Weiss-Weinstein bound of frequency estimation error for very weak GNSS signals

Abstract: Tightness remains the center quest in all modern estimation bounds. For very weak signals, this is made possible with judicial choices of prior probability distribution and bound family. While current bounds in GNSS assess performance of carrier frequency estimators under Gaussian or uniform assumptions, the circular nature of frequency is overlooked. In addition, of all bounds in Bayesian framework, Weiss-Weinstein bound (WWB) stands out since it is free from regularity conditions or requirements on the prior distribution. Therefore, WWB is extended for the current frequency estimation problem. A divide-and-conquer type of hyperparameter tuning method is developed to level off the curse of computational complexity for the WWB family while enhancing tightness. Synthetic results show that with von Mises as prior probability distribution, WWB provides a bound up to 22.5% tighter than Ziv-Zaka\"i bound (ZZB) when SNR varies between -3.5 dB and -20 dB, where GNSS signal is deemed extremely weak.