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Doppler Positioning with LEO Mega-Constellation: Equation Properties and Improved Algorithm

Authors :
Zichen Xu
Zongnan Li
Xiaohui Liu
Zhimin Ji
Qianqian Wu
Hao Liu
Chao Wen
Source :
Remote Sensing, Vol 16, Iss 16, p 2958 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

Doppler positioning, as an early form of positioning, has regained significant research interest in the context of Low Earth Orbit (LEO) satellites.Given the LEO mega-constellation scenario, the objective function of Doppler positioning manifests significant nonlinearity, leading to ill-conditioning challenges for prevalent algorithms like iterative least squares (LS) estimation, especially in cases where inappropriate initial values are selected. In this study, we investigate the causes of ill-posed problems from two perspectives. Firstly, we analyze the linearization errors of the Doppler observation equations in relation to satellite orbital altitude and initial value errors, revealing instances where traditional algorithms may fail to converge. Secondly, from an optimization theory perspective, we demonstrate the occurrence of convergence to locally non-unique solutions for Doppler positioning. Subsequently, to address these ill-conditioning issues, we introduce Tikhonov regularization terms in the objective function to constrain algorithm divergence, with a fitted model for the regularization coefficient. Finally, we conduct comprehensive simulation experiments in both dynamic and static scenarios to validate the performance of the proposed algorithm. On the one hand, when the initial values are set to 0, our algorithm achieves high-precision positioning, whereas the iterative LS fails to converge. On the other hand, in certain simulation scenarios, the iterative LS converges to locally non-unique solutions, resulting in positioning errors exceeding 50 km in the north and east directions, several hundred kilometers in the vertical direction, and velocity errors surpassing 120 m/s. In contrast, our algorithm demonstrates typical errors of a position error of 6.8462 m, velocity error of 0.0137 m/s, and clock drift error of 8.3746 × 10−6 s/s. This work provides an effective solution to the sensitivity issue of initial points in Doppler positioning and can serve as a reference for the algorithm design of Doppler positioning receivers with LEO mega-constellations.

Details

Language :
English
ISSN :
20724292
Volume :
16
Issue :
16
Database :
Directory of Open Access Journals
Journal :
Remote Sensing
Publication Type :
Academic Journal
Accession number :
edsdoj.2f097f890dc402ca71038351e467555
Document Type :
article
Full Text :
https://doi.org/10.3390/rs16162958