Time-delay estimation applying the extended invariance principle with a polynomial rooting approach

This work treats the problem of 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 data models have been proposed for maximum likelihood (ML) estimators, whereas the former suffers from a severe performance degradation in some scenarios, and the latter involves huge complexity. In this work 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 much lower complexity than directly utilizing the structured model. We present how to improve the quality of the time-delay estimates obtained with an unstructured spatial model by introducing DOA estimates. DOA estimates are derived either directly applying EXIP with a polynomial rooting approach or with decoupled estimators for temporal and spatial parameters applying Unitary ESPRIT. Both methods are compared with respect to estimation accuracy and complexity. Exemplarily, simulation results for time-delay estimation for GPS (Global Positioning System) are shown and confirm that our proposals both approach the Cramer-Rao lower bound (CRLB) of the structured model.