Constrained bearings-only target motion analysis via monte carlo markov chains

Abstract

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 constraints about kinematic parameters. It is assumed that the target motion is rectilinear and uniform which leads us to restrict to batch algorithms. Poor observability is generally resulting from a (very) limited amplitude of the observer maneuvers. In these situations, classical methods perform very poorly (especially for range estimation) and including constraints is uneasy and not reliable. We consider here methods for determining a confidence interval for the range based on the highest probability density (HPD) intervals, by taking into account prior informations about the kinematics parameters. Two types of prior constraints are considered: first the kinematics parameters are supposed belonging to intervals, without supposing a particular distribution, and second the target trajectory is supposed to be staying in a known area. The determination of an HPD interval requires a Markov chain Monte Carlo (MCMC) sampling. The HPD interval method is illustrated by simulation results