Towards Navigation with Non-Cooperative LEO Satellites: Resolving Ephemeris and Timing Errors

Zaher Kassas, Joe Saroufim, Samer Hayek, Sharbel Kozhaya, and Will Barrett

Peer Reviewed

Abstract:	LEO PNT (low Earth orbit positioning, navigation, and timing) has captivated in recent years the research community, government agencies, and private industry [1]. The concept of LEO PNT, however, is not new. In fact, Transit, the first satellite-based navigation system, was LEO-based. Nevertheless, it took nearly an hour to produce a position estimate, necessarily waiting for enough satellites to pass overhead [2]. GPS, whose space vehicles (SVs) reside in medium Earth orbit (MEO), alleviated the inherent limitation of LEO PNT, whereby one needs orders of magnitude more satellites in LEO to achieve comparable PNT performance to what could be achieved with MEO-based SVs [3]. This paved the way for MEO-based global navigation satellite systems (GNSS) to dominate satellite-based PNT. And so, LEO PNT has been “shelved.” The past few years have heralded a new era in LEO. The number of LEO SVs orbiting Earth increased by an order of magnitude, from about 800 in 2019, to about 8,400 by the end of 2023. This is mainly attributed to the birth of so-called megaconstellations. Each of these constellations comprises hundreds to thousands of SVs launched into LEO with the purpose of providing high-speed internet connectivity virtually everywhere on Earth. At this point, SpaceX’s Starlink leads the megaconstellation “race,” with the most number of SVs in orbit (?5,400) and the most planned SVs (?12,000 with possible extension to ?42,000). Other megaconstellations include Amazon’s Kuiper (3,236), OneWeb (648), and Telesat (198). Similar to past “space races,” as the idea of LEO megaconstellations picked up steam in the late 2010’s, several players jumped on the promise of launching their own constellations, but then retracted and their promised constellations faded away. For example, Boeing initially planed a constellation of 2,956 LEO SVs, which was scaled down to 147, but eventually bowed down and relinquished its license in late 2023. Still, the LEO space race is just heating up. Despite some players dropping out, others are joining the race, which is expanding to beyond private industry to include government agencies. The European Union approved in early 2024 the Infrastructure for Resilience, Interconnectivity and Security by Satellite (IRIS2) LEO megaconstellation, comprising 450 SVs, while China is planning its “own version of Starlink,” comprising about 12,000 LEO SVs. Signals from LEO SVs offer attractive PNT attributes, compared to MEO SVs. First, LEO SVs transmit their signals in a wide swath of the frequency spectrum, making them more resilient to interference than MEO signals. Second, with a significantly higher relative velocity than MEO SVs, LEO SVs offer more informative Doppler measurements, leading to increased positioning accuracy. Third, LEO SVs are around twenty-times closer to Earth compared to GNSS SVs, which results in less spreading loss, improving the carrier-to-noise ratio by about 30 dB. Fourth, the sheer number of LEO SVs that will cover the Earth in diverse orbits offers favorable position dilution of precision (PDOP), particularly in “harsh GNSS environments,” in which there may not be clear line-of-sight from the receiver to the SVs [4]. LEO PNT concepts can be classified into four categories: 1. LEO-augmented GNSS: signals from LEO are fused with MEO GNSS signals for improved PNT [5] 2. Dual-purposed LEO: the hardware already designed and the spectrum already allocated for the SVs’ primary mission is dual-purposed for PNT [6] 3. PNT-dedicated LEO: the LEO constellation is launched for the sole purpose of providing PNT services [7] 4. Opportunistic LEO PNT: signals from whichever LEO constellation, whether PNT-dedicated or otherwise, are exploited for PNT [8] The opportunistic LEO PNT approach offers the most space and spectrum sustainability compared to the first three approaches, alleviating space congestion, generation of space debris, and allocation of scarce spectrum. Nevertheless, one needs to address three challenges associated with opportunistic LEO PNT with non-cooperative SVs, namely the unknown nature of the LEO SVs’: (i) downlink signal, (ii) clock error and synchronization schemes, and (iii) ephemerides. The first challenge has been addressed in the recent literature, where the signal structure of some unknown LEO SVs has been reported [9] and the ability to produce navigation observables (pseudorange, Doppler, and carrier phase) from partially known LEO SVs have been demonstrated [10]. Most notably, the paradigm of cognitive opportunistic navigation has proven its efficacy in blindly acquiring and tracking several non-cooperative LEO constellations: Starlink, OneWeb, Orbcomm, Iridium, and National Oceanic and Atmospheric Administration (NOAA), without assuming prior knowledge about the signal’s structure [11]–[12]. As for the second challenge, some solutions have been recently proposed in [13]–[14]. This paper focuses on the third challenge. Unlike GNSS SVs, most non-cooperative LEO SVs do not publicly transmit information about their ephemerides. Some information, albeit imprecise, can be obtained from so-called two-line element (TLE) files, published daily by the North American Aerospace Defense Command (NORAD). TLE files contain satellite-specific designated and temporal data in the first line, while the second line defines the SV’s Keplerian orbit, comprising a set of six parameters (inclination angle, right ascension of ascending node, eccentricity, argument of perigee, mean anomaly, and mean motion). The TLE file can be used to compute an estimate of the SV’s states, which in turn initializes orbit propagation algorithms including two- body, two-body with J2, simplified general perturbations 4 (SGP4), etc. The two-body model uses the Keplerian elements to predict the trajectory of spacecrafts and celestial bodies considering two spherical masses, subject to gravitational interaction. Nevertheless, celestial bodies are relatively far from spherical, and the model does not account for space perturbations caused by sun’s, moon’s, and planets’ gravitational pulls, as well as drag forces from fringes of the atmosphere. Although SGP4 accounts for various perturbations, the estimated Keplerian elements in the TLE files are imprecise, leading to several kilometers in the SV’s position uncertainty upon few hours of propagation, mainly concentrated in the SV’s along track direction. This challenge has been addressed by employing closed-loop SV tracking algorithms aiming to refine the SV’s ephemeris, utilizing pseudorange and/or Doppler measurements extracted from LEO downlink signals [15]. Another traditional and effective approach to reduce the effect of ephemerides error is differential navigation. Such approach consists of a rover with unknown states, and a base station with knowledge of its position, communicating navigation data to improve the rover’s positioning accuracy. This technique was first introduced in GNSS-based navigation, showing elimination or significant reduction of common mode errors (e.g., SV ephemerides errors, atmospheric delays, and SV clock errors). Recently, LEO-based differential navigation has showed promising performance with carrier phase measurements from Orbcomm LEO SVs [16] and Doppler measurements from Iridium NEXT satellites [17], [18]. This paper deals with LEO PNT navigation with non-cooperative SVs with poorly known ephemerides. The following problem is considered. A rover (e.g., a pedestrian or ground/aerial vehicle), equipped with an inertial measurement unit (IMU) and GNSS and LEO receivers, is navigating in an environment comprising multiple LEO satellites, from which the LEO receiver extracts navigation observables (pseudorange or Doppler). When GNSS signals are available, the vehicle navigates by fusing GNSS, IMU, and altimeter measurements. When GNSS signals are cut off, LEO navigation observables are fused with the IMU in a tightly-coupled fashion via an extended Kalman filter (EKF). To address the problem of poorly known ephemerides, the simultaneous tracking and navigation (STAN) framework has been proposed [19], in which the LEO SV states are simultaneously estimated with the navigator’s states. STAN was later evolved to include a differential STAN (DSTAN) [20], with the incorporation of a differential base station with a known position. Preliminary simulation results have been conducted comparing STAN and DSTAN, showing that while STAN could achieve meter-level accuracy, DSTAN could achieve submeter-level accuracy. The simulation considered a fixed-wing aerial vehicle that traveled a 28 km trajectory for 300 seconds over Columbus, Ohio, USA. The vehicle was equipped with a tactical-grade IMU, an altimeter, a GNSS receiver, and a Starlink LEO receiver that produced pseudorange and Doppler measurements. The simulated environment also included three base stations, equipped with Starlink LEO receivers that produced pseudo- range and Doppler observables which were communicated to the aerial vehicle along with the base position positions. Fig. 1 (in the extended abstract) shows the vehicle’s trajectory, while Fig. 2 and 3 (in the extended abstract) show the EKF error plots with pseudorange and Doppler measurements. On the other hand, preliminary experimental results have demonstrated the efficacy of STAN (see Fig. 4 in the extended abstract). This paper builds on these promising results to study systematically the error sources in STAN and DSTAN, EKF divergence and boundedness, and sensitivity to varying the system parameters (number of LEO SVs, IMU and oscillator quality, and base stations). References [1] F. Prol, R. Ferre, Z. Saleem, P. Va ?lisuo, C. Pinell, E. Lohan, M. El- sanhoury, M. Elmusrati, S. Islam, K. Celikbilek, K. Selvan, J. Yliaho, K. Rutledge, A. Ojala, L. Ferranti, J. 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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:	796 - 801
Cite this article:	Kassas, Zaher, Saroufim, Joe, Hayek, Samer, Kozhaya, Sharbel, Barrett, Will, "Towards Navigation with Non-Cooperative LEO Satellites: Resolving Ephemeris and Timing Errors," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 796-801.
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