Instant Positioning by Single Satellite: Delay-Doppler Analysis Method Enhanced by Beam-Hopping

Terminal positioning using a single low earth orbit (LEO) communication satellite is an important means to compensate for the loss of positioning capability under global navigation satellite system (GNSS) denial. Traditional single-satellite positioning relies on the accumulative measurement over a segment of the trajectory, resulting in a long response time. In this paper, we propose a novel single-satellite positioning scheme, achieving instant positioning through the joint use of time-frequency Doppler analysis of signals and communication beam switching. First, through wide beam reception, range and velocity information are extracted using interpolation enhanced parameter estimation to determine candidate coordinates. To eliminate ambiguity in this process, further disambiguation is achieved through the high directivity of the narrow beam. The proposed scheme is proved to reach the Cramér-Rao lower bound (CRLB) while achieving real-time positioning with the central limit theorem (CLT). Simulation results indicate that at a signal-to-noise ratio (SNR) of 17 dB, the probability of positioning error being lower than 50 meters can reach 97.5%, demonstrating performance comparable to existing schemes.