Algebraic analysis of Doppler-based positioning with application to LEO satellites

In this paper we revisit positioning from Doppler measurements, using techniques from algebraic geometry to produce new theoretical insights and efficient localization algorithms. First, we give a full characterization of the problem, identifying for each problem their minimal configurations, that is the minimum number of receivers and transmitters to have a finite number of solutions. We also study the degree of each configuration. Finally, we show how these algebraic techniques can be applied to obtain an accurate position estimation in challenging environments, such as in the presence of noise and outliers. We also describe how the derived optimized algebraic solver can be integrated in a positioning engine for Low Earth Orbit position, navigation and timing (LEO PNT) systems.