Constrained bearings-only target motion analysis via Markov chain Monte Carlo methods

The aim of this paper is to develop methods for estimating the range of a moving target from bearings-only observations and for weakly observable scenarios, by including general constraints about the target trajectories. Throughout this manuscript, it is assumed that the target motion is conditionally deterministic, which leads us to focus on batch algorithms. Another common assumption is poor observability, which results from another constraint: (very) limited amplitude of the observer maneuvers. Classical batch algorithms are based on iterative methods (such as gradient techniques), but they perform very poorly in this context and including constraints is not easy and not reliable in this way. Instead, we consider simulation-based methods, i.e., Monte Carlo Markov chain (MCMC) sampling, developed in a Bayesian context. In this way, it is possible to take into account any type of constraint, and to drastically improve estimation of weakly observable parameters. As a by-product, an estimate of confidence intervals is obtained. This is the aim of the highest probability density (HPD) intervals. This study is illustrated by simulation results, while the benefits of constraint inclusion are analyzed via geometric methods