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

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.