Title: An Interacting Multiple Model Estimator of LEO Satellite Clocks for Improved Positioning

Authors: Nadim Khairallah and Zaher (Zak) M. Kassas

We are witnessing a space renaissance. Tens of thousands of broadband low Earth orbit (LEO) satellites are expected to be launched by the end of this decade. These planned megaconstellations of LEO satellites along with existing constellations will shower the Earth with a plethora of signals of opportunity, diverse in frequency and direction. These signals could be exploited for navigation in the inevitable event that GNSS signals become unavailable (e.g., in deep urban canyons, under dense foliage, during unintentional interference, and intentional jamming) or untrustworthy (e.g., under malicious spoofing attacks).

In order to use LEO satellites’ signals for time-of-arrival (TOA)-based positioning, the LEO satellites’ clock error must be known. Unlike global navigation satellite system (GNSS) satellites, LEO satellites generally do not openly transmit information about their clock error in their downlink signals. While the clock error states (bias and drift) can be estimated, the stability of the oscillator is generally unknown. Knowledge of the oscillator’s stability is essential to calculate the covariance matrix of the process noise driving the clock error states.

This paper addresses this challenge by developing an interacting multiple-model (IMM) estimator to adaptively estimate the process noise covariance of LEO satellite clocks. Experimental results are presented showing a stationary ground receiver localizing itself with carrier phase measurements from a single Orbcomm LEO satellite. The developed IMM is shown to reduce the localization error and improve filter consistency over two fixed, mismatched extended Kalman filters (EKFs). Starting with an initial receiver position error of 1.45 km, the IMM yielded a final error of 111.26 m, while the errors of a conservative and optimistic EKFs converged to 254.71 m and 429.35 m, respectively.

Nadim Khairallah received his M.S. in Mechanical and Aerospace Engineering from the University of California, Irvine and B.E. in Mechanical Engi- neering with High Distinction from the American University of Beirut. He was a member of the Autonomous Systems Perception, Intelligence, and Navigation (ASPIN) Laboratory. He is a recipient of the 2022 IEEE Vehicular Technology Conference best student paper award. His research interests in- clude satellite-based opportunistic navigation, sensor fusion, and estimation theory.

Zaher (Zak) M. Kassas is a professor at The Ohio State University and director of the Autonomous Systems Perception, Intelligence, and Navigation (ASPIN) Laboratory. He is also director of the U.S. Department of Transportation Center: CARMEN (Multimodal AssurED (Center for Automated Vehicle Research with d Navigation), focusing on navigation resiliency and security of highly automated transportation systems. He received a B.E. in Electrical Engineering from the Lebanese American University, an M.S. in Electrical and Computer Engineering from The Ohio State University, and an M.S.E. in Aerospace Engineering and a Ph.D. in Electrical and Computer Engineering from The University of Texas at Austin. He is a recipient of the 2018 National Science Foundation (NSF) CAREER award, 2019 Office of Naval Research (ONR) Young Investigator Program (YIP) award, 2022 Air Force Office of Scientific Research (AFOSR) YIP award, 2018 IEEE Walter Fried Award, 2018 Institute of Navigation (ION) Samuel Burka Award, and 2019 ION Col. Thomas Thurlow Award. He is a Senior Editor of the IEEE Transactions on Intelligent Vehicles and an Associate Editor of the IEEE Transactions on Aerospace and Electronic Systems and the IEEE Transactions on Intelligent Transportation Systems. His research interests include cyber-physical systems, estimation theory, navigation systems, autonomous vehicles, and intelligent transportation systems.