First Results of Differential Doppler Positioning with Unknown Starlink Satellite Signals

This paper shows the first results of differential Doppler positioning with unknown low Earth orbit (LEO) Star-link satellite signals. To this end, a receiver capable of acquiring and tracking the Doppler frequency of Starlink satellites is developed. A sequential method is proposed to estimate the number of active Starlink satellites and their corresponding reference signals (RSs). The proposed method is based on the classic linear model, where it is shown that the classic linear model results in the so-called matched subspace detector. A closed form of the probability of false alarm in the presence of Doppler estimation error is derived. Next, a Doppler tracking algorithm is designed, which is based on the generalized likelihood ratio (GLR) detector. In order to compensate for the high dynamics of Starlink LEO satellites, a linear chirp model is employed in the Doppler tracking algorithm, and a Kalman filter (KF)-based tracking algorithm is designed to track the chirp parameters. To validate the proposed framework, experimental results are presented in which a base with a known position and a rover with an unknown position were equipped with the proposed receiver. Despite the unknown nature of Starlink satellite signals, it is shown that the proposed receiver is capable of acquiring three Starlink satellites and tracking their Doppler frequencies. Next, two baselines between the base and rover receivers were considered: 1 km and 9 m. Despite the fact that the satellites' ephemerides are poorly known (with errors on the order of several kilometersm since they are predicted from two-line element (TLE) files and an SGP4 propagator), the proposed differential framework was able to estimate the rover's two-dimensional position with an error of 5.6 m and 2.6 m, respectively.