Abstract-This paper treats the problem of joint estimation of time-delay, Doppler frequency, and spatial (direction-of-arrival or DOA) parameters of several replicas of a known signal in an unknown spatially correlated noise field. Both spatially unstructured and structured data models have been proposed for this problem and corresponding maximum likelihood (ML) estimators have been derived. However, structured models require a high computational complexity and are sensitive to the antenna array response, while unstructured models are unable to achieve good performance in some scenarios. In this paper, it is shown how the extended invariance principle (EXIP) can be applied to obtain estimates with the quality of a spatially structured model, but with much lower complexity than directly utilizing a structured