In this paper differences between Fisher Information Matrix (FIM) and inverse covariation matrix of normalized correlation estimations for white and colored noise are investigated. It’s shown that implementation of normalized correlation function estimation leads to modification of maximum likelihood estimation FIM elements, so in case of arbitrary energy affected parameter vector, variance of estimation by normalized correlation function maximization is not equal to Cramer–Rao lower bound. Statistical characteristics of joint Doppler stretch and delay estimation by maximization of normalized correlation function for signal with nuisance parameters are derived in this paper. It’s shown that normalized correlator is equal to wideband ambiguity function, but this method of estimation follows from Cauchy–Schwarz inequality without using energy conservation assumptions. Besides, it is proved that estimation of Doppler stretch and delay by normalized correlation function or WBAF of signal with random initial phase and gain is asymptotically unbiased and effective.
On the Correlation Function of an Arbitrary Distributed Continuous Markov Process
