RT Journal Article
SR Electronic
T1 Weiss–Weinstein Bound of Frequency Estimation Error for Very Weak GNSS Signals
JF NAVIGATION: Journal of the Institute of Navigation
JO NAVIGATION
FD Institute of Navigation
SP navi.654
DO 10.33012/navi.654
VO 71
IS 3
A1 Zhang, Xin
A1 Zhan, Xingqun
A1 Huang, Jihong
A1 Liu,, Jiahui
A1 Xiao, Yingchao
YR 2024
UL https://navi.ion.org/content/71/3/navi.654.abstract
AB Tightness remains the primary goal in all modern estimation bounds. For very weak signals, tightness is enabled by appropriately selecting the prior probability distribution and bound family. While current bounds in global navigation satellite systems (GNSSs) assess the performance of carrier frequency estimators under Gaussian or uniform assumptions, the circular nature of frequency is overlooked. Of all bounds in the Bayesian framework, the Weiss–Weinstein bound (WWB) stands out because it is free from regularity conditions or restrictions on the prior distribution. Therefore, the WWB is extended for the current frequency estimation problem. A divide-and-conquer type of hyperparameter tuning method is developed to mitigate issues of computational complexity for the WWB family while enhancing tightness. Synthetic results show that for a von Mises prior probability distribution, the WWB provides a bound up to 22.5% tighter than the Ziv–Zakaï bound when the signal-to-noise ratio varies between –3.5 dB and –20 dB, where the GNSS signal is deemed extremely weak.