimeslots thattimeslots share that duplex share frequency duplex frequency band. There band. are There 2250 symbols are 2250 per symbols TDMA per frame TDMA at a frame channel at aburst channel burst modulation rate of 25 ksps. rate A of 2400 25 bpsksps. tra Affi c2400 channel bps usestraffic one channel uplink anduses one one downlink uplink and timeslot one downlinkper frame [timeslot12]. The per simplex frame frequency [12]. The accesses simplex are fr onlyequency used accesses for downlink are only signals used and for they downlink are the signalsonly frequencies and they are that the may only be frequencies transmitted that during may the be simplex transmitted timeslot. during Four the messaging simplex timeslot. channels Four and messagingone ring alert channels channel and are one available ring alert during channel the simplexare available timeslot. during the simplex timeslot. TheThe simplex simplex signal signal and and duplex duplex signal signal are are both bursts. Each Each burst burst has has an an un-modulated un-modulated tone, tone, uniqueunique word (BPSK)(BPSK) andand informationinformation data data (QPSK) (QPSK) [13 [13].]. The The simplex simplex bursts bursts (The (The ring ring alert alert signal signal and andthe primarythe primary message signal) signal) are always are always transmitted transmitted from Iridium from Iridium satellite satellite and can and be passive can be receivedpassive receivedby the receiver, by the receiver, which means which they means can bethey used can for be Iridiumused for SOPs Iridium positioning. SOPs positioning. Actually, Actually, the IRIDIUM the IRIDIUMNEXT burst NEXT signals burst of signals simplex of channels simplex thatchannels are collected that are bycollected us are fromby us 6.5 are to from 20.32 6.5 ms. to 20.32 ms. 3. The Estimation of Iridium Satellite Signal Doppler-Shift in Weak Signal Environment 3. The Estimation of Iridium Satellite Signal Doppler-Shift in Weak Signal Environment The Doppler-shift measurement is the basis of positioning using Iridium satellite SOPs. A new The Doppler-shift measurement is the basis of positioning using Iridium satellite SOPs. A new method of estimating Iridium satellite SOPs Doppler-shift in weak environment is proposed in this method of estimating Iridium satellite SOPs Doppler-shift in weak environment is proposed in this section. The detail principle of the new method is given, and every part of the new method is introduced section. The detail principle of the new method is given, and every part of the new method is in detail. We first give the principle and the process of the new method. The differences from the introduced in detail. We first give the principle and the process of the new method. The differences from the traditional Iridium Doppler-shift estimation method and the advantage of the new method are also carried out. Then, the mathematic model of the new method is presented.

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Electronicstraditional 2020, 9, Iridiumx FOR PEER Doppler-shift REVIEW estimation method and the advantage of the new method are also4 of 18 carried out. Then, the mathematic model of the new method is presented. 3.1. The Principle of Estimating Iridium Satellite Signal Dopller-Shift in Weak Signal Environment 3.1. The Principle of Estimating Iridium Satellite Signal Dopller-Shift in Weak Signal Environment Considering the Iridium satellite SOPs are non-cooperative and non-navigational radio signals, Considering the Iridium satellite SOPs are non-cooperative and non-navigational radio signals, the the quadratic square accumulating instantaneous Doppler estimation (QSA-IDE) algorithm is quadratic square accumulating instantaneous Doppler estimation (QSA-IDE) algorithm is proposed in proposed in this paper to realize the Doppler-shift accuracy estimation in weak signal environment. this paper to realize the Doppler-shift accuracy estimation in weak signal environment. The algorithm The algorithmsquares the squares signal twice the beforesignal estimatingtwice before Doppler-shift. estimating An Doppler-shift. open-loop measurement An open-loop method measurement is used methodto measure is used Doppler-shiftto measure Doppler-shift in weak signal in environment weak signal since environment the Iridium since signals the are Iridium discontinuous signals are discontinuousbursts. The bursts. QSA-IDE The has QSA-IDE two parts: has Signal two detection parts: Signal and signal detection acquisition. and signal The Iridium acquisition. bursts The Iridiumin the bursts continuously in the continuously received data received are funded data by ar detectione funded part by and detection the start part times and of the burstsstart times are of the burstslocked. are The burstslocked. are The then interceptedbursts are andthen sent inte to thercepted acquisition and processsent to for the Doppler-shift acquisition estimation. process for Doppler-shiftThe principle estimation. of QSA-IDE The is principle shown in Figureof QSA-IDE2. is shown in Figure 2.

FigureFigure 2. 2.PrinciplePrinciple of thethe quadratic quadratic square square accumulating accumulating instantaneous instantaneous Doppler estimation Doppler algorithm. estimation algorithm. The Iridium signals from the are transformed into an intermediate frequency (IF) digital sequenceThe Iridium after processingsignals from by radio the frequencyantenna frontare endtran (RFFE).sformed The into pre-processing an intermediate module firstfrequency divides (IF) the IF data into consecutive multiple data blocks d (i = 1, ... , M). The length of time of d is longer digital sequence after processing by radio frequencyi front end (RFFE). The pre-processingi module than a TDMA frame time. The IF signals in every data block are squared= twice and filtered to remove first divides the IF data into consecutive multiple data blocks dii ( 1,..., M ) . The length of time of the high frequency part. The new data blocks are denoted by si(i = 1, ... , M). si may include the di isquadratic longer than square a IridiumTDMA signals frame and time. the The quadratic IF signals square in noise every signals, data or block only includes are squared the quadratic twice and = filteredsquare to remove noise signals. the high The quadratic frequency square part. Iridium The new signals data remove blocks the are situation denoted of phase by flipsii (1,...,) caused M by . si may theinclude unique the word quadratic (BPSK) andsquare the informationIridium signals (QPSK). and Then, the quadratic the si is sent square into detection noise signals, module or for only detecting whether the Iridium burst is existing or not. includes the quadratic square noise signals. The quadratic square Iridium signals remove the In the detection module, the matched filter is used to judge whether there is a quadratic square situation of phase flip caused by the unique word (BPSK) and the information (QPSK). Then, the s Iridium signal. Once finding the target signal, it enters the capture process. At the same time, the i is sentquadratic into detection square Iridium module signal for detecting is intercepted whether after lockingthe Iridium its start burst and is time, existing and its or time not. stamp and theIn the number detection of si aremodule, marked. theThe matched detection filter threshold is used valueto judge can whether be obtained there from is a the quadratic pure noise square Iridiumsignal signal. in the Once actual finding environment. the target It assumed signal, that it enters total N thedata capture blocks haveprocess. Iridium At signals,the same the time, first the quadraticone and square the last Iridium one are signal block isp andintercepted block q, respectively.after locking These its start Iridium and signalstime, and are denotedits time bystamp r (k = 1, ... , N; N < M). N target signals S = r4(k = 1, ... , N; N < M) are received after finishing and thek number of si are marked. The detectionk k threshold value can be obtained from the pure the above processing. Then, the quadratic square Iridium signals S (k = 1, ... , N; N < M) are sent to noise signal in the actual environment. It assumed that total N k data blocks have Iridium signals, acquisition module. the first one and the last one are block p and block q , respectively. These Iridium signals are = ==4 denoted by rkk ( 1,...,N;N

Electronics 2020, 9, 37 5 of 18

The main work of acquisition module is Doppler-shift estimation. The center frequency of the quadratic square Iridium signals can be obtained by fast Fourier transform (FFT) processing. The Doppler-shift can be directly calculated since the standard frequency is known. However, the Doppler-shift measurement accuracy is affected by the FFT resolution. This process is called Doppler-shift coarse estimation. The maximum likelihood estimator (MLE) algorithm [14] can be used to realize Doppler-shift fine estimation. This needs a receiver to search the target signals in frequency space. Multiplying the incoming signals with the locally generated duplicated signals, the correlation between the duplicated signals and the incoming signals is detected by signal power that Electronics 2020, 9, x FOR PEER REVIEW 8 of 18 is calculated by coherent integration and squaring. If the frequency of the local carrier matches the incoming signal frequency, the output will be significantly greater than if any of these criteria were not obtainedfulfilled. by the During QSA-IDE the search algorithm process, the discussed local carrier ab frequencyove. The parameter two-line can beelement searched set within format the (TLE) providedFFT from resolution NOARD is used or a wideras the frequency Iridium range. sate Ifllite the maximumorbital ephemeris. output power It value consists exceeds of orbital parametersthe acquisitionand time threshold, information. the frequency We use of the the local SG carrierP4 prediction corresponding model to the maximum to realize power the is purpose the of satellite carrierorbit reconstruction frequency estimation [16]. value of the current signal. The Doppler-shift fine estimation can be easily calculated once the center frequency of the quadratic square Iridium signal is searched successfully. NOARDWhen periodically the quadratic updates square the processing Iridium module TLE sets in Figure once3 or is twice removed, every the day. principle The of TLE the data can be receivedtraditional directly Iridium from SOPs the Doppler-shift NORAD estimation website incelestrak.com. open sky comes out.The InIridium this case, satellite only tone position calculatedsignal with in anTLE Iridium data burst is with is used an since error the that unique ca wordn be signalfrom and100 the m information to several signal kilometers. will lead toWhile the correspondingacquisition velocity failure dueerrors to the are phase optimistic, flip. The traditional the value method can ofbe Doppler-shift approximately estimation 3 m/s. cannot The be position errors andused velocity in weak errors signal environment.are rather smaller It can cause in the the radial bursts missingdirection due than to the for interference cross and caused along by direction. signal blockage. The situation that the starting time of the tone signal cannot be precisely locked may After obtaining the Doppler-shift measurements and Iridium orbital, the receiver positioning can be appear when the burst is detected. If it happens, the tone signal may contain a unique word signal achieved(BPSK) by instantaneous and information Doppler signal (QPSK) positioning which can algorithm, affect the correlation and the results position of MLE. accuracy As a result, can the be further improvedtraditional by height method aiding. fails to estimate Doppler-shift.

FigureFigure 3. Basic 3. Basic Iridium Iridium SOPs SOPs positioning positioning principleprinciple in in weak weak signal signal environment. environment.

The new method (QSA-IDE) can overcome the above problems since it squares the Iridium Theburst Iridium twice continuously and the tone signal, transmits unique ring word alert signal, signal and (simplex information 7 channel) signal instead and ofprimary tone are message signal (simplexused simultaneously 11 channel) to to measure the ground. Doppler-shift. The quatemary On the other message hand, the signal signal (simplex power can 3 still channel) be and tertiary messageaccumulated signal in weak (simplex signal environment 4 channel) by are increasing occasionally the coherent transmitted. integration In time this of paper, MLE since the the simplex 7 and simplexwhole 11 Iridium channel burst signals is used. are As aused result, for the receiver QSA-IDE position, algorithm respectively. can measure Doppler-shift in weak signal environment. The Doppler-shift caused by the relative motion between the satellite and the receiver provides the basis for receiver positioning [17]. The instantaneous Doppler positioning uses multiple intersections of equal Doppler cones to obtain a receiver position instead of using integral Doppler-shift measurements of the hyperbolic positioning method. The Doppler-shift is expressed as [18]: rr− ρε=++ku  v  f ρ kuk − k (16) rrku where ρ is the Doppler-shift of satellite k and its unit is m/s. r = []rrr is the receiver k u uuuxyz vvv=− v =[vvv ]T position vector and ksiu denotes the relative velocity vector, si sixyz si si and v =[vvv ]T f u uuuxyz are the satellite and receiver velocity vectors, respectively. u is the receiver clock frequency drift and ε ρ is the Doppler-shift error. The navigation equation of the instantaneous k Doppler positioning for static receiver is presented here directly which is:

T ()rr− v ()−−1 u0 1 Δ vrr11 u0 E 33× 1 ru 3 − x rr− rr1 u0 1 u0 Δ ru =+y d ε (17) Δr T uz ()rr− v ()−−ku0 k Δ vrrkk u0 E33× 1 fu − 3 rr− rrku0 ku0

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3.2. The Mathematical Model of Estimating Iridium Satellite Signal Doppler-Shift in Weak Signal Environment

Let tone signal, unique word signal, and information signal in one burst be denoted by stone, suni, and sd. The corresponding time periods are Ttone, Tuni, Td, respectively t0 is the starting time of the burst. Then, the expression of the burst signal can be written as:   stone(t); t0 t Ttone  ≤ ≤ SItri(t) =  suni(t); Ttone < t Tuni (1)  ≤  s (t); T < t T d uni ≤ d

The signals stone, suni, and sd are needed to be squared twice, respectively before Doppler-shift estimation when we use the QSA-IDE algorithm. This process is easy for tone signal than for the unique word signal and information signal since the tone is without modulation. The expression of sd(t) is: s (t) = √P d (t)cos(2π f t + ϕ ) + √P dq(t) d d i 0 d d · (2) sin(2π f0t + ϕd) + nd(t) where Pd is the signal power, f0 is the carrier frequency, ϕd is the initial phase. di and dq are the binary information code sequences of I and Q arms. nd(t) is the noise signal. We get the quadratic square signal rd(t) by squaring the sd(t) twice, and the rd(t) can be written as:

3 2 1 2 2 r (t) = p p cos(8π f t + 4φ ) + 2p d (t)dq(t) sin(4π f t+ d 2 d − 2 d n 0 d d i 0 2φd) + 2pd √pd[di(t) cos(2π f0t + φd) + dq(t) sin(2π f0t+ 2 o n φ )n (t) + n (t) + 2p d (t)dq(t) sin(4π f t + 2φ ) √p [d (t) d d d d i 0 d d i · 2 o (3) cos(2π f0t + φ ) + dq(t) sin(2π f0t + φ )]n (t) + n (t) + n d d d d √pd[di(t) cos(2π f0t + φd) + dq(t) sin(2π f0t + φd)]nd(t)+ o2 2( ) nd t

We can see that r (t) have four parts, the base band signal is 3 p2, the 4 f IF signal is 1 p2 cos(8π f t + d 2 d 0 − 2 d 0 ) 2 ( ) ( ) ( + ) 4φd , the 2 f0 IF signal is 2pddi t dq t sin 4π f0t 2φd , and the noise signal. The 4 f0 IF signal and 2 f0 IF signal can be obtained, respectively by filtering. However, the di(t)dq(t) in 2 f0 IF signal can cause the phase flip, which means the coherent integration in signal acquisition will be affected. This situation will not happen for 4 f0 IF signal, which means we can use this signal to estimate Doppler-shift. After filtering, we get: 1 m (t) = P2 cos(8π f t + 4ϕ ) + N (t) (4) d −2 d 0 d d where md(t) denotes the 4 f0 IF signal and Nd(t) is the noise. The expression of suni(t) is: p suni(t) = 2Puniduni(t)cos(2π f0t + ϕuni) + nuni(t) (5) where Puni is the signal power, f0 is the carrier frequency, ϕuni is the initial phase. duni(t) is the binary information code (789 hex). nuni(t) is the noise signal. We get the quadratic square signal runi(t) by squaring the suni(t) twice, and the runi(t) can be written as:

r (t) = 3 P2 + 1 P2 cos(8π f t + 4ϕ )+2P2 cos(4π f t+ uni 2 uni 2 uni 0 uni uni · 0 2ϕ ) + (2 √2P d (t)n (t) cos(2π f t + ϕ ) + n2 (t)) uni uni uni uni 0 uni uni · (6) [2P cos(4π f t + 2ϕ ) + P ] + (2 √2P d (t)n (t) uni 0 uni uni uni uni uni · ( + ) + 2 ( ))2 cos 2π f0t ϕuni nuni t

( ) 3 2 We can see that runi t have four parts, the base band signal is 2 Puni, the 4 f0 IF signal is 1 P2 cos(8π f t + 4ϕ ), the 2 f IF signal is 2P2 cos(4π f t + 2ϕ ), and the noise signal. The 4 f IF 2 uni 0 uni 0 uni · 0 uni 0 Electronics 2020, 9, 37 7 of 18

signal and 2 f0 IF signal are both without binary information code sequences, which means they will not cause phase flip in signal acquisition. If we want use both information signal and unique signal to estimate Doppler-shift, their center frequency needs to be the same. As a result, 4 f0 IF signal is used here and the 2 f0 IF signal is removed by filtering. Then, we get:

1 m (t) = P 2 cos(8π f t + 4ϕ ) + N (t) (7) uni 2 uni 0 uni uni where muni(t) denotes the 4 f0 IF signal, and Nuni(t) is the noise. Let mtone(t) denotes the 4 f0 IF signal of the quadratic square tone signal. Then, the quadratic square Iridium burst signal MItri(t) can be written as:   mtone(t); t0 t Ttone  ≤ ≤ MItri(t) =  muni(t); Ttone < t Tuni (8)  ≤  m (t); T < t T d uni ≤ d Let u(t) denotes the local signal, the expression is:

u(t) = exp( j2π 4 f t) (9) − · The signal, after multiplication with the local carrier, assumes the form:

M (t) u(t) = P2 cos(8π f t + 4ϕ ) exp( j2π 4 f t)+ Itri · · 0 uni · − · (10) N(t) exp( j2π 4 f t) · − · In (10), P is the signal power and N(t) is the noise. The high-frequency signal and noise of I and Q arms are removed by integration of the low filter. The expression of the result of the coherent integration can be written as [15]:

 1  a sin (2π fe T ) T 2 coh j[2π f (t + coh )+θ ] r (n) = · · exp e 1 2 e (11) p 1 (2π fe T ) 2 · coh 2 In (11), a is the mean power of the real input signals, t1 denotes the starting time of the coherent integration, fe denotes the difference between real signal frequency and local signal frequency, and θe is the phase difference. The length of the time of the coherent integration is Tcoh = Ttone + Tuni + Td. Expression (11) can also be written as:

Tcoh j[2π fe(t + )+θe] rp(n) = a sin c( fe T ) exp 1 2 (12) · coh The expressions of the output of the coherent integration in I and Q arms are:

Ip(n) = a sin c( fe T ) cos(φe) (13) · coh

Qp(n) = a sin c( fe T ) sin(φe) (14) · coh   Tcoh where φe = 2π fe t1 + 2 + θe is the phase difference. The correlation amplitude between input signal and local duplicated signal can be written as:

q 2 2 E(n) = Ip (n) + Qp (n) = a sin c( fe T ) (15) · coh In (15), we can see that the degree of correlation between real signal and the local signal depend on sin c( fe Tcoh). When Tcoh is constant, the closer the local signal frequency is to the actual signal · frequency, the larger the value of sin c( fe T ) . During the acquisition process, the local signal · coh Electronics 2020, 9, 37 8 of 18 frequency is continuously adjusted and the maximum correlation amplitude is searched to complete the Doppler-shift estimation.

4. Positioning Using Iridium Satellite SOPs in Weak Signal Environment The essential elements of Iridium satellite SOPs positioning are observation information acquisition, satellite orbit calculation, and positioning algorithm. The principle of Iridium SOPs positioning in weak signal environment is presented in Figure3. The solid part denotes the hard platform and the dotted part denotes the software algorithm. A wide-band antenna with a frequency band from 380 to 20 GHz and 5 dB gain connects to a front end (RFFE). There are typically three main modules in the software processing: Doppler-shift estimation, satellite orbit reconstruction, and positioning solution. The Doppler-shift measurements are obtained by the QSA-IDE algorithm discussed above. The two-line element set format (TLE) provided from NOARD is used as the Iridium satellite orbital ephemeris. It consists of orbital parameters and time information. We use the SGP4 prediction model to realize the purpose of satellite orbit reconstruction [16]. NOARD periodically updates the Iridium TLE sets once or twice every day. The TLE data can be received directly from the NORAD website celestrak.com. The Iridium satellite position calculated with TLE data is with an error that can be from 100 m to several kilometers. While the corresponding velocity errors are optimistic, the value can be approximately 3 m/s. The position errors and velocity errors are rather smaller in the radial direction than for cross and along direction. After obtaining the Doppler-shift measurements and Iridium orbital, the receiver positioning can be achieved by instantaneous Doppler positioning algorithm, and the position accuracy can be further improved by height aiding. The Iridium continuously transmits ring alert signal (simplex 7 channel) and primary message signal (simplex 11 channel) to the ground. The quatemary message signal (simplex 3 channel) and tertiary message signal (simplex 4 channel) are occasionally transmitted. In this paper, the simplex 7 and simplex 11 channel signals are used for receiver position, respectively. The Doppler-shift caused by the relative motion between the satellite and the receiver provides the basis for receiver positioning [17]. The instantaneous Doppler positioning uses multiple intersections of equal Doppler cones to obtain a receiver position instead of using integral Doppler-shift measurements of the hyperbolic positioning method. The Doppler-shift is expressed as [18]:

. r r k u . ρk = vk − + fu + ερ (16) · r ru k k k − k . where ρk is the Doppler-shift of satellite k and its unit is m/s. ru = [rux ruy ruz ] is the receiver position T T vector and v = v vu denotes the relative velocity vector, v = [v v v ] and vu = [vu vu vu ] k si − si six siy siz x y z are the satellite and receiver velocity vectors, respectively. fu is the receiver clock frequency drift and ε . is the Doppler-shift error. The navigation equation of the instantaneous Doppler positioning for ρk static receiver is presented here directly which is:

 T  (r1 ru0) v1    v1 (r1 ru0) − E3 3 1  ∆rux  r r 3 r1 ru0    · − k 1− u0k − k − k ×    . .  ∆ruy  d =  . .   + ε (17)  . .  ∆r   T  uz   (rk ru0) vk    vk (rk ru0) − E3 3 1  ∆ fu r r 3 rk ru0 · − k k− u0k − k − k × . . . . T where d denotes the range residual between the Doppler-shift observation vector ρ = [ρ1 ρ2 ρk] ^ ··· . . . . T = [ˆ ˆ ˆ ] u = [rT ] and estimation vector ρ ρ1 ρ2 ρk . 0 u0 fu0 is the prior information of the state of receiver. ··· T E3 3 is the unit , ∆u = [∆rux ∆ruy ∆ruz ∆ fu] is the vector update of receiver state, and ε denotes × the measurement errors and any approximation errors from the linearization. Electronics 2020, 9, x FOR PEER REVIEW 9 of 18 where d denotes the delta range residual between the Doppler-shift observation vector ρ= []ρρ ρT ρˆ = []ρρˆ ˆ  ρˆ T ur=[T f ] 12 k and estimation vector 12 k . 0u00 u is the prior information T E × Δ=ΔΔurrr[] Δ Δf of the state of receiver. 33 is the unit matrix, uuuuxyz is the vector update of receiver state, and ε denotes the measurement errors and any approximation errors from the linearization. Generally, the number of the Iridium satellite that can be seen simultaneously in weak signal environment is less than four in a low latitude area. When the number of visible satellites is insufficient, a multi-epoch positioning method can be used for static receiver [19]. The receiver continuously collects signals in a period of time, and the data is centralized processing, which means the receiver position is calculated with many Doppler-shift measurements of different time of different satellites.Electronics 2020, 9, 37 9 of 18

5. Experimental ResultsGenerally, the number of the Iridium satellite that can be seen simultaneously in weak signal environment is less than four in a low latitude area. When the number of visible satellites is insufficient, In this section,a multi-epoch we present positioning some method experimental can be used for results static receiver based [19]. on The real receiver Iridium continuously data collected in the weak signal environment.collects signals The in a period IRID ofIUM time, and NEXT the data data is centralized are collected processing, whichby a meansstatic the receiver receiver under a dense position is calculated with many Doppler-shift measurements of different time of different satellites. forest of BUAA university for 30 min, as shown in Figure 4. The Iridium signals are sent into the 5. Experimental Results software in PC for analyzing and positioning after down-conversion and conversion from analog to In this section, we present some experimental results based on real Iridium data collected in the digital signals byweak a signal RF environment. front end The IRIDIUMand NEXTan Ir dataidium are collected antenna. by a static Compared receiver under a densewith the open sky environment, theforest average of BUAA power university loss for 30 of min, the as shownIridium in Figure signal4. The Iridiumin this signals case are reaches sent into the 8 dB. The IF data software in PC for analyzing and positioning after down-conversion and conversion from analog to collector receivesdigital the signalsraw data by a RF with front end a sampling and an Iridium rate antenna. of Compared112 MHz with at the a open RF skycenter environment, frequency of 1626.25 MHz, and the centerthe average frequency power loss of of the the Iridium recorded signal indata this case is 28.25 reaches 8MHz. dB. The The IF data received collector receives signals are from two the raw data with a sampling rate of 112 MHz at a RF center frequency of 1626.25 MHz, and the downlink-only channelscenter frequency which of the recordedare ring data isalert 28.25 MHz.signal The received(7 channel) signals are and from twoprimary downlink-only message signal (11 channel). Two channelchannels which signals are ring are alert us signaled (7for channel) positioning, and primary message respectively. signal (11 channel). The Tworesults channel of Iridium signal signals are used for positioning, respectively. The results of Iridium signal Doppler-shift estimation Doppler-shift estimationand Iridium SOPsand positioningIridium are SOPs presented, posi astioning described below.are presented, as described below.

Figure 4. IRIDIUM NEXT data collection in weak signal environment. Figure 4. IRIDIUM NEXT data collection in weak signal environment. 5.1. Estimating Doppler-Shift of Iridium Satellite Signal in Weak Signal Environment In this section, we will show the Doppler-shift estimation results of the real IRIDIUM NEXT 5.1. Estimating Doppler-Shiftsignals by the new of Iridium QSA-IDE algorithm.Satellite TheSignal Iridium in 7 Weak channel Signal simplex Environment signal, ring alert, can be obtained after filtering the IF data from RFFN. The signal standard frequency is 1626.270833 MHz In this section,and thewe corresponding will show IF is the 28.270833 Doppler-shift MHz. We first give estimation the Iridium signal results time-domain of the plot, real then IRIDIUM NEXT signals by the newDoppler-shift QSA-IDE estimation algorithm. results are carried The out. channel simplex signal, ring alert, can be The Iridium signals are the discontinuous burst signals. The time length of the most bursts is obtained after filteringabout 6.5 ms,the and IF the data maximum from time RFFN. length is The 20.32 ms.signal The timestandard domain plot frequency of a 9 ms collected is 1626.270833 MHz and the correspondingsignal after IF filtering is 28.270833 (the filter bandwidth MHz. isWe corresponding first give to the the Iridium Iridium ring alert signal signal bandwidth) time-domain plot, then is shown in Figure5a. An Iridium burst signal exists in this 9 ms data. The first 2 ms data is the Doppler-shift estimationpure noise signal, results then theare following carried 6.6 msout. data is the Iridium burst signal, the last 0.4 ms data is the The Iridiumpure signals noise signal. are Thethe amplitude discontinuous of the Iridium burst signal is sign not significantlyals. The higher time than length for noise of since the most bursts is about 6.5 ms, and the maximum time length is 20.32 ms. The time domain plot of a 9 ms collected signal after filtering (the filter bandwidth is corresponding to the Iridium ring alert signal bandwidth) is shown in Figure 5a. An Iridium burst signal exists in this 9 ms data. The first 2 ms data is the pure noise signal, then the following 6.6 ms data is the Iridium burst signal, the last 0.4 ms data is the pure noise signal. The amplitude of the Iridium signal is not significantly higher than for noise since the power of the Iridium signal is decreased due to the occlusion environment. The

Electronics 2020, 9, 37 10 of 18

Electronics 2020, 9, x FOR PEER REVIEW 10 of 18 the power of the Iridium signal is decreased due to the occlusion environment. The Doppler-shift of Doppler-shift of this Iridium signal cannot be obtained by the traditional Doppler-shift estimation this Iridium signal cannot be obtained by the traditional Doppler-shift estimation method since the method since the signal fails to detect, even the tone signal of the Iridium signal that is used by signal fails to detect, even the tone signal of the Iridium signal that is used by traditional Doppler-shift traditional Doppler-shift estimation method cannot be correctly locked. As a result, the estimation method cannot be correctly locked. As a result, the Doppler-shift cannot be estimated Doppler-shift cannot be estimated by the traditional method in weak signal environment. However, by the traditional method in weak signal environment. However, Doppler-shift can be estimated by Doppler-shift can be estimated by the QSA-IDE algorithm proposed above. The first step of the new the QSA-IDE algorithm proposed above. The first step of the new method is the quadratic square method is the quadratic square processing, this can be finished by Equations (1)–(7). Squaring this 9 processing, this can be finished by Equations (1)–(7). Squaring this 9 ms data twice, that is, to multiply ms data twice, that is, to multiply it by itself three times. The time domain plot of the quadratic it by itself three times. The time domain plot of the quadratic square data after filtering is shown square data after filtering is shown in Figure 5b. It can be seen that the power of the quadratic in Figure5b. It can be seen that the power of the quadratic square Iridium signal is stronger than square Iridium signal is stronger than for noise signal power. The signal-to-noise ratio is very for noise signal power. The signal-to-noise ratio is very optimistic after quadratic square processing. optimistic after quadratic square processing. The quadratic square Iridium signal near the baseband The quadratic square Iridium signal near the baseband after filtering can be used for Doppler-shift after filtering can be used for Doppler-shift estimation once it was detected by the matched filter. estimation once it was detected by the matched filter. The Doppler-shift estimation result is shown in The Doppler-shift estimation result is shown in the following. the following.

20 40

15 30

10 20 Amplitude(dB) Amplitude(dB) 5 10

0 0 0 2 4 6 8 0 2 4 6 8 Tmie(s) -3 Time(s) -3 x 10 x 10 (a) (b)

FigureFigure 5. 5.Magnitude Magnitude of of collected collected 9 ms 9 ms data: data: (a) Magnitude(a) Magnitude of the of collectedthe collected data data after after filtering filtering with thewith Iridiumthe Iridium ring alert ring signal alert frequencysignal frequency band; ( bband;) magnitude (b) magnitude of collected of collected data after data square after quadratic square quadratic square processingsquare processing and filtering and with filtering the Iridiumwith the ring Iridium alert ring signal alert frequency signal frequency band. band.

AfterAfter detecting detecting the the quadratic quadratic square square Iridium Iridium signal signal and and locking locking the the starting starting time, time, the the quadratic quadratic squaresquare Iridium Iridium signal signal is is intercepted intercepted and and sent sent into into the the FFT FFT process process module. module. The The FFT FFT results results of of the the quadraticquadratic square square signal signal are are shown shown in in Figure Figure6. The6. Th centere center frequency frequency of of the the quadratic quadratic square square Iridium Iridium signalsignal is is about about 1,192,618.629174 1,192,618.629174 Hz. Hz. With With the the help help of of the the standard standard frequency frequency of of ring ring alert, alert, we we can can getget the the Doppler-shift Doppler-shift coarse coarse estimation. estimation. However, However, the the Doppler-shift Doppler-shift fine fine estimation estimation is is necessary necessary sincesince the the error error of of the the Doppler-shift Doppler-shift coarse coarse estimation estimation caused caused by by the the FFT FFT resolution resolution is is insupportable. insupportable. GeneratingGenerating a a local local carrier carrier based based on on the the FFT FFT results results according according to to Equation Equation (9). (9). Let Let it it correlate correlate with with thethe quadratic quadratic square square signal signal according according to to Equation Equation (10). (10). The The fine fine center center frequency frequency of of the the quadratic quadratic squaresquare Iridium Iridium signal signal can can be receivedbe received by usingby using the MLEthe MLE discussed discussed above. above. The correlationThe correlation results results can becan obtained be obtained by Equations by Equations (11)–(15), (11)–(15), and are and shown are shown in Figure in Figure7. The 7. frequency The frequency corresponding corresponding to the to correlationthe correlation peak is peak 1,192,697.914173989 is 1,192,697.914173989 Hz, which Hz, means which the means fine frequency the fine frequency estimation estimation of the quadratic of the squarequadratic Iridium square signal Iridium is obtained. signal is The obtained. real quadratic The real square quadratic signal square of ring signal alert of near ring the alert baseband near the isbaseband 1,083,332 is Hz. 1,083,332 Then, the Hz. Doppler-shift Then, the Doppler-shift of this ring of alert this burst ring signalalert burst is 27.34147854349727 signal is 27.34147854349727 Hz after simpleHz after numerical simple numerical calculation. calculation.

Electronics 2020, 9, 37 11 of 18 ElectronicsElectronics 2020 2020, ,9, 9, x x FOR FOR PEER PEER REVIEW REVIEW 1111 of of 18 18

88 xx 1010

88

66

44 FFT value FFT value

22

00 1.151.15 1.21.2 1.251.25 FrequencyFrequency (Hz)(Hz) 66 xx 1010 FigureFigureFigure 6. 6. 6.FFT FFT FFT resultsresults results ofof of thethe the quadraticquadratic quadratic squaresquare square IRIDIUM IRIDIUM IRIDIUM ring ring ring alert alert alert signal. signal. signal.

1212 xx 1010 2.52.5

22

1.51.5

11 Correlation value Correlation value 0.50.5

00 1.19221.1922 1.19241.1924 1.19261.1926 1.19281.1928 1.1931.193 FrequencyFrequency （ （HzHz）） 66 xx 1010 FigureFigureFigure 7. 7. 7.Correlation Correlation Correlation resultsresults results betweenbetween between local lo localcal carrier carrier carrier and and and real real real signal. signal. signal. The discussion above gives the detail of the Iridium weak signal Doppler-shift estimation by the TheThe discussiondiscussion aboveabove givesgives thethe detaildetail ofof thethe IridIridiumium weakweak signalsignal DopplerDoppler-shift-shift estimationestimation byby new QSA-IDE algorithm and shows that QSA-IDE algorithm can effectively estimate Doppler-shift in thethe newnew QSA-IDEQSA-IDE algorithmalgorithm andand showsshows thatthat QSA-IDEQSA-IDE algorithmalgorithm cancan effectivelyeffectively estimateestimate weak signal environment. In the collected 30 min IRIDIUM NEXT data, most Iridium signal powers are Doppler-shiftDoppler-shift inin weakweak signalsignal environment.environment. InIn thethe collectedcollected 3030 minmin IRIDIUMIRIDIUM NEXTNEXT data,data, mostmost close to the power of the Iridium signal in Figure5a, even the power is lower for it. The Doppler-shift IridiumIridium signalsignal powerspowers areare closeclose toto thethe powerpower ofof ththee IridiumIridium signalsignal inin FigureFigure 5a,5a, eveneven thethe powerpower isis curves of the ring alert signal and primer message signal corresponding to the collected 30 min data lowerlower forfor it.it. TheThe Doppler-shiftDoppler-shift curvescurves ofof thethe ringring alertalert signalsignal andand primerprimer messagemessage signalsignal obtained by QSA-IDE algorithm and the results of positioning using the Iridium satellite SOPs in weak correspondingcorresponding toto thethe collectedcollected 3030 minmin datadata obtaobtainedined byby QSA-IDEQSA-IDE algorithmalgorithm andand thethe resultsresults ofof signal environment are shown in the next section. positioningpositioning usingusing thethe IridiumIridium satellitesatellite SOPsSOPs inin weakweak signalsignal environmentenvironment areare shownshown inin thethe nextnext section. 5.2.section. Positioning Based on Iridium Satellite SOPs in Weak Signal Environment

5.2.5.2. PositioningIn Positioning this section, Based Based weon on Iridium realizeIridium Sate theSatellitellite receiver SOPs SOPs positioningin in Weak Weak Signal Signal based Environment Environment on real collected IRIDIUM NEXT. The IRIDIUM NEXT signal Doppler-shift estimation results are given, then the positioning results InIn this this section, section, we we realize realize the the receiver receiver positioning positioning based based on on real real collected collected IRIDIUM IRIDIUM NEXT. NEXT. The The based on IRIDIUM NEXT SOPs in weak signal environment is carried out. IRIDIUMIRIDIUM NEXT NEXT signal signal Doppler-shift Doppler-shift estimation estimation results results are are given, given, then then the the positioning positioning results results based based The entire collected IRDIUM NEXT data (30 min) are divided into 5000 continuous data blocks onon IRIDIUM IRIDIUM NEXT NEXT SOPs SOPs in in weak weak sign signalal environment environment is is carried carried out. out. (the time length of every data block is 360 ms), and the Doppler-shift will be estimated if the data block TheThe entire entire collected collected IRDIUM IRDIUM NEXT NEXT data data (30 (30 min) min) are are divided divided into into 5000 5000 continuous continuous data data blocks blocks contains the Iridium burst. The Doppler-shift estimation results obtained by the traditional method (the(the timetime lengthlength ofof everyevery datadata blockblock isis 360360 ms),ms), andand thethe Doppler-shiftDoppler-shift willwill bebe estimatedestimated ifif thethe datadata are shown in Figure8a,b. The Doppler-shift curves of the ring alert signal (downlink-only 7 channel) blockblock containscontains thethe IridiumIridium burst.burst. TheThe Doppler-shiftDoppler-shift estimationestimation resultsresults obtainedobtained byby thethe traditionaltraditional methodmethod are are shown shown in in Figure Figure 8a,b. 8a,b. The The Doppler-shift Doppler-shift curves curves of of the the ring ring alert alert signal signal (downlink-only (downlink-only 7 7

Electronics 2020, 9, x FOR PEER REVIEW 12 of 18

channel) is shown in the left plot and the Doppler-shift curves of the primary message signal Electronics(downlink-only2020, 9, 37 11 channel) is shown in the right plot. The x-axis is the data block number and12 of the 18 y-axis is the Doppler-shift (the unit is Hz). Every circle in the plot denotes the Doppler estimation result from the corresponding data block. Generally, the Doppler-shift curve of the satellite is a kid isof shown S-shape in curve the left and plot the and different the Doppler-shift S-shape curves curves be oflong the to primary a different message satellite, signal the (downlink-only Doppler value 11close channel) to zero is means shown the in satellite the right is plot.located The near x-axis the istop the of datathe receiver, block number and the and Doppler-shift the y-axis isvalue the Doppler-shiftclose to dozens (the of unit kHz is Hz).means Every the circle elevation in the of plot th denotese satellite the is Doppler low. We estimation can see resultthat only from two the correspondingIRIDIUM NEXT data satellite block. signal Generally, Doppler-shift the Doppler-shift estimation curve results of the can satellite be obtained is a kid by of S-shapethe traditional curve andmethod, the di whichfferent means S-shape in curvesthis case belong only totwo a disatellitesfferent satellite, can be seen the Dopplerby the receiver. value close In this to zero case, means when thethe satellitetwo IRIDIUM is located NEXT near thesatellites top of theare receiver, near the and top the of Doppler-shift the receiver, value the closeDoppler-shift to dozens ofcan kHz be meansestimated the elevationby the traditional of the satellite method is since low. Wethe cansignal see is that strong only enough. two IRIDIUM However, NEXT the satellitenumbersignal of the Doppler-shiftDoppler-shift estimationestimation results results can is bevery obtained small, bywhich the traditionalmeans only method, several which strong means signals in this(average case onlypower two is satellitesabout 4 dB can higher be seen than by the for receiver. noise) can In thisbe used case, by when the thetraditional two IRIDIUM method. NEXT Most satellites signals areare nearweak the due top to ofthe the occlusion receiver, environment the Doppler-shift and fail can to beestimate estimated Doppler-shift by the traditional by the traditional method since method. the signalIn is this strong case, enough. when the However, static receiver the number position of the is calculated Doppler-shift by multi-epoch estimation resultspositioning is very method, small, whichthe geometric means only dilution several of strong precision signals of (averagethe instantaneous power is aboutDoppler 4 dB positioning higher than algorithm for noise) is can very be usednegative by the since traditional the satellites method. are in Most the signalssame orbi aret weakand few due Doppler-shift to the occlusion measurements environment are and obtained. fail to estimateAs a result, Doppler-shift receiver positioning by the traditional cannot be method. achieved since the algorithm does not converge.

4 4 x 10 x 10 4 4

2 2

0 0

-2 -2 Doppler frequency(Hz) Doppler Doppler frequency(Hz) -4 -4 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 Data block(0.36s) Data block(0.36s) (a) (b)

FigureFigure 8.8. Doppler-shiftDoppler-shift estimationestimation resultsresults ofof thethe IRIDIUMIRIDIUM NEXTNEXT signalssignals obtainedobtained byby thethe traditionaltraditional method:method: ((aa)) IridiumIridium ringring alertalert signalsignal Doppler-shiftDoppler-shift estimationestimation results;results; ((bb)) IridiumIridium primaryprimary messagemessage signalsignal Doppler-shiftDoppler-shift estimation estimation results. results.

InThe this QSA-IDE case, when algorithm the static can receiver estimate position the IRIDIUM is calculated NEXT by multi-epochsignal Doppler-shift positioning in method,weak signal the geometricenvironment, dilution as shown of precision in Figure of the9a,b. instantaneous The meaning Doppler of the x-axis positioning and y-axis algorithm in Figures is very 8 and negative 9 are sincethe same. the satellites The Doppler-shift are in the same curves orbit andof fewthe Doppler-shiftring alert signal measurements is shown are inobtained. Figure 9a As and a result, the receiverDoppler-shift positioning curves cannot of the be primary achieved message since the signal algorithm is shown does in not Figure converge. 9b. We can see that four IRIDIUMThe QSA-IDE NEXT satellites algorithm can can be estimateseen in this the IRIDIUMcase, and NEXTboth ring signal alert Doppler-shift signal Doppler-shift in weak signalcurves environment,and primary asmessage shown insignal Figure Doppler-shift9a,b. The meaning curves of theare x-axismore andoptimistic y-axis inthan Figures for8 theand 9traditional are the same.method. The The Doppler-shift Doppler curves curves ofin theFigure ring alert9a,b signalhave exactly is shown the in Figuresame 9profilea and thesince Doppler-shift the signals curvescorresponding of the primary to every message pair of curves signal is belong shown to in the Figure same9b. satellites. We can seeThethat new four QSA-IDE IRIDIUM method NEXT not satellitesonly can can see be more seen inIridium this case, satellites and both but ring also alert significantly signal Doppler-shift increases curves the visible and primary times messageof every signalsatellite. Doppler-shift The low elevation curves are satellite more optimistic signal Doppler-shift than for the is traditional also estimated method. successfully. The Doppler The curves first insatellite Figure just9a,b begins have exactly to be seen the same at low profile elevation. since theThese signals four correspondingsatellites are located to every at pairthe same of curves orbit belongsince the to theDoppler-shift same satellites. curves The of all new these QSA-IDE four sa methodtellites have not onlythe same can see shape. more Although Iridium satellitesonly one butsatellite also significantlycan be viewed increases simultaneously the visible times under of everythe occlusion satellite. Theenvironment, low elevation the satelliteDoppler-shift signal Doppler-shiftmeasurements is of also these estimated satellites successfully. are enough The for first static satellite receiver just begins positioning to be seen by atthe low multi-epoch elevation. Thesepositioning four satellites method. are located at the same orbit since the Doppler-shift curves of all these four satellites have the same shape. Although only one satellite can be viewed simultaneously under the occlusion environment, the Doppler-shift measurements of these satellites are enough for static receiver positioning by the multi-epoch positioning method. Electronics 2020, 9, 37 13 of 18 ElectronicsElectronics 2020 2020, ,9, 9, x x FOR FOR PEER PEER REVIEW REVIEW 1313 of of 18 18

4 4 x 104 4 x 10 xx 10 10 4 4 44

22 22

00 00

-2-2 -2-2 Doppler frequency (Hz) frequency Doppler Doppler frequency (Hz) frequency Doppler Doppler frequency (Hz) frequency Doppler Doppler frequency Doppler (Hz) -4-4 -4-4 0 1000 2000 3000 4000 5000 00 10001000 20002000 30003000 40004000 50005000 0 1000 2000 3000 4000 5000 Data block (0.36s) Data block (0.36s) Data block (0.36s) Data block (0.36s) ((aa)) ((bb))

FigureFigure 9. 9.9. Doppler-shift DopplerDoppler-shift-shift estimation estimationestimation results resultsresults of the ofof IRIDIUM thethe IRIDIUMIRIDIUM NEXT NEXTNEXT signals signalssignals obtained obtainedobtained by the new byby the method:the newnew (methodamethod:) Iridium: ( (aa)) ringIridium Iridium alert rringing signal aalertlert Doppler-shift signalsignal DopplerDoppl estimationer-shift-shift estimationestimation results; results (results;b) Iridium; ( (bb)) Iridium Iridium primary pprimaryrimary message mmessageessage signal Doppler-shiftsignalsignal Doppler Doppler-shift estimation-shift estimation estimation results. results results..

TheseTThesehese four fourfour IRIDIUM IRIDIUMIRIDIUM NEXT NEXTNEXT satellites satellitessatellites are simulated areare simulatedsimula withted the withwith satellite thethe s toolsatelliteatellite kits (STK).ttoolool kkits Theits (STK)(STK). simulation. TheThe timesimulationsimulation is in accordance timetime isis inin accordanceaccordance with the time withwith of thethe the timetime real ofof IRIDIUM thethe realreal IRIDIUMIRIDIUM NEXT collected. NEXTNEXT collected.co Thellected. simulation TThehe simulationsimulation results correspondingresultsresults correspondingcorresponding to the starting toto thethe startingstarti timeng of timetime the real ofof thethe IRIDIUM realreal IRIDIUMIRIDIUM NEXT NEXT collectedNEXT colcollectedlected are shown areare shownshown in Figure inin Figure Figure10a,b. The10a,10a,b.b. red TheThe point redred denotes pointpoint denotesdenotes the receiver thethe receiver locationreceiver location andlocation the yellowandand thethe point yellowyellow denotes pointpoint the denotesdenotes satellite thethe locations. satellitesatellite Thelocalocations. satellitestions. TheThe are satellitessatellites IRIDIUM areare 41918U, IRIDIUMIRIDIUM IRIDIUM 41918U,41918U, 41919U, IRIDIUMIRIDIUM IRIDIUM 41919U,41919U, 41917U, IRIDIUMIRIDIUM and IRIDIUM 41917U41917U,, 43479U. andand IRIDIUMIRIDIUM We can see43479U.43479U. that the WeWe first cancan satellite, seesee thatthat 41918U,thethe firstfirst justsatellite,satellite, comes 41918U,41918U, into view justjust at comescomes a low into elevationinto viewview location, atat aa lowlow thenelevationelevation following locationlocation, the, otherthenthen following threefollowing Iridium thethe satellites.otherother threethree These IridiumIridium four satellites. satellitessatellites. are TThesehese located fourfour at satellitessatellites the same areare orbit locatedlocated and the atat the correspondingthe samesame orbitorbit sub-tracksandand thethe correspondingcorresponding are near the receiver. subsub-tracks-tracks The areare conclusion nearnear thethe is receiver.receiver. in accordance TheThe conclusion withconclusion the analysis isis inin accordanceaccordance results from withwith the real thethe Doppler-shiftanalysisanalysis resultsresults curves fromfrom discussed thethe realreal DopplerDoppler-shift above. We-shift give curvescurves the sky discusseddiscussed plot by taking above.above. the WWee first givegive IRIDIUM thethe skysky NEXTplotplot byby satellite takingtaking forthethe example, firsfirstt IRIDIUMIRIDIUM as shown NEXTNEXT in Figure satellitesatellite 11. for Thefor example,example, red point as denotesas shownshown the inin Iridium FigureFigure satellite 11.11. TThehe position redred pointpoint corresponding denotesdenotes thethe toIridiumIridium the starting satellitesatellite time positionposition of the real correspondingcorresponding Iridium data toto collected thethe startingstar andting the timetime receiver ofof thethe locates realreal IridiumIridium at the centraldatadata collectedcollected of the circle. andand Inthethe this receiverreceiver case, although locateslocates atat the thethe receiver centralcentral isofof located thethe circlecircle. at. an InIn occlusion thisthis case,case, environment, aalthoughlthough thethe wereceiverreceiver can still isis locatedlocated estimate atat the aann Iridiumocclusionocclusion Doppler-shift. environment,environment, we we can can still still estimateestimate the the Iridium Iridium Doppler Doppler-shift.-shift.

(a) (b) (a) (b) Figure 10. SimulationSimulation results results of ofthe the four four visible visible IRIDIUM IRIDIUM NEXT NEXT satellites satellites based based on onSTK STK:: (a) Figure 10. Simulation results of the four visible IRIDIUM NEXT satellites based on STK: (a) (Threea) Three-dimensional-dimensional (3D) (3D) graphics graphics of the of simulation the simulation result result;; (b) two (b-)dimensional two-dimensional (2D) g (2D)raphics graphics of the Three-dimensional (3D) graphics of the simulation result; (b) two-dimensional (2D) graphics of the ofsimulation the simulation result. result. simulation result.

Electronics 2020, 9, 37 14 of 18 Electronics 2020, 9, x FOR PEER REVIEW 14 of 18

FigureFigure 11.11. SkySky plotplot ofof thethe firstfirst visiblevisible IRIDIUMIRIDIUM NEXTNEXT satellite.satellite.

AfterAfter obtaining the the Doppler-shift Doppler-shift measurements, measurements, we we can can realize realize the thereceiver receiver positioning. positioning. The TheIRIDIUM IRIDIUM NEXT NEXT TLE TLE data data downloaded downloaded from from the the NOARD NOARD web web are are obtained obtained as as the satellitesatellite ephemeridesephemerides andand thethe orbitalorbital predictionprediction modelmodel isis usedused toto calculatecalculate thethe IridiumIridium satellitesatellite positionposition andand velocity.velocity. TheThe DopplerDoppler positioningpositioning andand heightheight aidingaiding areare usedused forfor receiverreceiver positionposition calculation.calculation. ForFor thethe staticstatic receiver,receiver, thethe multi-epochmulti-epoch positioningpositioning methodmethod isis usedused here.here. WeWe useuse totaltotal 2525 Doppler-shiftDoppler-shift measurementsmeasurements toto form form the the positioning positioning solution solution equations equations and theand least the squares least squares (LS) is used(LS) tois calculateused to thecalculate receiver the position. receiver These position. 25 measurements These 25 measuremen come fromts four come diff erentfrom satellites.four different As a result,satellites. for everyAs a satellite,result, for the every measurements satellite, the corresponding measurements to corresponding different moments to different are used moments together. are used together. TheThe receiverreceiver solutionssolutions calculatedcalculated withwith didifferenfferentt Doppler-shiftDoppler-shift measurementmeasurement combinationscombinations areare didifferent.fferent. TheThe Doppler-shift Doppler-shift measurement measurement accuracy accura correspondingcy corresponding to diff erentto different satellites satellites and different and momentsdifferent aremoments different. are Here,different. the positioning Here, the positioning results with diresultsfferent with Doppler different measurement Doppler measurement combinations arecombinations shown. Every are shown. combination Every hascombination 25 Doppler has measurements 25 Doppler measurements from four satellites, from four and satellites, the receiver and positionthe receiver calculations position are calculations run for a total are of run 800 for times. a total The positioningof 800 times. error The statistic positioning results error with thestatistic ring alertresults signal with are the carried ring alert out first.signal The are mean carried error out and first. root The mean mean square error (RMS) and root are calculated,mean square as shown(RMS) inare Table calculated,1. as shown in Table 1. Table 1. Error statistic results of positioning with the ring alert signal in weak signal environment. Table 1. Error statistic results of positioning with the ring alert signal in weak signal environment. Parameters East-Error/m North-Error/m Up-Error/m Parameters East-Error/m North-Error/m Up-Error/m Mean value 147 162 58 Mean value 147 −−162 58 RMS value 371 149 161 RMS value 371 149 161

ItIt cancan bebe seenseen thatthat comparedcompared withwith thethe north-directionnorth-direction andand thethe up-direction,up-direction, thethe receiverreceiver hashas aa largerlarger positioningpositioning error error in in the the east-direction. east-direction. The The east-direction east-direction average average position position error error reaches reaches 147 147 m, andm, and the errorthe error is with is largewith fluctuations.large fluctuations. The mean The value mean of up-directionvalue of up-direction position error position is optimistic, error is however,optimistic, the however, fluctuation the rangefluctuation is about range 10 m is more about than 10 m the more north-error. than the The north-error. 3D position The error 3D position RMS in thiserror case RMS is aboutin this 400case m. is Theabout statistical 400 m. The results statistical of height results aiding of areheight shown aiding in Tableare shown2. in Table 2.

TableTable 2.2. Error statistic results of positioningpositioning with the ringring alertalert signalsignal andand heightheight aidingaiding inin weakweak signalsignal environment.environment.

ParametersParameters East-Error/m East-Error/m North-Error/m North-Error/m MeanMean value value 21 21 −108108 − RMSRMS value value 144 144 137 137

The positioning performance can be improved with height aiding, especially in the east-direction. The position error mean in the east-direction can be 21 m. However, the fluctuation range of position error in the east-direction is still larger than for north-direction. This is caused by

Electronics 2020, 9, 37 15 of 18

The positioning performance can be improved with height aiding, especially in the east-direction. The position error mean in the east-direction can be 21 m. However, the fluctuation range of position error in the east-direction is still larger than for north-direction. This is caused by the special IRIDIUM orbital characteristic. As a result, the 2D position error RMS in this case is 198 m. The positioning results presented above are based on the ring alert signal. Then, the receiver position can still be obtained after performing the same step for the primer message signal. The statistical positioning results of height aiding are shown in Table3.

Table 3. Error statistic results of positioning with the primer message signal and height aiding in weak signal environment.

Parameters East-Error/m North-Error/m Mean value 30 113 − − RMS value 121 110

The 2D position error RMS in this case is 163 m. It can be seen that the positioning error mean value of north-direction in Table3 is close to the corresponding error mean in Table2. However, the error mean value of north-direction in Tables2 and3 is di fferent. On the other hand, the positioning error RMS values calculated with the primer message signal are more optimistic than for the ring alert signal. This is because the power of the ring alert signal is generally stronger than for the primer message signal. As a result, the Doppler-shift measurement accuracy of the primer message signal is better than for the ring alert signal, and the fluctuation of positioning error is smaller. Considering the Doppler-shift measurement accuracy for different satellites and different moments is different, the Kalman filtering (KF) is used to process the least squares (LS) solutions from different Doppler measurement combinations. As a result, the position estimations calculated with the two channel signals are both about 110 m away from the real location. The positioning errors in east-west direction are more optimistic than for south-north direction in two cases. The common features of positioning error are caused by the satellite orbital error.

6. Discussion We introduce the technique of receiver positioning based on Iridium SOPs in weak signal environment in this paper. Since its point is the Iridium SOPs Doppler-shift estimation in weak signal environment, we present a new method, termed QSA-IDE algorithm, to obtain Doppler-shift after analyzing the Iridium orbital and signal characteristics, and we show the principle and mathematical model of the QSA-IDE algorithm. The concept and principle of Iridium SOPs positioning in weak signal environment also appeared. Finally, we show the test results using the real collected IRIDIUM NEXT data, and the corresponding result analysis. The OpNav and COpNav have emerged for many years. Using the Iridium satellite to offer location service is very popular in recent years. The Iridium satellite LLC, in 2016, announced that the service termed satellite time and location (STL) based on the Iridium satellite network can provide solutions for time and location. It can aid GPS or replace GPS. Recently, the scholar from Saint Petersburg State University also conducted the research about Iridium Next LEO satellites as an Alternative PNT in GNSS denied environment. These techniques treat the Iridium satellite signals as the cooperation signals instead of SOPs. Many scholars also study the technique of Iridium assisted GNSS, such as improve the GNSS satellite geometry distribution, decrease the time of integer ambiguity solution of the GNSS carrier phase positioning. Our work about Iridium satellite signal positioning treat the Iridium signal as the SOPs and realize positioning with the Iridium satellites alone. Our early work studied the concept of Iridium satellite SOPs positioning in open sky environment. We show the research result of Iridium satellite SOPs positioning in weak signal environment in this paper based on the early work. We show the test results based on real data. The Doppler-shift estimation results suggest the new QSA-IDE algorithm can effectively measure Iridium SOPs Doppler-shift in weak Electronics 2020, 9, 37 16 of 18 signal environment. The positioning results show, in weak signal environment, that the receiver 2D position accuracy can achieve between 100 and 200 m. The positioning accuracy is reasonable since many error influences are not removed, such as satellite orbital information is calculated with TLE data. Even so, we still realize the positioning under the occlusion environment using Iridium weak SOPs. Our work in this paper also has shortcomings. The positioning accuracy cannot match GPS. Treating the Iridium signals as the SOPs, the result is that only partially known characterizations, such as lack of satellite ephemeris. However, the satellite orbital errors and other errors should be estimated with the receiver position. The positioning accuracy will be improved. On the other hand, in this paper, only Iridium SOPs are used to realize receiver positioning. There are plentiful satellites operational today, and many of them also have potential for positioning. Further work on this topic can cover the improvement of positioning accuracy by orbital error correction or the differential positioning technique. Other LEO satellite SOPs are also considered to be used for positioning.

7. Conclusions This article studies the positioning using Iridium satellite signals in weak signal environment. The Iridium satellite signals here are treated as the non-cooperative SOPs for positioning. The key difficulty of the Iridium satellite SOPs positioning in weak environment is the Doppler-shift estimation. The new method termed QSA-IDE algorithm is proposed to estimate the Iridium satellite SOPs Doppler-shift in weak environment after detailed analysis of the Iridium satellite orbit and signal characteristics. The new algorithm mainly includes signal detection and signal acquisition, the former is used to find Iridium burst signals and the latter is used to estimate Doppler-shift. The quadratic square processing in the new method and the whole Iridium burst signal (including tone signal, unique signal, and information signal) is used to estimate that Doppler-shift are the core of the new algorithm. The mathematical model is created after introducing the principle of the QSA-IDE algorithm. We use the MLE to search Iridium signals and obtain the Doppler-shift fine estimations. The maximum correlation of MLE is not affected by the modulation mode of Iridium signal after quadratic square processing. For the Iridium SOPs positioning, the satellite position and velocity are calculated by the satellite TLE data and SGP4 prediction model, the instantaneous Doppler positioning technique is used after estimating Iridium satellite signal Doppler-shift. The new concept is tested using real collected data. The real IRIDIUM NEXT satellite data is collected under a dense forest where the Iridium signal is weak due to the occlusion environment. An Iridium antenna and a RF front end are used to obtain the Iridium IF data, and the software in the PC is used to realize Doppler-shift estimation and Iridium SOPs positioning. The Doppler-shift estimation results show that the new algorithm can effectively measure Doppler-shift in weak signal environment compared to the traditional method. It can see enough satellites and increase the number of the Doppler-shift measurement for every satellite. As a result, the new algorithm can used for Iridium SOPs positioning in weak signal while the traditional method is not. By continuously measuring the Iridium SOPs Doppler-shift and combining the satellite orbit information, the receiver positioning results based on real collected data in weak signal environment are carried out. When the Iridium ring alert signal is used, the positioning error mean values of east-direction and north-direction can be 147 and 162 m, while the value is only 58 m corresponding − to the up-direction. The positioning error RMS value is larger for east-direction than for north-direction and up-direction. When the height aiding is used, the error mean value of east-direction is only 21 m and the value corresponding to north-direction is 108 m. The error RMS value of east-direction and − north-direction is 144 and 137 m, respectively. In this case, the 2D positioning error RMS is 198 m. After performing the same step for the primer message signal, we got the approximate positioning results. In this case, the positioning error mean value of east-direction is 30 m and the value corresponding to − the north-direction is 113 m, the 2D positioning error RMS is 163 m. The Kalman filtering is used to − average the solutions from different Doppler-shift measurement combinations. As a result, the 2D Electronics 2020, 9, 37 17 of 18 positioning accuracy in both cases can achieve 110 m. The receiver solutions in two cases are both located at the south of real receiver position, the positioning error in east-west direction are more optimistic than for south-north direction in two cases. The common features of positioning error are caused by the Iridium satellite orbital error.

Author Contributions: Writing—original draft preparation, Conceptualization, Data curation, Investigation, methodology, Software, Writing—review and editing, Z.T.; Conceptualization, Funding acquisition, Resources, Writing—review and editing, H.Q., L.C.; Investigation, C.Z. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the National and Technology Special Zone Project. Conflicts of Interest: The authors declare no conflict of interest.

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