An Algebraic Closed-Form Solution for Bearings-Only Maneuvering Target Motion Analysis From a Nonmaneuvering Platform

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.