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A Novel Batch Bayesian WIV Estimator for Three-Dimensional TMA Using Bearing and Elevation Measurements

In this paper, we derive a novel batch Bayesian weighted instrumental variable estimator for the three-dimensional (3D) target motion analysis (TMA) problem using bearing and elevation measurements. Unlike most existing 3D estimators based on instrumental variables, the proposed approach is able to incorporate a priori information into the estimation process and is proven to be approximately asymptotically unbiased. An approximate asymptotic covariance matrix is also presented to evaluate the performance of the estimator. Simulation results show that the proposed estimator outperforms its non-Bayesian counterpart and has an estimation performance on par with the conventional iterative maximum a posteriori estimator, while being orders of magnitude faster in a passive sonar TMA problem. Moreover, it was shown that the proposed approach can provide an accurate initialization for recursive estimators.