Abstract
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula> -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.
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