Misspecified Time-delay and Doppler estimation over high dynamics non-Gaussian scenarios

This article focuses on the study of time-delay and Doppler estimation under high dynamic non-Gaussian scenarios. We aim at analysing the Mean Squared Error (MSE) performance of a misspecified receiver architecture which deliberately simplifies the signal model by neglecting the acceleration parameter and assumes the noise process as complex normal distributed. Specifically, we derive the pseudo-true parameters by minimazing the Kullback-Leibler (KL) divergence between the true and assumed models and the related Misspecified Cramér-Rao Bound (MCRB) will be provided in closed form. Theoretical derivations are validated via Monte Carlo simulations showing the asymptotic efficiency of the Misspecified Maximum Likelihood Estimator (MMLE). One remarkable outcome of this study is that the lack of knowledge of the true statistical noise model does not lead to asymptotic performance degradation in the estimation of the parameters of interest.