Nadim Khairallah and Zak Kassas; University of California, Irvine

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Abstract:

Low Earth orbit (LEO) space vehicles (SVs) have the potential to revolutionize navigation in the near future. As of March 2021, there are around 5,000 SVs in low Earth orbits [1] and this number is expected to reach the 57,000 satellites planned to be launched by the end of the decade [2] as the LEO space race is fueled by the design of mega-constellations [3]. The most notable example is the Starlink constellation built by SpaceX which has filed with the Federal Communications Commision (FCC) for permission to launch 30,000 LEO SVs, in addition to the already approved 12,000 Starlink satellites [4]. As a consequence, LEO SVs present an amazing promise as navigation sources for a receiver leveraging many of their inherently advantageous characteristics: abundance, geometric and spectral diversities, and high received powers. However, the first prerequisite to navigate using SVs’ signals is to know the SVs’ ephemeris. Being mainly launched by private companies for communication and broadband Internet, LEO SVs do not usually broadcast their ephemerides in their proprietary signals. Therefore, in order to be used for navigation, LEO SVs have to be exploited as signals of opportunity (SOPs), but two main challenges present themselves for opportunistic navigation with LEO SVs’ signals: (i) processing the partially known or even completely mysterious LEO SVs’ signals to extract navigation observables and (ii) determining the LEO SVs’ ephemeris, clock offset from a reference time base, and rate of change of this clock offset. The first challenge can be addressed with the design of specialized software-defined radio (SDR) receivers that exploit the periodic signals with favorable correlation properties transmitted by LEO SVs to extract navigation observables [5-6]. Even mysterious signals can be meaningfully processed by cognitive receivers to obtain useful navigation information [7-8]. Furthermore, with the development of these receivers, code phase (i.e., pseudorange) measurements could be extractable from LEO SVs’ signals in addition to Doppler (i.e., pseudorange rate) measurements. The second challenge to be addressed for LEO opportunistic navigation is to deal with the uncertain SVs’ ephemeris and unknown clock error states. The most accurate publicly available source to calculate the ephemeris of LEO SVs are two-line element (TLE) sets constantly updated by the North American Aerospace Defense Command (NORAD), which consist of a list of mean orbital elements (inclination angle, right ascension of ascending node, eccentricity, argument of perigee, mean anomaly, and mean motion) given at a specified time epoch [9] that a simplified general perturbation model SGP4, can propagate to a desired inquiry time [10]. Although SGP4 takes into account the variation of the orbital elements due to Earth’s oblateness, atmospheric drag, and various short and long-term perturbations, the TLE-propagated satellite position suffers from error of a few kilometers from the actual satellite position, which degrades any navigation performance. [11] presented a complete framework to tackle this challenge by refining the SVs’ ephemeris and clock states via closed-loop tracking of LEO SVs by a receiver opportunistically extracting pseudorange and Doppler measurements from the SVs’ signals. [11] first proposed a method to characterize the process noise covariance of the LEO SVs’ orbital motion; then implemented an extended Kalman filter (EKF) to track the LEO SVs’ states using (i) pseudorange, (ii) Doppler, and (iii) fused pseudorange and Doppler measurements; and finally showcased the effect of the refined SVs’ ephemeris in the context of stationary receiver localization. In addition to matching the process noise covariance for the SV motion as was done in [11], it is also important to correctly characterize the process noise covariance of the LEO SV clock states as any mismatch will degrade the estimation performance. This process noise covariance of the clock states depends on the oscillator stability onboard the LEO SVs. The quality of these oscillators vary widely between temperature-compensated crystal oscillator (TCXO), oven-controlled crystal oscillator (OCXO), and chip-scale atomic clock (CSAC) and can be determined from the power-law coefficients, which characterize the power spectral density of the fractional frequency deviation of the oscillators [12]. Oscillator quality of cellular towers, used opportunistically for navigation, was investigated using adaptive estimation techniques, namely maximum likelihood (ML)-based adaptive EKF and interacting multiple-model (IMM) in [13]. This paper will perform a similar study to characterize the process noise covariance of the clock error states associated with oscillators onboard LEO SVs with the goal of improving LEO-based opportunistic navigation. An IMM adaptive estimator, developed in [14], will be implemented to adaptively estimate the LEO clock states process noise covariance online and thus characterize the stability of the oscillators onboard LEO SVs. Simulations will be performed to show that the IMM estimator converges to the simulated process noise, thus correctly identifying the clock quality. Experimental demonstration of the proposed estimator with a receiver opportunistically extracting carrier phase measurements from Orbcomm SVs’ signals will be performed to characterize the stability of the oscillators onboard Orbcomm SVs, which is expected to improve the navigation solution. References [1] A. Boley and M. Byers, “Satellite mega-constellations create risks in Low Earth Orbit, the atmosphere and on Earth,” Scientific Reports, vol. 11, no. 1, pp. 1–8, 2021. [2] International Business Times, “57,000 Satellites To Jostle For Space Around Earth's Orbit By 2029” https://www.ibtimes.com/57000-satellites-jostle-space-around-earths-orbit-2029-2914462 [3] G. Ritchie and T. Seal, “Why low-Earth orbit satellites are the new space race,” https://www.washingtonpost.com/business/why-low-earth-orbit-satellites-are-the-new-space-race/2020/07/10/51ef1ff8-c2bb-11ea-8908-68a2b9eae9e0 story.html, July 2020. [4] J. Brodkin, “SpaceX says 12,000 satellites isn’t enough, so it might launch another 30,000,” https://arstechnica.com/information-technology/2019/10/spacex-might-launch-another-30000-broadband-satellites-for-42000-total, October 2019. [5] R. Landry, A. Nguyen, H. Rasaee, A. Amrhar, X. Fang, and H. Benzerrouk, “Iridium Next LEO satellites as an alternative PNT in GNSS denied environments–part 1,” Inside GNSS Magazine, vol. 14, no. 3, pp. 56–64., May 2019. [6] J. Khalife, M. Neinavaie, M. Orabi, and Z. Kassas, “Experimental demonstrations of positioning with signals of opportunity from multi-constellation LEO satellites: Starlink, Orbcomm, and Iridium,” in Proceedings of ION GNSS Conference, September 2021, accepted. [7] M. Neinavaie, J. Khalife, and Z. Kassas, “Blind Doppler tracking and beacon detection for opportunistic navigation with LEO satellite signals,” in Proceedings of IEEE Aerospace Conference, March 2021, pp. 1–8. [8] J. Khalife, M. Neinavaie, and Z. Kassas, “The first carrier phase tracking and positioning results with Starlink LEO satellite signals,” IEEE Transactions on Aerospace and Electronic Systems, 2021, accepted. [9] North American Aerospace Defense Command (NORAD), “Two-line element sets,” http://celestrak.com/NORAD/elements/. [10] D. Vallado and P. Crawford, “SGP4 orbit determination,” in Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit, August 2008, pp. 6770–6799. [11] N. Khairallah and Z. Kassas, “Ephemeris Closed-Loop Tracking of LEO Satellites with Pseudorange and Doppler Measurements,” in Proceedings of ION GNSS Conference, September 2021, accepted. [12] J. Curran, G. Lachapelle, and C. Murphy, “Digital GNSS PLL design conditioned on thermal and oscillator phase noise,” IEEE Trans. on Aerospace and Electronic Systems, vol. 48, no. 1, pp. 180–196, Jan. 2012. [13] Z. Kassas, V. Ghadiok, and T. Humphreys, “Adaptive estimation of signals of opportunity,” in Proceedings of ION GNSS Conference, September 2014, pp. 1679–1689. [14] Y. Bar-Shalom, X. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation. New York, NY: John Wiley & Sons, 2002.