Bayesian WIV Estimators for 3-D Bearings-Only TMA With Speed Constraints

This paper develops Bayesian weighted instrumental variable (WIV) estimators under equality and inequality speed constraints for the three-dimensional (3-D) bearings-only target motion analysis (TMA) problem, which show improved estimation accuracies compared to their unconstrained counterpart. Incorporating the speed constraint information into our previously proposed Bayesian WIV estimator imposes a quadratic constraint on this problem. Finding an optimal solution for the resulting non-convex problem is by no means straightforward. The main problem with iterative optimization methods such as the maximum a posteriori is that they require initialization and may converge to a local minimum if poorly initialized. Using advanced linear and nonlinear algebra techniques, non-iterative accurate estimators under equality and inequality constraints are developed for this problem. Furthermore, it is proven that the proposed equality constrained estimator is approximately asymptotically unbiased and that the inequality constrained estimator is the optimal solution. An approximate covariance matrix has also been developed for the constrained WIV under equality constraint. Simulation results indicate that the equality and inequality constrained estimators outperform their unconstrained counterpart in the simulated scenarios.