The extended invariance principle applied to joint time-delay, frequency, and DOA estimation

This paper deals with the joint estimation of temporal (time-delay, Doppler frequency) and spatial (direction-of-arrival, DOA) parameters of several replicas of a known signal in an unknown spatially correlated field. Unstructured and structured models have been proposed in the literature. The former suffers from a severe performance degradation in some scenarios, whereas the latter involves huge complexity. It is shown how the extended invariance principle (EXIP) can be applied to obtain estimates with the quality of those of the structured model, but with the complexity of the unstructured one. We present a method to improve the quality of the time-delay and Doppler estimates obtained with an unstructured spatial model when an estimate of the DOAs is available. Exemplarily, simulation results for time-delay estimation for GPS (Global Positioning System) are included and confirm that our proposal approaches the Cramer-Rao lower bound (CRLB) of the structured model even when suboptimal DOA estimates obtained by ESPRIT are introduced.