  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.
