Simultaneous Tracking of Orbcomm LEO Satellites and Inertial Navigation System Aiding using Doppler Measurements

Joshua Morales1, Joe Khalife1, and Zaher M. Kassas1,2 1Department of Electrical Engineering and Computer Science, University of California, Irvine, USA 2Department of Mechanical and Aerospace Engineering, University of California, Irvine, USA Emails: [email protected], [email protected], [email protected]

Abstract—A framework for simultaneously tracking Orbcomm an abundance of signal sources [9]; and (3) each broadband low Earth orbit (LEO) satellites and using Doppler measurements provider will deploy satellites into unique orbital constellations drawn from their signals to aid a vehicle’s inertial navigation transmitting at different frequency bands, making their signals system (INS) is developed. The developed framework enables a navigating vehicle to exploit ambient Orbcomm LEO satellite diverse in frequency and direction [20]. signal Doppler measurements to aid its INS in a tightly-coupled To exploit LEO satellites for navigation, their positions fashion in the event global navigation satellite system (GNSS) and clock states, namely the clock bias and drift of the signals become unusable. An overview of the extended Kalman transmitter, must be known. The position of any satellite filter-based simultaneous tracking and navigation (STAN) frame- may be parameterized by its Keplerian elements: eccentricity, work is provided. Experimental results are presented showing an unmanned aerial vehicle (UAV) aiding its INS with Doppler mea- semi-major axis, inclination, longitude of the ascending node, surements drawn from two Orbcomm LEO satellites, reducing argument of periapsis, and true anomaly. These elements are the final position error from 31.7 m to 8.9 m after 30 seconds of tracked, updated once daily, and made publicly available by GNSS unavailability. the North American Aerospace Defense Command (NORAD) in the form of two-line element (TLE) files [21]. The infor- I.INTRODUCTION mation in these files are used to initialize a simplified general A global navigation satellite system (GNSS)-aided inertial perturbation (SGP) model to propagate a satellite in its obit. navigation system (INS) makes use of the complementary However, the simplified models of perturbing forces, which properties of each individual system: the short-term accuracy include non-uniform Earth gravitational field, atmospheric and high data rates of an INS and the long-term stability of drag, solar radiation pressure, third-body gravitational forces a GNSS solution to provide periodic corrections. However, (e.g., gravity of the Moon and Sun), and general relativity in the inevitable event that GNSS signals become unavailable [22], cause errors in a propagated satellite orbit as high as (e.g., in deep urban canyons, near dense foliage, and in the three kilometers. In contrast to GNSS, where corrections to the presence of unintentional interference or intentional jamming) orbital elements and clock errors are periodically transmitted or untrustworthy (e.g., during malicious spoofing attacks), the to the receiver in a navigation message, such orbital element INS’s errors will grow unboundedly. and clock corrections may not be available for LEO satellites; Signals of opportunity (SOPs) have been considered as an in which case they must be estimated simultaneously with alternative navigation source in the absence of GNSS signals the navigating vehicle’s states: orientation, position, velocity, [1], [2]. SOPs include AM/FM radio [3], cellular [4], [5], inertial measurement unit (IMU) biases, and receiver’s clock digital television [6], and low Earth orbit (LEO) satellites errors. The main contribution of this paper is to present [7]–[9]. These signals have been demonstrated to yield a a novel framework that estimates the LEO satellites’ states standalone meter-level-accurate navigation solution on ground simultaneously with the navigation vehicle’s states and to vehicles [10]–[13] and a centimeter-level-accurate navigation demonstrate the framework’s performance. solution on aerial vehicles [14], [15]. Moreover, these signals The exploitation of LEO satellites for navigation has been have been used as an aiding source for lidar [16], [17] and considered in other contexts. In [23], simulated LEO satellite INS [18], [19]. Doppler measurements from known satellite positions were LEO satellites are particularly attractive aiding sources for used to complement a cellular radio frequency pattern match- a vehicle’s INS in GNSS-challenged environments for several ing algorithm for localizing emergency 911 callers. In [24], reasons: (1) they are around twenty times closer to Earth simulated Doppler measurements from one LEO satellite with compared to GNSS satellites which reside in medium Earth known position and velocity were used to localize a receiver. orbit (MEO), making their received signals between 300 to In [25], the position, velocity, and clock errors of a receiver 2,400 times more powerful than GNSS signals [20]; (2) were estimated using simulated LEO satellite time-difference thousands of broadband internet satellites will be launched into of arrival (TDOA) and frequency-difference of arrival (FDOA) LEO by OneWeb, SpaceX, Boeing, among others, bringing measurements using a reference receiver with a known posi- tion. In contrast to these previous approaches which assumed Platform perfectly known LEO satellite position states and used sim- EKF Prediction IMU GNSS ulated measurements, the framework presented in this paper INS estimates the LEO satellites’ position states along with the Receiver states of a navigating vehicle using real LEO satellite signals. State LEO EKF A similar framework to estimate the position and clock states Initialization Propagation Update of stationary terrestrial transmitters while simultaneously aid- ing a vehicle’s INS with pseudorange observables drawn from TLE Clock Models LEO such transmitters was presented and studied in [18], [26]. This Files Receiver paper presents a more complex framework, which enables the tracking of mobile LEO transmitters’ states. Specifically, a Fig. 1. Simultaneous LEO satellite tracking and navigation framework. simultaneous tracking and navigation (STAN) framework is presented, which tracks the states of Orbcomm LEO satellites while simultaneously using Doppler measurements extracted where xr is the state vector of the vehicle-mounted IMU and B from their signals to aid a vehicle’s INS. A preliminary receiver which consists of Gq¯, which is a four-dimensional presentation of the framework was presented in [27], [28]; (4-D) unit quaternion representing the orientation of a body however, details of the framework were not provided. In this frame B fixed at the IMU with respect to a global frame G; rr paper, details of the framework’s components are discussed and r˙ r are the three-dimensional (3-D) position and velocity and its performance is demonstrated through an experiment of the IMU; bg and ba are 3-D biases of the IMU’s gyroscopes ˙ on an unmanned aerial vehicle (UAV). and accelerometers, respectively; δtr and δtr are the clock bias The remainder of this paper is organized as follows. Section and drift of the receiver, respectively; and c is the speed of th II describes the LEO satellite signal-aided INS framework and light. The vector xleom represents the states of the m LEO discusses the LEO satellite dynamics model and the receiver satellite, which consists of rleom and r˙ leom , which are the 3-D ˙ measurement model. Section III provides an overview of the satellite position and velocity, respectively; δtleom and δtleom Orbcomm satellite system. Section IV presents experimental are the satellite’s transceiver clock bias and drift, respectively; results demonstrating a UAV navigating with Orbcomm signals and m = 1,...,M, with M being the total number of LEO using the LEO satellite signal-aided INS framework. Conclud- satellites visible to the receiver. ing remarks are given in Section V. 2) Vehicle Dynamics Model: The vehicle’s orientation, po- sition, and velocity are modeled to evolve in time according to II. STAN NAVIGATION FRAMEWORK INS kinematic equations driven by a 3-D rotation rate vector An extended Kalman filter (EKF) framework is employed to Bω of the body frame and a 3-D acceleration vector Ga in aid the INS with LEO satellite pseudorange rates and GNSS the global frame. The gyroscopes’ and accelerometers’ biases pseudoranges (when available) in a tightly-coupled fashion. are modeled to evolve according to the discrete-time (DT) The proposed STAN framework, illustrated in Fig. 1, works dynamics, given by similarly to that of a traditional tightly-coupled GNSS-aided b (k +1)= b (k)+ w (k) (1) INS with two main differences: (i) the position and clock states g g bg of the LEO satellites are unknown to the vehicle-mounted ba(k +1)= ba(k)+ wba(k), k =1, 2,... (2) receiver; hence, they are simultaneously estimated with the where wbg and wba are process noise, which are modeled states of the navigating vehicle and (ii) Doppler measurements as DT white noise sequences with covariances Qbg and Qba, are used to aid the INS instead of GNSS pseudoranges. A respectively. The vehicle-mounted receiver’s clock error states similar framework was proposed in [18] to aid a vehicle’s INS are modeled to evolve in time according to using stationary terrestrial emitters. The framework presented in this paper is more complex since it includes a LEO xclkr (k +1)= Fclk xclkr (k)+ wclkr (k), (3) satellite dynamics model to propagate the positions of moving T 1 T x , cδt , cδt˙ , F = , LEO satellites. The EKF state vector, state dynamics model, clkr r r clk 0 1 receiver’s measurement model, and the EKF prediction and h i   w measurement update steps are discussed next. where clkr is the process noise, which is modeled as a DT white noise sequence with covariance

A. EKF State Vector and Dynamics Model T 3 T 2 Sw˜ T + Sw˜ Sw˜ δtr δt˙ r 3 δt˙ r 2 1) EKF State Vector: The EKF state vector is given by Qclk = 2 , (4) r S T S T " w˜δ˙t 2 w˜δ˙t # T T T T r r x = xr , xleo1 ,..., xleoM , and T is the constant sampling interval [29]. The terms Sw˜δtr T T T T T T and Sw˜ ˙ are the clock bias and drift process noise power B   ˙ δtr xr = Gq¯ , rr , r˙ r , bg , ba , cδtr, cδtr spectra, respectively, which can be related to the power-law 2 h iT coefficients, {hα,r} − , which have been shown through T T ˙ α= 2 xleom = rleom , r˙ leom , cδtleom , cδtleom , laboratory experiments to characterize the power spectral h i density of the fractional frequency deviation of an oscillator and velocity is performed by linearizing and discretizing (5). from nominal frequency according to S ≈ h0,r and Next, the measurement model and the EKF measurement w˜δtr 2 2 Sw˜ ≈ 2π h−2,r [30]. update is described. δ˙tr 3) LEO Satellite Dynamics Model: The position and veloc- ity dynamics of the mth LEO satellite are modeled as the sum C. Receiver Measurement Model and EKF Update of the two-body motion model equation and other perturbing The GNSS receiver makes pseudorange measurements at accelerations, given by DT instants on all available GNSS satellites, which after µ compensating for ionospheric and tropospheric delays is given r¨ (t)= − r (t)+ a˜ (t), (5) leom 3 leom leom by krleom (t)k2

d th zgnss (j)=krr(j) − rgnss (j)k2 where r¨leom = dt r˙ leom , i.e., the acceleration of the m LEO l l satellite, µ is the standard gravitational parameter of Earth, + c · δtr(j) − δtgnssl (j) +vgnssl (j), j =1, 2,... and a˜leom captures the overall perturbation in acceleration, (9) which includes perturbations caused by non-uniform Earth   where z , z′ −cδt −cδt ; δt and δt are gravitational field, atmospheric drag, solar radiation pressure, gnssl gnssl iono tropo iono tropo the ionospheric and tropospheric delays, respectively; z′ is third-body gravitational forces (e.g., gravity of the Moon and gnssl the uncompensated pseudorange; vgnss is the measurement Sun), and general relativity [22]. The perturbation vector a˜leom l is modeled as a white random process with power spectral noise, which is modeled as a DT zero-mean white Gaussian th sequence with variance σ2 ; and l =1,...,L, with L being Q gnssl density a˜leom . The m LEO satellite’s clock states time evolution are modeled according to the total number of GNSS satellites. The LEO receiver makes Doppler frequency measurements x k F x k w k , (6) clkleom ( +1)= clk clkleom ( )+ clkleom ( ) fD on the available LEO satellite signals, from which a where w is a DT white noise sequence with co- pseudorange rate measurement ρ˙leo can be obtained from clkleom c ρ˙leo = − fD, where fc is the carrier frequency. The pseu- variance of identical structure to Qclk in (4), except that fc r th dorange rate measurement ρ˙leom from the m LEO satellite Sw˜δt and Sw˜ ˙ are replaced with the LEO satellite clock r δtr is modeled according to specific spectra Sw˜δt and Sw˜ ˙ , respectively, where leo,m δtleo,m h0,leom 2 S ≈ and S ≈ 2π h− . The next T [rr(j) − rleom (j)] w˜δtleo,m 2 w˜δt˙ 2,leom leo,m ρ˙leom (j) = [r˙ leom (j) − r˙ r(j)] section discusses how these models are used in the EKF krr(j) − rleom (j)k2 prediction. ˙ ˙ ˙ + c · δtr(j) − δtleom (j) + cδtionom (j) B. IMU Measurement Model and EKF Prediction ˙ h i + cδttropom (j)+ vleom (j), The vehicle-mounted IMU which contains a triad-gyroscope ˙ ˙ and a triad-accelerometer produces angular rate and specific where δtionom and δttropom are the drifts of the ionospheric th force measurements, which are modeled as and tropospheric delays, respectively, for the m LEO satel- lite; and vleo is the measurement noise, which is modeled B m ωimu(k)= ω(k)+ bg(k)+ ng(k) (7) as a white Gaussian random sequence with variance σ2 . leom B G G Note that the variation in the ionospheric and tropospheric aimu(k)=R Gq¯(k) a(k) − g(k) +ba(k)+na(k), (8) delays during LEO satellite visibility is negligible compared where Gg is the acceleration due to gravity
in the global frame to the errors in the satellite’s estimated velocities [32]; hence, and n and n are measurement noise vectors, which are ˙ ˙ g a δtionom and δttropo are ignored in the measurement, yielding 2 m modeled as white noise sequences with covariances σg I3×3 the measurement model given by 2 and σg I3×3, respectively. T r j r j , E j [ r( ) − leom ( )] The EKF prediction step produces xˆ(k|j) [x(k)|Z ] of ρ˙leom (j) ≈ [r˙ leom (j) − r˙ r(j)] krr(j) − rleo (j)k x(k), and an associated estimation error covariance Px(k|j), m 2 E j , ˙ ˙ where [·|·] is the conditional expectation operator, Z + c · δtr(j) − δtleom (j) + vleom (j). (10) {z(i)}j are the set of measurements available up to and i=1 h i including time index j, and k > j. The measurements The STAN framework operates in a tracking mode when available z will be discussed in the next subsection. GNSS measurements are available and a STAN mode when The IMU measurements (7) and (8) are processed through GNSS signals are unavailable. In the tracking mode, the mea- strapdown INS equations using an Earth-centered Earth-fixed surement vector z processed by the EKF update is defined by B stacking all available GNSS pseudoranges and LEO satellite (ECEF) frame as frame G to produce G¯qˆ(k|j), rˆr(k|j), and ˆr˙ r(k|j) [31]. The gyroscopes’ and accelerometers’ biases Doppler measurements and is given by predictions b˙ g(k|j) and bˆa(k|j) follow from (1) and (2), T , T T respectively. The prediction of the clock states of both the z zgnss, ρ˙ leo , (11) receiver and the LEO satellite transceivers follow from (3) and h i , T , T (6), respectively. The prediction of the LEO satellites’ position zgnss zgnss1 ,...,zgnssL , ρ˙ leo [ρ ˙leo1 ,..., ρ˙leoM ] .   The EKF measurement update step produces xˆ(j|j) and an (i) Subscriber Communicators (SCs): There are several associated posterior estimation error covariance Px(j|j). The types of SCs. Orbcomm’s SC for fixed data applications uses corresponding measurement Jacobian of z is given by low-cost, very high frequency (VHF) electronics. The SC for T mobile two-way messaging is a hand-held, stand-alone unit. T T H = H , H , (12) zgnss ρ˙ leo (ii) Ground Segment: The ground segment consists of gate- way control centers (GCCs), gateway Earth stations (GESs), where H is the measurementh Jacobiani of z , which is zgnss gnss and the network control center (NCC). The GCC provides given by switching capabilities to link mobile SCs with terrestrial based T T 0 × h 0 × h 0 × customer systems via standard communications modes. GESs 1 3 gnss1 1 9 clk 1 8M . . . . . link the ground segment with the space segment. GESs mainly H = . . . . . , zgnss  . . . . .  T T track and monitor satellites based on orbital information from 01×3 hgnss 01×9 hclk 01×8M the GCC and transmit to and receive from satellites, the GCC,  L    where or the NCC. The NCC is responsible for managing the Orb- comm network elements and the gateways through telemetry rˆr − rgnss 1 h = l , h = . monitoring, system commanding, and mission system analysis. gnssl krˆ − r k clk 0 r gnssl   (iii) Space Segment: Orbcomm satellites are used to com- The measurement Jacobian of ρ˙ leo is given by plete the link between the SCs and the switching capability at the NCC or GCC. H H Hρ˙ leo = ρ˙ leo,r ρ˙ ,leo ,   B. Orbcomm LEO Satellite Constellation H ˙ ,r = ρleo The Orbcomm constellation, at maximum capacity, has up T T T T T 01×3 −(h − h hvleo h ) −h b to 47 satellites in 7 orbital planes A–G, illustrated in Fig. 2. vleo1 rleo1 1 rleo1 rleo1 . . . . Planes A, B, and C are inclined at 45◦ to the equator and  . . . .  , T T T T T each contains 8 satellites in a circular orbit at an altitude of 0 × h h h h h b ◦  1 3 −( vleo − rleo vleo rleo ) − rleo   M 1 M M M  approximately 815 km. Plane D, also inclined at 45 , contains  ˆ ˆ  7 satellites in a circular orbit at an altitude of 815 km. PlaneE rˆr − rˆleom r˙ r − r˙ leom ◦ hr = , hv = , is inclined at 0 and contains 7 satellites in a circular orbit at leom krˆ − rˆ k leom krˆ − rˆ k ◦ r leom r leom an altitude of 975 km. Plane F is inclined at 70 and contains T 2 satellites in a near-polar circular orbit at an altitude of 740 b = [ 01×7, 1 ] , Hρ˙ ,leo = diag [Hρ˙ ,leo1 ,..., Hρ˙ ,leoM ] , km. Plane G is inclined at 108◦ and contains 2 satellites in a near-polar elliptical orbit at an altitude varying between 785 H = ρ˙ ,leom km and 875 km. T T T T (hv − hr hvleo hr ) hr 0 −1 . leom leom m leom leom ◦ Plane G (108 ) Planes A, B, and C: 8 satellites Whenh GNSS measurements become unavailable, the frame-i each with orbital altitude 815 km 45◦ work switches to the STAN mode, at which point the mea- Plane D ( ) Plane D: 7 satellites with orbital altitude 815 km ◦ surement vector (11) and the measurement Jacobian (12) are Plane B (45 ) ′ ′ Plane E: 7 satellites with orbital altitude 975 km replaced with z = ρ˙ leo and H = Hρ˙ , respectively. The ◦ leo Plane E (0 ) next section discusses the Orbcomm LEO satellite constella- Plane F: 2 satellites tion from which the Doppler measurements were drawn to aid Equator with orbital altitude 740 km the INS in the UAV experiment presented in Section IV. 45◦ Plane G: 2 satellites Plane C ( ) with orbital altitude 785{875 km

III. ORBCOMM SYSTEM 45◦ Plane A ( ) Existing Satellites This section gives an overview of the Orbcomm satellite Future Satellites 70◦ constellation and discusses the signals that were exploited to Plane F ( ) Note: Drawing not to scale the INS. Fig. 2. Orbcomm LEO satellite constellation. Map data: Google Earth. A. Orbcomm System Overview The Orbcomm system is a wide area two-way commu- C. Orbcomm Downlink Signals nication system that uses a constellation of LEO satellites to provide worldwide geographic coverage for sending and The LEO receiver draws pseudorange rate observables from receiving alphanumeric packets [33]. The Orbcomm system Orbcomm LEO signals on the downlink channel. Satellite consists of three main components: (i) subscriber commu- radio frequency (RF) downlinks to SCs and GESs are within nicators (users), (ii) ground segment (gateways), and (iii) the 137–138 MHz VHF band. Downlink channels include 12 space segment (constellation of satellites), which are briefly channels for transmitting to SCs and one gateway channel, discussed next. which is reserved for transmitting to the GESs. Each satellite transmits to SCs on one of the 12 subscriber downlink chan- Storage LabVIEW MATLAB-based estimator nels through a frequency-sharing scheme that provides four- MATRIX SDR VHF dipole RTL-SDR fold channel reuse. The Orbcomm satellites have a subscriber antenna transmitter that provides a continuous 4800 bits-per-second DJI (bps) stream of packet data using symmetric differential- Matrice 600 Multi-frequency quadrature phase shift keying (SD-QPSK). Each satellite also GNSS antennas has multiple subscriber receivers that receive short bursts from GPS antennas the SCs at 2400 bps. Note that Orbcomm satellites are also equipped with a Integrated AsteRx-iV GNSS-IMU VN-100 IMU specially constructed 1-Watt ultra high frequency (UHF) trans- module mitter that is designed to emit a highly stable signal at 400.1 Fig. 3. Experimental setup. MHz. The transmitter is coupled to a UHF antenna designed to have a peak gain of approximately 2 dB. The UHF signal B. Results is used by the Orbcomm system for SC positioning. However, experimental data shows that the UHF beacon is absent. The UAV flew a commanded trajectory over a 120-second Moreover, even if the UHF beacon was present, one would period during which 2 Orbcomm LEO satellites were avail- need to be a paying subscriber to benefit from positioning able. Two estimators were implemented to estimate the flown services. Consequently, only downlink channel VHF signals trajectories: (i) the LEO signal-aided INS STAN framework are exploited to aid the INS. described in Section II and (ii) a traditional GPS-aided INS for comparative analysis. The receiver clock was modeled to be equipped with a IV. EXPERIMENTAL RESULTS typical temperature-compensated crystal oscillator (TCXO), −20 −21 with {h0,r,h−2,r} = {9.4 × 10 , 3.8 × 10 }. The values This section presents experimental results of a UAV navigat- 2 {h ,h− } corresponding to the LEO satellites’ ing with the proposed STAN framework. First, the experimen- 0,leom 2,leom m=1 clocks were solved for online while GPS signals were still tal setup is described, then experimental results are provided. available. The measurement noise variances of the LEO satel- 2 lite signal Doppler measurements σ2 were deter- leom m=1 A. Experimental Setup mined empirically offline while GPS measurements were still  An experimental test was conducted in Riverside, California available. The initial estimates of the position and velocity for each Orbcomm LEO satellite were found using an SGP to evaluate the performance of the proposed LEO signal-aided INS STAN framework. To this end, a DJI Matrice 600 UAV model and TLE files downloaded on June 15, 2018. The corresponding initial estimation error 1-standard deviations for was equipped with following hardware and software setup: 3 each satellite were set to (3 × 10 ) · I3×3 m and 100 · I3×3 • A low-cost VHF dipole antenna. m/s for the position and velocity, respectively, where I3×3 • An RTL-SDR dongle to sample Orbcomm signals. is a 3 × 3 identity matrix. The UAV’s position and velocity • A laptop computer to store the sampled Orbcomm and their corresponding uncertainties were initialized using signals. These samples were then processed by the the Septentrio AsteRx-i V integrated GNSS-IMU solution and Multi-channel Adaptive TRansceiver Information eXtrac- associated estimation error covariance, respectively. tor (MATRIX) software-defined quadrature phase-shift Each estimator had access to GPS for only the first 90 keying (QPSK) receiver developed by the Autonomous seconds of the run as illustrated in Fig. 4 (d). Fig. 4 (a) shows Systems Perception, Intelligence, and Navigation (AS- the trajectory of the 2 Orbcomm LEO satellites traversed over PIN) Laboratory to perform carrier synchronization and the course of the experiment. The 3-D position root mean- extract pseudorange rate observables [34]. squared error (RMSE) of the traditional GPS-aided INS’s • A Septentrio AsteRx-i V integrated GNSS-IMU, which is navigation solution after GPS became unavailable was 14.4 equipped with a dual-antenna, multi-frequency GNSS re- meters with a final error of 31.7 meters. The 3-D position ceiver and a Vectornav VN-100 micro-electromechanical RMSE of the UAV’s trajectory for the LEO signal-aided INS system (MEMS) IMU. Septentrio’s post-processing soft- was 6.8 meters with a final error of 8.8 meters. The estimated ware development kit (PP-SDK) was used to process satellite trajectory and the along-track, radial, cross-track 95th- Global Position System (GPS) carrier phase observables percentile final uncertainty ellipsoid of one of the satellite’s collected by the AsteRx-i V and by a nearby differential position states are illustrated in Fig. 4 (b). GPS base station to obtain a carrier phase-based nav- igation solution. This integrated GNSS-IMU real-time V. CONCLUSIONS kinematic (RTK) system [35] was used to produce the This work presented a STAN framework which simultane- ground truth results with which the proposed navigation ously tracks LEO satellites and uses Doppler measurements framework was compared. drawn from their signals for aiding a vehicle’s INS in the The experimental setup is shown in Fig. 3. absence of GNSS signals. An overview of the EKF-based Orbcomm LEO satellite 1 [11] J. Khalife and Z. Kassas, “Navigation with cellular CDMA signals – part trajectory Riverside, California II: Performance analysis and experimental results,” IEEE Transactions on Signal Processing, vol. 66, no. 8, pp. 2204–2218, April 2018. [12] M. Driusso, C. Marshall, M. Sabathy, F. Knutti, H. Mathis, and Orbcomm F. Babich, “Vehicular position tracking using LTE signals,” IEEE Trans- LEO satellite 2 actions on Vehicular Technology, vol. 66, no. 4, pp. 3376–3391, April trajectory 2017. (c) [13] K. Shamaei and Z. 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