Observability Analysis of Opportunistic Receiver Localization with LEO Satellite Pseudorange Measurements

Ralph Sabbagh, Zaher M. Kassas

Abstract: An observability analysis of terrestrial receiver localization via pseudorange measurements extracted from a single low Earth orbit (LEO) satellite is presented. It is concluded that a stationary receiver with an unknown state (position and time) can localize itself with measurements from a LEO satellite with a known state (position, velocity, and time). In addition, bounds on the determinant of the observability matrix are derived. The relationship between the satellite’s relative orbital inclination angle and geometric diversity of the line-of-sight vectors from the receiver to the satellite is analyzed, leading to geometric interpretations indicating directions of poor observability. Experimental results are presented showcasing the conclusions of the observability analysis for a receiver localizing itself with a single Starlink LEO satellite or a single Orbcomm LEO satellite. Finally, an observability-aided LEO satellite selection strategy is discussed.
Published in: Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022)
September 19 - 23, 2022
Hyatt Regency Denver
Denver, Colorado
Pages: 1890 - 1901
Cite this article: Sabbagh, Ralph, Kassas, Zaher M., "Observability Analysis of Opportunistic Receiver Localization with LEO Satellite Pseudorange Measurements," Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022), Denver, Colorado, September 2022, pp. 1890-1901. https://doi.org/10.33012/2022.18540
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