Observability Analysis of Receiver Localization via Pseudorange Measurements From a Single LEO Satellite

This letter presents an observability analysis for terrestrial receiver localization via pseudorange measurements extracted from a single low Earth orbit (LEO) satellite. It is shown that a stationary receiver with an unknown state (position and time) can theoretically localize itself with a LEO satellite with a known state (position, velocity, and time). In addition, bounds on the determinant of the $l$ -step observability matrix are derived and geometric interpretations are presented indicating directions of poor observability. The implications of the analysis on observability-aided LEO satellite selection are discussed. Experimental results are presented showcasing the conclusions of the observability analysis for a receiver localizing itself with a single Starlink satellite or a single Orbcomm satellite.