Opportunistic Navigation with Doppler Measurements from Iridium Next

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Opportunistic Navigation with Doppler Measurements from Iridium Next and Orbcomm LEO Satellites Mohamad Orabi Joe Khalife Department of Electrical Engineering Department of Mechanical and Computer Science and Aerospace Engineering University of California, Irvine University of California, Irvine Irvine, CA 92697 Irvine, CA 92697 [email protected] [email protected] Zaher M. Kassas Department of Mechanical and Aerospace Engineering Department of Electrical Engineering and Computer Science University of California, Irvine Irvine, CA 92697 [email protected]

Abstract—A framework for opportunistic navigation with multi- could results in large-scale disruptions and millions of dollars constellation low Earth orbit (LEO) satellite signals is pro- worth of losses [7], especially that jamming and spoofing posed. A receiver architecture suitable for processing both capabilities are becoming alarmingly accessible to the masses time division (TDMA) and frequency division multiple access [8]. While some signal processing techniques have been (FMDA) signals from Orbcomm and Iridium NEXT satellites developed to detect and mitigate such attacks [9–11], they is presented to produce Doppler frequency measurements from multi-constellation LEO satellites. An extended Kalman filter do not provide full protection against jamming or spoofing. (EKF)-based estimator is formulated to solve for a stationary Instead of relying mainly on GNSS, which makes them a receiver’s position using the resulting Doppler measurements. single point of failure, a more robust way to address their Experimental results are presented showing receiver positioning vulnerabilities is by exploiting other sources for navigation, with one Orbcomm satellite and four Iridium NEXT satellite such as signals of opportunity (SOPs). with an unprecedented final position error 22.7 m. SOPs are abundant and span wide frequency bands, which makes them far more robust than GNSS signals against jamming and spoofing attacks. Previous work has demonstrated TABLE OF CONTENTS navigation solutions for both (i) terrestrial SOPs, such as AM/FM radio [12–15], cellular [16–26], and digital televi- 1. INTRODUCTION ...... 1 sion signals [27–31], as well as (ii) non-terrestrial signals 2. RECEIVED SIGNAL MODEL AND LEO RECEIVER from low Earth orbit (LEO) satellites [32–36]. Although ARCHITECTURE ...... 2 SOPs were not designed with PNT in mind, they are still ca- 3. MULTI-CONSTELLATION LEO SATELLITE-BASED pable of providing submeter-level accuracy on aerial vehicles NAVIGATION FRAMEWORK ...... 3 as was shown in [37–39]. What is more, the exploitation of 4. OVERVIEW OF THE IRIDIUM NEXT AND ORB- cellular SOPs for resilient navigation in GPS-denied environ- COMM LEO CONSTELLATIONS ...... 4 ments under GPS jamming conditions has been shown to be 5. EXPERIMENTAL RESULTS ...... 6 effective in [40]. 6. CONCLUSION ...... 7 In addition to cellular SOPs, LEO broadband communication ACKNOWLEDGEMENTS ...... 7 satellite signals have been considered as possible reliable REFERENCES ...... 7 sources for navigation by various theoretical and experimental studies [41–47]. Tens of thousand of LEO satellites will be launched for broadbandcommunication in the next five years. 1. INTRODUCTION These signals have desirable attributes for opportunistic navigation, namely: (i) their location in LEO provides higher As cyber-physical systems move towards full autonomy, received signal power than that of GNSS satellites which the need for accurate and resilient positioning, navigation, reside in medium Earth orbit (MEO); (ii) LEO satellites are and timing (PNT) is now more critical than ever. This more abundant due to the larger number of satellites required need is also nourished by emerging technologies such as to provide full earth coverage; and (iii) LEO satellites are autonomous vehicles [1]. Furthermore, PNT has become deployed into unique constellations and are transmitting in entangled with critical infrastructure that could affect the different frequency bands, providing both spatial and spectral national and economic security of the entire Nation [2]. On diversity. a similarly important front, PNT is envisioned to enable high-rate, low-latency communication systems, particularly The potential of these future LEO megaconstellations has by enabling beam-forming for fifth-generation (5G) cellular triggered a renaissance of research in LEO-based PNT. The networks [3, 4]. Global navigation satellite systems (GNSS) approaches in the literature can be grouped into three cate- have been the leading providers of PNT solutions. However, gories: (i) LEO GNSS, (ii) GNSS augmentation with LEO they are vulnerable to unintentional interference, intentional satellite signals, or (iii) opportunistic navigation exclusively jamming, and malicious spoofing [5,6]. These vulnerabilities with LEO satellite signals. In the first approach, LEO satellites are assumed to be equipped with navigation pay- 978-1-7281-7436-5/21/$31.00 ©2021 IEEE loads to provide PNT services similar to traditional GNSS

1 [41,43]. While GNSS-like performance can be achieved in ing stationary receiver positioning using Doppler measure- such approaches, the additional cost of navigation payloads ments from the Iridium NEXT and Orbcomm constellations is imposed on the LEO broadband companies and the users. simultaneously, with a final two-dimensional (2–D) position In the second approach, LEO satellite signals are fused with error of 23 m. Next to [54] 1, this paper presents the first GNSS signals, such as in [48], where simulated pseudorange experimental results for multi-constellation LEO satellite- measurements from Iridium NEXT satellites were used to based opportunistic navigation. augment the pseudoranges from GPS satellites with the goal of reducing the dilution of precision. The third approach is 100 fully opportunistic, either in a simultaneous tracking and navigation (STAN) framework that estimates both the receiver’s Orbcomm and satellites’ states using Doppler and/or pseudorange mea- 80 Iridium NEXT surements from real LEO satellite signals [35], or in a differ- Multi-constellation ential framework using LEO carrier phase differential (CD- 60 LEO) measurements [49]. These opportunistic frameworks were experimentally demonstrated on ground vehicles and 40 unmanned aerial vehicles (UAVs) using exclusively signals from two Orbcomm LEO satellites (without GNSS), achiev- ing position root mean-squared errors (RMSEs) of (i) 416 m Percentage of time 20 for a ground vehicle using the STAN framework after traversing a 7.5 km trajectoryin 258 seconds, the last 228 seconds of 0 which without GNSS signals [35], (ii) 5.3 m for a UAV using 1 2 3 4 5 6 7 8 the STAN framework after traversing a 1.53 km trajectory Number of visible satellites in 155 seconds, the last 30 of which without GNSS signals Figure 1. Percentage of time when L or more satellites are [47]; (iii) 14.8 m for a UAV using the CD-LEO framework visible simultaneously for Orbcomm and Iridium NEXT and traversing a 1.14 km trajectory in 2 minutes [36], all of satellite constellations for a simulated duration of 2 days. which without GNSS signals []; and (iv) 21.2 m for a UAV using a blind Doppler tracking approach within the CD-LEO framework after traversing a 782 m trajectory in 90 seconds, all of which without GNSS signals [50]. Experimental results The rest of the paper is organized as follows. Section with Iridium NEXT satellite signals using an opportunistic 2 describes the received signal model and LEO receiver approach were presented in [51], where a 22 m RMSE was architecture. Section 3 presents an EKF-based framework achieved for a stationary receiver over a 30-minute period. to navigate with the Doppler measurements estimated by One challenge in using LEO satellite signals opportunistically the multi-constellation LEO receiver. Section 4 gives an is the unknown nature of the LEO satellite positions and overview of the Iridium NEXT and Orbcomm LEO satellite velocities. While two-line element (TLE) files and orbit constellations. Section 5 presents experimental results. Sec- determination software (e.g., simplified general perturbation tion 6 gives concluding remarks. 4 (SGP4)) could be used to predict LEO satellite positions and velocities, the resulting estimates could be off by a few kilometers and a few meters per second, respectively [35,52]. 2. RECEIVED SIGNAL MODELAND LEO RECEIVER ARCHITECTURE Despite these errors in the predicted LEO satellite orbits, the aforementioned experimental results have shown remarkable This section presents the received multi-constellation LEO potential for opportunistic navigation with LEO satellites. signal model and the proposed receiver architecture. However, the experiments therein only utilized signals from a single LEO constellation, which does not exploit the spatial Received LEO Satellite Signal Model and spectral diversity of LEO constellations. Moreover, LEO This paper considers a stationary receiver that listens to both satellites are designed to cover as much of the Earth’s surface continuous signals and burst signals from multi-constellation with as few satellites as possible, making it improbable to LEO satellites on various channels. Let L denote the total listen to a largenumberof satellites (6 or more) from thesame number of visible LEO satellites and U the total number of constellation simultaneously. This is illustrated in Figure constellations to which these satellites belong. Furthermore, 1, which shows the percentage of time L or more satellites let Lu denote the number of visible satellites in the u- are simultaneously visible over a period of 2 days. The th constellation, where u = 1, 2,...,U. It follows that LEO satellite trajectories were generated using TLE files U Lu = L. The baseband received signal for the u-th and SGP4 software [53]. Figure 1 shows the importance of Pu=1 being able to exploit multi-constellation LEO satellites for constellation at the input of an opportunistic LEO receiver PNT. Currently, the literature presenting experimental results can be modeled as with multi-constellation LEO-based PNT is rather sparse. As opposed to [51], which investigated opportunistic navigation Lu r (i)= s u (i)+ n (i), i =0, 1,...,u =1, 2,...,U, using only Iridium NEXT satellites, this paper uses both u X l u Iridium Next and Orbcomm satellite signals to investigate lu=1 multi-constellation LEO satellite-based opportunistic navi- (1) , gation. This paper makes three contributions. First, an where nu(i) nIu (i) + jnQu (i), with nIu and nQu are extended Kalman filter (EKF)-based full opportunistic frame- modeled as zero-mean white Gaussian noise with variance N0 work for navigating with Doppler measurements from multi- ; Ts is the sampling time; i represents time ti , t0 + iTs constellation LEO satellite signals is developed. Second, 2Ts a receiver architecture capable of producing such Doppler measurements from multi-constellation LEO satellite signals 1The results in this work were achieved independently from [54], which is provided. Third, experimental results are presented, show- was published shortly after the first submission of this manuscript, which achieved a 2–D position error of 132 m.

2 { Data{ Block 1 Data Block 2 for some initial time t0; slu (i) is given by M-PSK Burst No Signal M-PSK Burst No Signal , slu(i) Clu alu(i)exp {j2π[fD,lu (i)+fIF,lu ]iTs +jθlu(i)}, T T p burstu dumpu P where Clu is the received signal power of the lu-th satel- burstu lite; alu is the transmitted symbol at time i; fD,lu (i) and Figure 2. TDMA data block. θlu (i) are the time-varying Doppler frequency and carrier phase of the lu-th satellite, respectively; and fIF,lu is the intermediate frequency of the lu-th satellite. It is assumed k M that the symbols alu are drawn from an M-ary phase shift 3. The data blocks dlu are then raised to the -th power to q2π wipe off the M-PSK symbols, resulting in a pure tone at a keying (M-PSK) constellation, i.e., a u , exp j for l M frequency of M f i . q , ,...,M . · D,lu ( ) ∈{0 1 − 1} 4. A Fast FourierTransform(FFT) of the signal is then taken, It is important to note that (1) holds for both continuously which results in an impulse-like peak at the next Doppler ˆ ˆ transmitted and burst signals. The difference between these frequency MfD,lu (k), which will be around MfD,lu (k − 1). ˆ signals is the domain of the time index i. For continuous Therefore,the search for the FFT peakis limited to [fD,lu (k− signals, i goes from zero to infinity. For burst signals, i is ˆ 1)−∆f, fD,lu (k−1)+∆f], where ∆f is chosen to be greater defined only over burst intervals, which requires knowledge than the maximum expected frequency deviation in a period of the burst start-time, period, and duration. The burst period of Tblocku . The Doppler estimates are then normalized by M. and duration are known for the signals of interest (Iridium 5. In order to successfully track a burst signal, it is important NEXT), and the start-time can be acquired through an energy to update the burst start time acquired at the initialization detector. of the receiver. This is due to the change in the distance and hence delay between the satellite and the receiver. The Multi-Constellation LEO Receiver Architecture delay can be predicted from the estimated Doppler frequency The navigation receiver architecture in Figure 3, which oper- according to ates on the samples of ru(i) from (1), was designed to account ˆ for both time-division multiple access (TDMA) schemes fD,lu (k) (used by Iridium NEXT) and frequency-division multiple tburstlu (k)= tburstlu (k − 1) − Pburst, (4) f f access (FDMA) schemes (used by both Iridium NEXT and c,u + IF,lu Orbcomm). The receiver performs recursively the steps f u discussed next to obtain an estimate of the Doppler frequency where c,u is the carrier frequency of the -th constellation. The burst start time index is then updated accordingly. Com- ˆ for the lu-th satellite, denoted fD,lu . An extra step is required pensating for the change delay using (4) results in slight for TDMA signals at initialization to acquire the burst start variations in the value of Tdump . time, which can be done using an energy detector. To this lu end, it is assumed that an initial Doppler frequency estimate The receiver architecture is summarized in Figure 3. ˆ fD,lu (0) and the burst start time tburstlu (0) and associated IF 1 index i0lu are given. f , 1. The receiver first wipes-off the intermediate frequency Dumped Peak fˆD,1 Data Block dk (.)M FFT fIF,lu to obtain lu Samples Detection fIF 2 , , dlu (i) ru(i) exp[−j2πfIF,lu iTs]. (2)

Dumped Peak fˆD,2 2. Next, the receiver groups samples of dlu (i) into data Data Block dk (.)M FFT EKF lu Samples Detection blocks of size Nu, denoted by fIF,l k dlu = [dlu (kNu + i0lu ), dlu (kNu +1+ i0lu ),..., ˆ k Dumped M Peak fD,l dlu ((k + 1)Nu − 1+ i0l )], Data Block d (.) FFT u lu Samples Detection where k = 0, 1,..., is the data block index. These data blocks have a duration Tblocku = NuTs, which is equal Figure 3. Block diagram for the mutli-constellation receiver to that of the burst for satellites that employ TDMA, or architecture presented in this paper. The dashed lines that is an integer multiple of the symbol period Tsymbu for represent optional feedback of the estimated Doppler to continuously transmitting satellites. For TDMA schemes, update Tdump . only samples of the burst signal are chosen to form the data u blocks. For a burst duration Tburstu and period Pburstu ≥ Tburstu , the samples between two bursts are dumped by the receiver. The duration of the dumped samples is given by 3. MULTI-CONSTELLATION LEO Tdumpu = Pburstu − Tburstu , as shown in Figure 2. It is clear that Pburstu > Tburstu for TDMA signals, which SATELLITE-BASED NAVIGATION makes Tdumpu strictly positive, and Pburstu = Tburstu for FRAMEWORK continuous signal transmission, which implies T = 0. dumpu This section develops an EKF-based framework to navigate It is assumed the Doppler frequencies are approximately with the Doppler measurements estimated by the multi- constant during a data block duration, i.e., constellation LEO receiver discussed in Section 2. The goal is to estimate the receiver’s three dimensional (3–D) position fD,lu (i)= fD,lu [k], kNu ≤ i< (k + 1)Nu, k =0, 1,.... T (3) vector rr , [xr,yr,zr] using the Doppler measurements 3 obtained from the receiver developed in the paper. In what covariance time-update equations are given by follows, the pseudorange rate model is ﬁrst described and the EKF model is then provided. xˆ(k +1|k)= xˆ(k|k), P(k +1|k)= P(k|k)+ Q,

Pseudorange Rate Measurement Model where Q is the process noise covariance. Note that Q should theoretically be a zero matrix; however, in order to prevent fˆ k Given a Doppler measurement D,lu ( ), a pseudorange rate the estimation error covariance from converging to zero, Q measurement can be formed according to is chosen to be Q ≡ ǫI(3+L)×(3+L), where ǫ is a very small positive number. Given an innovation vector ν(k + 1), the fˆ k , D,lu ( ) state and covariance measurement update equations are given zleo,lu (k) c , k =0, 1,..., (5) fc,u + fIF,lu by where lu = 1,...,Lu, u = 1,...,U, and c is the xˆ(k +1|k +1)= xˆ(k +1|k)+ K(k + 1)ν(k + 1), speed of light. Let the pseudorange rate measurements U P(k +1|k + 1) = [I − K(k + 1)H(k + 1)] P(k +1|k), z k Lu for k , ,..., be re-indexed ac- { leo,lu ( )}lu=1 = 0 1 n ou=1 L where K(k + 1) is the standard Kalman gain, H(k + 1) is the cording {zleo,l(k)}l=1 for compactness of notation. Hence, measurement Jacobian given by the pseudorange rate measurement of the l-th satellite produced by the receiver could be expressed as T H(k + 1) = [hleo,1(k + 1) ... hleo,L(k + 1)] , T T T T r˙ (k)[rr −rleo,l(k)] h , h e leo,l leo,l(k + 1) r,l(k + 1), l zleo,l(k)= +c[δt˙ r(k) − δt˙ leo,l] (6) h i krr −rleo,l(k)k e + c δt˙ (k)+ δt˙ (k) + v (k), where l is the standard L×1 basis vector whose l-th element h iono,l trop,l i leo,l is 1 and the remaining elements are 0, where r and r˙ are the l-th LEO satellite’s 3–D po- leo,l leo,l r˙ leo,l(k + 1) ˙ ˙ hr,l(k) , sition and velocity vectors, respectively; δtr and δtleo,l are krˆ (k +1|k) − r (k + 1)k the receiver’s and l-th LEO satellite’s clock drifts, respec- r leo,l − [rˆr(k +1|k) − rleo,l(k + 1)] tively; δt˙ iono,l and δt˙ trop,l are the l-th satellite’s ionospheric rT r r and tropospheric delay rates, respectively; and vleo,l is the ˙ leo,l(k + 1) [ˆr(k +1|k) − leo,l(k + 1)] measurement noise, which is modeled as a zero-mean white × 3 , 2 krˆr(k +1|k) − rleo,l(k + 1)k Gaussian random sequence with variance σleo,l. It is assumed that the receiver’s clock drift δt˙ r and the satellites’ clock L and rˆr(k +1|k) is the receiver’s position prediction at time- ˙ step k . The innovation vector ν k is formed according drifts nδtleo,lo are constant within the 10-minute satellite +1 ( +1) l=1 to visibility window. Moreover, since it not necessary to estimate the receiver and satellite’s clock drifts individually, they T ν(k + 1) = [νleo,1(k + 1),...,νleo,L(k + 1)] , will be lumped into one term ∆δt˙ l , δt˙ r − δt˙ leo,l. In case of L multiple passes, ∆δt˙ l are re-initialized at the beginning where νleo,l(k +1) = zleo,l(k + 1) − zˆleo,l(k + 1), such that n ol=1 of each pass. Note that at any time-step k, the l-th satellite’s rT r r position and velocity vectors can be obtained from the TLE ˙ leo,l(k + 1) [ˆr(k +1|k) − leo,l(k + 1)] zˆleo,l(k +1)= ﬁles and SGP4 software. For the brief duration of LEO krˆr(k +1|k) − rleo,l(k + 1)k satellite visibility, the ionospheric and tropospheric delay ˙ ˙ c δtˆ˙ k k . rates are negligible; hence, δtionol and δttropl are ignored in + ∆ l( +1| ) the measurement, yielding the measurement model given by It is important to note that the altitude of the receiver is rT r r assumed to be known. Therefore, the initial estimate of ˙ leo,l(k)[ r − leo,l(k)] zleo,l(k) ≈ + c∆δt˙ l + vleo,l(k). zr is set to the known altitude and its corresponding initial krr − rleo,l(k)k uncertainty is set to be very small. (7)

EKF Model 4. OVERVIEW OF THE IRIDIUM NEXT AND From (7), it can be seen that the state vector to be estimated ORBCOMM LEO CONSTELLATIONS T x , rT ˙ ˙ is h r ,c∆δt1,...,c∆δtLi . Subsequently, an EKF is This section provides an overview of the two LEO constel- x k m x k lations used in the experimental results: Iridium NEXT and designed to produce an estimate ˆ( | ) of ( ) using all Orbcomm. pseudorange rate measurements from time-step 1 to m ≤ k. The estimation error is denoted x˜(k|m) , x(k) − xˆ(k|m). Iridium NEXT System Overview The EKF also calculates the estimation error covariance T P k m , E x k m x k m . Given a prior x and The Iridium NEXT constellation is the next-generation Irid- ( | ) h˜( | )˜ ( | )i ˆ(0|0) ium constellation which provides voice and data informa- P(0|0), the standard EKF equations are iterated. Since the tion coverage to satellite phones, pagers, and integrated state vector x is constant, the EKF state and estimation error transceivers over the entire Earth surface on the L-band [55]. 4 Iridium NEXT LEO Satellite Constellation— The Iridium Orbcomm System Overview Next constellation consists of 75 active satellites that orbit the Earth in 6 different orbital planes spaced 30◦ apart [55], The Orbcomm system is a wide area two-way communication as shown in Figure 4. The planes are near-polar orbits system that uses a constellation of LEO satellites to provide with 86.4◦ inclination angle and 780 km orbital altitude. worldwide geographic coverage for sending and receiving Originally, the Iridium constellation was designed to incor- alphanumeric packets [56]. porate 66 satellites (gathered in 6 groups of 11) in order to Orbcomm LEO Satellite Constellation— provide coverage for the entire Earth surface. Later, Iridium The Orbcomm con- decided to enlarge the initial constellation (referred to as the stellation, at maximum capacity, has up to 47 satellites in 7 orbital planes A–G, illustrated in Figure 5. Planes A, B, NEXT campaign) by launching 12 extra satellites in order to ◦ provide 24/7 real-time coverage, which would add two extra and C are inclined at 45 to the equator and each contains 8 satellites in a circular orbit at an altitude of approximately satellites on each of the originalorbital planes. Unfortunately, ◦ 3 of them are not active since they experienced technical 815 km. Plane D, also inclined at 45 , contains 7 satellites in a circular orbit at an altitude of 815 km. Plane E is inclined difﬁculties once they were launched and thus the current ◦ at 0 and contains 7 satellites in a circular orbit at an altitude constellation remains at 75 satellites. ◦ of 975 km. Plane F is inclined at 70 and contains 2 satellites in a near-polar circular orbit at an altitude of 740 km. Plane Latitude lines Seam ◦ Communication Plane 6 G is inclined at 108 and contains 2 satellites in a near-polar link elliptical orbit at an altitude varying between 785 km and 875 Satellite km. Latitude cutoﬀ for communication link Plane 5

◦ Orbital Plane G (108 ) Planes A, B, and C: 8 satellites direction each with orbital altitude 815 km 45◦ Plane D ( ) Plane D: 7 satellites with orbital altitude 815 km ◦ Plane 4 Plane B (45 ) Plane E: 7 satellites with orbital altitude 975 km ◦ ◦ 80 Plane E (0 ) 70 ◦ Plane F: 2 satellites Equator with orbital altitude 740 km 60 ◦ ◦ Plane G: 2 satellites 50 ◦ Plane C (45 ) Plane 3 with orbital altitude 785{875 km 40 ◦ ◦ 30 ◦ Plane A (45 ) Equator 20 ◦ Existing Satellites ◦ 10◦ 0 Future Satellites ◦ Seam Plane F (70 ) Note: Plane 1 Plane 2 Drawing not to scale Figure 5. Orbcomm LEO satellite constellation. Map data: Figure 4. Polar view of the Iridium NEXT Constellation. Google Earth.

Iridium NEXT Downlink Signals—Iridium NEXT signals are transmitted over the 1616–1626.5 MHz band, which is part of the L-band. There are 252 carriers in both the uplink Orbcomm Downlink Signals— Orbcomm uses an FDMA and downlink channels, with carrier spacings of 41.6667 kHz scheme for downlink channel multiplexing. Satellite radio with a required bandwidth of 35 kHz [55]. These carrier frequency (RF) downlinks are within the 137–138 MHz VHF frequencies are grouped into sub-bands of 8 carriers, with band. Downlink channels include 12 channels for transmit- the 32nd group containing 4 carriers. A small portion of ting to users and one gateway channel, which is reserved for the Iridium NEXT spectrum, namely 1626–1626.5 MHz is transmitting to the ground stations. Each satellite transmits to assigned for paging and acquisition [55]. On this part of users on one of the 12 subscriber downlink channels through the spectrum are 5 simplex downlink channel with the same a frequency-sharing scheme that provides four-fold channel frequency spacing as the standard channels and with 35 kHz reuse. The Orbcomm satellites have a subscriber transmitter of bandwidth. Doppler measurements are extracted from the that provides a continuous 4800 bits-per-second (bps) stream simplex downlink channels. of packet data using symmetric differential-quadrature phase shift keying (SD-QPSK). Each satellite also has multiple Iridium NEXT uses a TDMA scheme for downlink chan- subscriber receivers that receive short bursts from the users nel multiplexing. The signal structure over the uplink and at 2400 bps. downlink channels consists of signal bursts that are sent periodically over the TDMA frame. Each burst is composed Note that Orbcomm satellites are also equipped with a spe- of an unmodulated tone, succeeded by a unique word and the cially constructed 1-Watt ultra high frequency (UHF) trans- information data. On the simplex channel, Iridium NEXT mitter that is designed to emit a highly stable signal at 400.1 satellites transmit the ring alert as well as paging/acquisition MHz. The transmitter is coupled to a UHF antenna designed messages, which have the same burst structure as the standard to have a peak gain of approximately2 dB. The UHF signal is carriers. As such, the pure tone transmitted at the beginning used by the Orbcomm system for user positioning. However, of each burst can be used to extract Doppler measurements. experimental data shows that the UHF beacon is absent. However, the burst duration is 2.56 ms and the burst period Moreover, even if the UHF beacon was present, one would is about 1700 times longer at 4.32 seconds. This large need to be a paying subscriber to beneﬁt from positioning scaling will yield poor Doppler frequency measurements if services. Consequently, only downlink channel VHF signals not accounted for, as discussed in Section 2. are exploited for navigation. 5 5. EXPERIMENTAL RESULTS TLE Measured 6k An experiment was conducted to demonstrate the proposed Iridium 180 receiver architecture and navigation framework. To this end, 4k two universal software radio peripherals (USRPs) Ettus E312 2k Orbcomm were used to collect multi-constellation LEO satellite signals. FM 116 Iridium 122 One USRP was equipped with a VHF quadriﬁlar helix an- 0 tenna to sample Orbcomm signals at a carrier frequency of -2k 137.5 MHz, which is the central frequency of the Orbcomm Iridium 168 band [56], and the other was equipped with an AT 1621-12 -4k Iridium 119

Iridium antenna to sample Iridium NEXT signals at a carrier Pseudorange rate (m/s) . frequency of 1626 2708 MHz, which is the central frequency -6k of the Iridium ring alert burst signal according to [51]. Both 0 50 100 150 200 250 300 350 400 USRPs were set to sample data at 2.4 Msps over a 410-second Time (s) period. The samples were stored for offline processing, and a software-defined radio (SDR) implementation of the afore- Figure 7. Pseudorange rates time history predicted using mentioned receiver architecture was used to post-process the TLE files for the satellites tracked by the proposed receiver collected data. The experimental setup is illustrated in Figure along with the actual measurements produced by the 6. Moreover, the M-PSK constellation size was set to 2 for receiver. the Orbcomm signals and 1 for the Iridium signals, respectively. Note that Orbcomm satellites transmits quadrature PSK (QPSK) signals (M = 4); however, raising the signal to the second power yielded better results than M = 4. The M-PSK constellation size was chosen to be 1 for Iridium NEXT since their satellites transmit a pure tone as part of the burst. Moreover, Tblock and Tdump, where set to 100 ms and zero, respectively, for the Orbcomm constellation. For the Iridium constellation, they were set to Tblock = 2.56 ms and Tdump =4.3174 s, enabling burst processing for a signal with a period of Pblock =4.32 s, equivalent to that of the ring alert burst signal. The SDR produced Doppler measurements for five satellites, consisting of (i) one continuously transmitting Orbcomm satellite and (ii) four burst transmitting Iridium Receiver NEXT satellites. The Doppler measurements were provided Position at a rate of 100 ms for the Orbcomm satellite and 4.32 s for the Iridium NEXT satellites. The satellites’ positions Figure 8. Skyplot and satellite positions of the tracked and velocities were determined using a MATLAB-based SGP4 Orbcomm and Iridium NEXT satellites. propagation software and publicly available TLE files. The positions of the satellites along with the skyplot with respect to the receiver are shown in Figure 8. until the receiver starts extracting measurements from another Iridium NEXT satellite at 304 seconds. Figure 7 illustrate the availability of Orbcomm and Iridium NEXT satellites Laptop during the experiment window as well as the actual number of LEO satellites that were tracked by the receiver. It is worth mentioning that tracking an Iridium NEXT satellite for 100 seconds only produces around 23 pseudorange rate VHF quadrifilar Ettus E312 helix antenna USRP measurements.

Orbcomm Iridium NEXT Multi-constellation Tracked 6

Iridium Antenna Ettus E312 Post-Processing MATLAB-Based Receiver AT1621-12 USRP and Navigation Framework 4 Figure 6. Experimental setup. 3 2

Figure 7 shows the true and estimated pseudorange rates 1 Number of visible satellites obtained from the TLE files and the receiver, respectively, for 0 each of the five satellites. The satellites were not all tracked 0 50 100 150 200 250 300 350 400 for the entire duration of their availability due to bad signal Time (UTC) reception at low elevation angles. Figure 7 also illustrates the availability of the satellites within the 410 s window Figure 9. Number of tracked and available satellites as a when the data was recorded. The Orbcomm satellite was function of time. available throughout the entire window and was providing measurements every 100 ms. However, for the Iridium constellation, three satellites are tracked initially and are then The horizontal position estimate was initialized around 200 lost at 78, 118, and 217 s, respectively. The EKF continues to km away from the receiver’s true position, and the initial estimate the receiver’s position using one Orbcomm satellite horizontal uncertainty was set to 1010 m2. The receiver’s 6 altitude was initialized according to Section 3, with a 0.1 signals from Orbcomm and Iridium NEXT satellites to pro- m2 initial uncertainty. Figure 10 shows the time evolution duced Doppler frequency measurements to LEO satellites of the EKF position errors in the east and north coordinates was proposed. An EKF-based estimator was formulated along with the ±3σ bounds, reaching a final position error to solve for a stationary receiver’s position using Doppler of 22.7 m. The small jumps seen in the EKF errors happen measurements from multi-constellation LEO satellites. Un- at a period of 4.32 s, which is the rate at which pseudorange precedented experimental were presented showing receiver rate measurements were produced from the Iridium NEXT positioning with one Orbcomm satellite and four Iridium satellite signals. The receiver’s true and estimated positions NEXT satellite with a final position error less than 23 m. are shown in Figure 11. It is also worth noting that some of the position error could be attributed to errors in the LEO satellites’ positions and velocities predicted by the TLEs and ACKNOWLEDGEMENTS SGP4 orbit determination software.

Error 3 bounds This work was supported in part by the Ofﬁce of Naval 4 Research (ONR) under Grant N00014-19-1-2511 and in part 2 by the U.S. Department of Transportation (USDOT) un- 0 der University Transportation Center (UTC) Program Grant

-2 69A3552047138. The authors would also like to thank East (km) Carlos Acebes for his contributions to the paper and Nadim -4 0 50 100 150 200 250 300 350 400 Khairallah for his help with data collection. Time (s) 4

0 REFERENCES

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