Time delay estimation in a spatially structured model using decoupled estimators for temporal and spatial parameters

This paper deals with the joint estimation of time-delay 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 for maximum likelihood (ML) estimators 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 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.