On the efficiency of a bearings-only instrumental variable estimator for target motion analysis

The maximum-likelihood (ML) estimator for bearings-only target motion analysis does not admit a closed-from solution and must be implemented iteratively. Iterative ML estimators require an initialization close to the true solution to avoid divergence. Recently a closed-form asymptotically unbiased instrumental variable estimator has been proposed to alleviate the convergence problems associated with iterative ML estimators. This paper establishes the asymptotic efficiency of the closed-form instrumental variable estimator by showing that its error covariance matrix approaches the Cramer-Rao lower bound for sufficiently small bearing noise as the number of measurements tends to infinity.