Ultra-High Precision LEO Doppler Localization Facilitated by Rydberg Atomic Receivers

In this paper, we propose a low earth orbit (LEO) Doppler localization method facilitated by Rydberg atomic receivers (RARs), whose intrinsic ultra-high sensitivity enables a significant leap in the localization accuracy over traditional radio-frequency (RF) conductor-based antennas, achieving what we term <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ultra-high precision</i>. This method leverages Doppler shifts in the signals transmitted between ground users and fast-moving LEO satellites for precise localization. Initially, we formulate the signal reception model and analyze the operating principles of RARs, highlighting their inherent low-noise superiority over traditional antennas. To fully harvest the low-noise property of RARs, we develop an efficient and fidelity-robust Levenberg-Marquardt particle filter (LM-PF) algorithm for the joint localization using multiple RAR-equipped LEO satellites. Finally, we derive the Cramér-Rao lower bound (CRLB) for both the RAR-based and RF-based localization methods, which quantitatively characterize the performance gains offered by the low-noise property of RARs. Simulation results show that, when the transmit power is merely 7 dBm, where traditional antennas struggle to recover the precise user location, the RAR-based LEO localization can still achieve an error less than 10 meters.