Weiss-Weinstein Bound of Frequency Error Considering von Mises Distribution as Prior for Very Weak GNSS Signals

Xin Zhang, Xingqun Zhan, Jihong Huang, Jiahui Liu, Yingchao Xiao

Peer Reviewed

Abstract:	Frequency tracking, usually serving as the pull-in stage for phase tracking, is a fundamental estimation problem in global navigation satellite system (GNSS) receivers. A lower bound tighter than existing bounds is developed for predicting frequency estimation errors. The traditional way of lower bounding the estimation errors using Cramér-Rao lower bound (CRB) does not take into account the prior information. Of all bounds in Bayesian framework, Weiss-Weinstein bound (WWB) stands out since it is free from regularity conditions imposed on a priori distribution. Therefore, a WWB is developed for the current frequency estimation problem. It is evaluated against state-of-the-art estimation bounds. Synthetic results show that the WWB provides a tighter bound than other bounds and thus is a good candidate for exhausting the potentials of any maximum-a-posteriori (MAP) principled estimator.
Published in:	Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023) September 11 - 15, 2023 Hyatt Regency Denver Denver, Colorado
Pages:	3374 - 3404
Cite this article:	Zhang, Xin, Zhan, Xingqun, Huang, Jihong, Liu, Jiahui, Xiao, Yingchao, "Weiss-Weinstein Bound of Frequency Error Considering von Mises Distribution as Prior for Very Weak GNSS Signals," Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Denver, Colorado, September 2023, pp. 3374-3404. https://doi.org/10.33012/2023.19240
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