Warm Start Navigation with Non-Cooperative LEO Satellite via Online Ephemeris Error Estimation

Samer Hayek and Zaher Kassas

Peer Reviewed

Abstract:	The advent of recent and upcoming low Earth orbit (LEO) satellite megaconstellations is shaping a new era of satellite-based navigation. LEO-based communication has been offered over the past couple of decades by LEO constellations; such as Orbcomm, Iridium, and Globalstar; each of which composed of tens of LEO space vehicles (SVs). However, the launch of LEO megaconstellations; such as Starlink, OneWeb, Kuiper, Telesat, SpaceMobile; which are aggregately planning to launch tens of thousands of LEO SVs is promising to revolutionize several domains, bringing unprecedented high-resolution images; remote sensing; and global, high-availability, high-bandwidth, and low-latency Internet. Recently, the growing interest in utilizing LEO satellites for navigation purposes has been the subject of several theoretical and experimental studies [1–3]. While some studies proposed to design navigation-dedicated LEO satellite constellations [4], other research proposed to exploit LEO satellite signals for navigation in an opportunistic fashion [5–7]. The latter approach follows the paradigm of exploiting signals of opportunity (SOPs), which has shown substantial potential with terrestrial signals. Previous research that addressed opportunistic navigation with cellular signals has demonstrated meter-level navigation on ground vehicles [8] and submeter-accurate navigation on unmanned aerial vehicles [9]. LEO satellite signals have been regarded as an attractive navigation aiding source as they possess several desirable attributes [3]. First, the abundance of satellites in the LEO and the diversity of their distribution results in a favorable geometric dilution of precision (GDOP), and consequently more precise position and velocity estimates. Second, LEO satellites are typically deployed at altitudes around 500 - 1200 km, making their received signals to Earth-based receivers more powerful than GNSS signals, that reside in the medium Earth orbit (MEO) at 10 to 20 thousand kilometer altitudes. Third, different broadband LEO constellations transmit at various frequency bands that are favorable in terms of power efficiency, minimal propagation distortions and attenuation, and reduced noise and interference [3]. There are several challenges that need to be addressed to achieve reliable, opportunistic navigation with LEO satellite signals. Unlike GNSS satellites that transmit their precise ephemerides in their navigation message, most LEO constellations do not publicly transmit information about their position, velocity, and time. The North American Aerospace Defense Command (NORAD) publishes daily two line element files (TLE) that consist of the orbital elements of each satellite. Specifically, TLEs characterize a satellite’s orbit at a certain epoch time by its Keplerian elements: inclination, right ascension of ascending node, eccentricity, argument of perigee, mean anomaly, and mean motion. TLE files can be used to initialize orbit propagators such as the analytical Simplified General Perturbation (SGP4) model [10]. However, the resulting SV position errors are on the order of a few kilometers, which will inevitably induce growing navigation errors. Previous literature has demonstrated that propagation errors tend to be largest in the along-track direction, while the two other components, namely the cross-track and radial, have typically smaller errors [11]. Moreover, LEO satellites are not necessarily equipped with atomic clocks, nor are they precisely synchronized. In contrast to GNSS, where clock error corrections are periodically transmitted to users in the navigation message, such clock corrections may not be available for LEO satellites; in which case they must be estimated along with the receiver’s states. An improved LEO SV tracking framework was proposed in [12], entailing the estimation of the argument-of-latitude orbital element to mitigate the large ephemeris errors inherited from TLE-initialized SGP4 orbit propagation. The objective of this work is to develop a robust and accurate tracking approach for LEO SVs by a receiver extracting navigation observables from the SV’s downlink signals to enable reliable non-cooperative LEO PNT solutions. This research will examine the different error sources in the time and position domains, and how they impact pseudorange, carrier phase, and Doppler measurements. A preliminary simulation study was conducted to evaluate the proposed tracking framework’s performance for different LEO satellite constellations and different age-of-ephemeris. The simulations considered a known stationary tracking receiver extracting pseudorange measurements from four satellite constellations: Orbcomm, Starlink, OneWeb, and Iridium. A high-fidelity high precision orbit propagator (HPOP) is used to generate satellite orbit trajectories. For each of the four satellites, three different age-of-ephemeris sets are produced: the satellite is propagated forward for around 2, 10, and 20 hours with a time-step of one second to the initial time of visibility to a simulated tracking receiver located in Columbus, Ohio, USA. The LEO SV states obtained from TLE files are propagated using HPOP and SGP4, yielding two sets of ephemerides for the same satellite, with the HPOP ephemeris serving as the ground truth for the simulation study. The tracking receiver and LEO SVs were assumed to be equipped with oven-controlled crystal oscillators (OCXOs). The dynamics model adopted for the clock error states, the bias and drift, was the double integrator driven by white noise. The power-law coefficients of these oscillators are used to determine the discrete-time process noise covariance of the clock error states. The position, velocity, and clock error states for each LEO SV were estimated via an EKF and the resulting estimation errors are resolved in the SV RSW (along-track, cross-track, radial) reference frame. The initial argument of latitude tracking phase significantly decreases the errors in the along-track position and radial velocity states, while the errors in the other directions are refined when compared to the open-loop SPG4 during the rest of the tracking duration. The large initial errors of around 7.2 km in position and 7.59 m/s in velocity resulting from open-loop SGP4 propagation are decreased to 99.44 m and 0.65 m/s, respectively, at the end of the 300 second tracking duration. A preliminary experimental analysis was conducted with a ground vehicle equipped with a signal capture hardware setup for the VHF, L, and Ku frequency bands to collect Orbcomm, Iridium, Starlink, and OneWeb signals of opportunity. Doppler measurements were generated using the software-defined receiver (SDR) design described in [13–15] from 2 Orbcomm SVs, 1 Iridium NEXT SV, 4 Starlink SVs, and 1 OneWeb SV over the course of the experiment. While the vehicle traversed a total trajectory of 1.58 km during 70 seconds, GNSS signals were made unavailable for the final 1.054 km. The unaided solution resulted in a 3D RMSE of 110 m and diverged to a final error of 322 m. On the other hand, the LEO-aided solution, where the proposed timing and spatial ephemeris error compensation approach was implemented, resulted in a 3D vehicle position RMSE of 4.15 m and a final error 8.13 m. This paper aims to extend this work by presenting the following main contributions. First, comprehensive measurement models are specifically derived for pseudorange, carrier phase, and Doppler observables generated from non-cooperative LEO SV signals, including timing, orbit, and atmospheric effects. Second, the argument of latitude estimation performance is analyzed for different constellations and satellite-to-receiver relative geometry. Third, this work will present high-fidelity simulation results to evaluate the performance of the LEO SV tracking approach for various constellations, as well as the stationary positioning and LEO-aided inertial navigation performance when the refined orbits are employed. Fourth, the study will present experimental results where opportunistically extracted navigation observables from multi-constellation LEO SV signals are incorporated into an orbit estimation enabling vehicular LEO-aided inertial navigation system (INS). [1] T. Reid, T. Walter, P. Enge, D. Lawrence, H. Cobb, G. Gutt, M. O’Conner, and D. Whelan, “Position, navigation, and timing technologies in the 21st century,” vol. 2, ch. 43: Navigation from low Earth orbit – Part 1: concept, current capability, and future promise, pp. 1359–1379, WileyIEEE, 2021. [2] Z. Kassas, J. Khalife, and M. Neinavaie, “Navigation with differential carrier phase measurement from low Earth orbit satellites,” July 2020. [3] F. Prol, R. Ferre, Z. Saleem, P. V¨alisuo, C. Pinell, E. Lohan, M. Elsanhoury, M. Elmusrati, S. Islam, K. Celikbilek, K. Selvan, J. Yliaho, K. Rutledge, A. Ojala, L. Ferranti, J. Praks, M. Bhuiyan, S. Kaasalainen, and H. Kuusniemi, “Position, navigation, and timing (PNT) through low earth orbit (LEO) satellites: A survey on current status, challenges, and opportunities,” IEEE Access, vol. 10, pp. 83971–84002, 2022. [4] T. Reid, B. Chan, A. Goel, K. Gunning, B. Manning, J. Martin, A. Neish, A. Perkins, and P. Tarantino, “Satellite navigation for the age of autonomy,” in Proceedings of IEEE/ION Position, Location and Navigation Symposium, pp. 342–352, 2020. [5] W. Stock, R. Schwarz, C. Hofmann, and A. Knopp, “Survey on opportunistic pnt with signals from LEO communication satellites,” IEEE Communications Surveys & Tutorials, pp. 1–31, 2024. [6] C. Zhao, H. Qin, and Z. Li, “Doppler measurements from multiconstellations in opportunistic navigation,” IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–9, 2022. [7] M. Neinavaie, J. Khalife, and Z. Kassas, “Blind opportunistic navigation: Cognitive deciphering of partially known signals of opportunity,” in Proceedings of ION GNSS Conference, pp. 2748–2757, September 2020. [8] M. Maaref and Z. Kassas, “Autonomous integrity monitoring for vehicular navigation with cellular signals of opportunity and an IMU,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, pp. 5586–5601, June 2022. [9] K. Shamaei and Z. Kassas, “Sub-meter accurate UAV navigation and cycle slip detection with LTE carrier phase,” in Proceedings of ION GNSS Conference, September 2019. accepted. [10] D. Vallado and P. Crawford, “SGP4 orbit determination,” in Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit, pp. 6770–6799, August 2008. [11] P. Easthope, “Examination of SGP4 along-track errors for initially circular orbits,” IMA Journal of Applied Mathematics, vol. 80, no. 2, pp. 554–568, 2015. [12] S. Hayek, J. Saroufim, and Z. Kassas, “Ephemeris error correction for tracking non-cooperative leo satellites with pseudorange measurements,” in Proc. IEEE Aerosp. Conf, pp. 1–9, 2024. [13] S. Kozhaya, H. Kanj, and Z. Kassas, “Multi-constellation blind beacon estimation, Doppler tracking, and opportunistic positioning with OneWeb, Starlink, Iridium NEXT, and Orbcomm LEO satellites,” in Proceedings of IEEE/ION Position, Location, and Navigation Symposium, pp. 1184–1195, April 2023. [14] S. Kozhaya and Z. Kassas, “A first look at the OneWeb LEO constellation: beacons, beams, and positioning,” IEEE Transactions on Aerospace and Electronic Systems, 2024. submitted. [15] S. Kozhaya and Z. Kassas, “Unveiling Starlink for PNT,” NAVIGATION, 2024. submitted.
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	112 - 123
Cite this article:	Hayek, Samer, Kassas, Zaher, "Warm Start Navigation with Non-Cooperative LEO Satellite via Online Ephemeris Error Estimation," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 112-123.
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