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In bearings-only target motion analysis (TMA), the observer is often required to outmaneuver the target. However, under specific conditions, an observer moving with constant velocity is sufficient to compute the state of a target that changes its course. A maximum likelihood estimator (MLE) has been developed for this problem in the literature. Unfortunately, the MLE is not only computationally expensive but also prone to divergence problems when poorly initialised. To overcome these shortcomings, this paper proposes a novel quadratically constrained weighted instrumental variable (QC-WIV) estimator. Being a closed-form algorithm, the proposed QC-WIV is inherently more stable than the MLE while at the same time being computationally much more efficient. Moreover, it is shown analytically to be asymptotically unbiased. Numerical simulation studies are presented to corroborate the performance advantage of the proposed QC-WIV, where it is observed to be asymptotically efficient as well. In addition, the QC-WIV performance is on par with the MLE in small noise scenarios for both cases of known and unknown maneuver time. More importantly, the QC-WIV is observed to produce stable estimation performance in large noise levels at which the MLE suffers from divergence. Refereed/Peer-reviewed

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 nonconvex problem is by no means straightforward. The main problem with iterative optimization methods such as the maximum aposteriori 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. Refereed/Peer-reviewed

In our previous work [17], we derived a novel Bayesian weighted instrumental variable (WIV) estimator for the three-dimensional bearings-only target motion analysis problem. While the proposed approach has the desirable characteristic of incorporating a priori information in the estimation process and is proven to be approximately asymptotically unbiased, this estimator has a batch structure which is generally not suitable for online processing of measurements in practical applications. Therefore, in this paper we develop a recursive Bayesian WIV, which also uses an adaptive selective angle measurement approach to increase its stability. Simulations show that the proposed estimator outperforms the compared Bayesian algorithms with similar computational complexity for poorly observable scenarios. Refereed/Peer-reviewed

This paper considers the problem of three-dimensional target motion analysis using a combination of bearing, elevation, and time difference of arrival (TDOA) measurements. We propose a hybrid closed-form solution based on the weighted instrumental variables for this highly nonlinear problem. The proposed solution avoids the high computational complexity and convergence problems associated with iterative estimators. Furthermore, the simulation results suggest that the proposed estimator is nearly efficient, since its performance is very close to the best achievable performance as predicted by the Cramer-Rao lower bound Refereed/Peer-reviewed