# Is it possible to do better than Cramér Rao lower bound for different estimation methods

I’m new to learning about the Cramér Rao lower bound. Does the calculation of the CRLB imply that only particular estimation algorithms can be used (e.g. estimating delay and Doppler from a complex ambiguity surface) which satisfy the CRLB inequality? And, if I have additional algorithms to refine those estimates and get higher precision ones, could I ever do better than the CRLB?

Or in other words, does the CRLB always hold for any possible algorithm I come up with to compute/estimate the quantity of interest?

• It does! So, can you put that in a formula that begins with $\hat f_{\text{Doppler}} = \arg\max\limits_?\ldots$, replace the $?$ with your bin index symbol and add it to your question? – Marcus Müller Apr 21 '19 at 15:31