Joint maximum likelihood estimation of time delays and Doppler shifts

This paper deals with the problem of estimating the amplitudes, time delays and Doppler shifts of a set of known signals received by an array of antennas in temporally white but spatially colored noise. Applying the maximum likelihood approach, the estimation reduces to an optimization problem where the nonlinear parameters such frequency shifts and delays are jointly estimated by means of a minimization over a highly nonlinear cost function, which is derived in this paper. In addition, an iterative algorithm that performs these estimations is also presented.