Abstract: ln this paper, starting with the most elementary probability formula of Fisher matrix for time delay estimation, a rigorous asymptotic expression of Fisher matrix for time delay, Doppler shift and its higher derivative joint estimation is introduced by using the asymptotic equivalent property of Toeplitz matrix, circulant matrix, and the specrtum characteristic 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 excellent.

Key words: Toeplitz matrix, Cramer-Rao bound, time delay estimation