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This paper 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 severe performance degradation in some scenarios, and the latter involves huge complexity. In this paper, 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. They present how to improve the quality of the time-delay estimates obtained with an unstructured spatial model by introducing DOA estimates.
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