The Extended Invariance Principle for Signal Parameter Estimation in an Unknown Spatial Field

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 model and with greater robustness to errors in the model of the array response. EXIP improves the quality of the time-delay and Doppler frequency estimates obtained with a spatially unstructured model by introducing DOA estimates which are obtained in a second step through an innovative reparametrization. Simulation results for time-delay and Doppler frequency estimation for Global Positioning System (GPS) signals are presented and confirm that the proposed two-step approach attains the Cramer-Rao lower bound (CRLB) of the spatially structured model.