Time delay estimation in stationary and non-stationary environments

Abstract

We develop computationally efficient iterative algorithms for finding the Maximum Likelihood estimates of the delay and spectral parameters of a noise-like Gaussian signal radiated from a common point source and observed by two or more spatially separated receivers. We first consider the stationary case in which the source is stationary (not moving) and the observed signals are modeled as wide sense stationary processes. We then extend the scope by considering a non-stationary (moving) source radiating a possible non-stationary stochastic signal. In that context, we address the practical problem of estimation given discrete-time observations. We also present efficient methods for calculating the Jog-likelihood gradient (score), the Hessian, and the Fisher's information matrix under stationary and non-stationary conditions.