Doppler-Based Localization Under Hardware, Atmospheric, and Orbital Impairments for Single LEO Satellite Systems
In order to enable a wide range of applications anywhere and anytime, future communication systems are expected to employ low Earth orbit satellites to perform user verification. Single-satellite systems offer a cost-effective verification alternative, reducing implementation complexity and dependence on satellite constellations. This article develops a single-pass, single-satellite localization algorithm independent from global navigation satellite systems, supporting user verification and requiring only coarse coverage-region side information. The algorithm is based on the tracking of phase changes from received pilot signals originated from Doppler shifts, inherently related to the user's position. Our work addresses realistic channel and receiver conditions—encompassing carrier frequency offset, phase noise, and atmospheric propagation effects—while evaluating robustness against orbital perturbations, a combination that has not been jointly addressed in prior studies on Doppler-based localization. The proposed two-stage approach employs an extended Kalman filter for estimation of the referred phase shifts, followed by a weighted least squares solution. Algorithm performance is evaluated through simulations in terms of mean and $90{\text{th}}$ percentile distance error, together with the time to reach a 10-km error level, an accuracy benchmark discussed in verification studies by 3rd Generation Partnership Project (3GPP). Results demonstrate improved accuracy with respect to compatible Doppler-based baselines, with $90{\text{th}}$ percentile errors falling below the 10-km mark under the considered narrowband and line-of-sight conditions, suggesting that the method may support user verification. The time required to achieve such accuracy, particularly, may require a significant portion of the satellite's visibility window in strong phase noise conditions.