On the asymptotic analysis of Cramer-Rao bound for time delay estimation

Starting with the most elementary probability formula of the Fisher matrix for time delay estimation in radar signals, a rigorously asymptotic expression of the Fisher matrix for time delay, Doppler shift and its higher derivatives, joint estimation is derived by using the asymptotic equivalent property of the Toeplitz matrix and circulant matrix, and the spectrum characteristics of circulant matrices. The present result is more accurate than the commonly used one. A comparison between the two results shows that under certain conditions the agreement of the two results is seen to be excellent