A consistent estimation criterion for multisensor bearings-only tracking

The problem of multitarget tracking using bearings-only measurements is addressed, when the number of targets is unknown a priori. The minimum description length (MDL) criterion of Rissanen is first chosen as a natural way to determine the number of targets when a prior distribution is unavailable. However, it is shown that MDL results in inconsistent estimates of the number of targets, and hence a modified estimation criterion, which is shown to yield unbiased target estimates, is proposed. The resulting asymptotically unbiased target identification (AUTI) algorithm corresponds to the computation of joint maximum likelihood (ML) estimates of target states and associations, with an additional penalty term to prevent overparameterization. The problem of data association is solved using a set of parallel simulated annealing algorithms over the sensors and scans. As the associations are formed by annealing, a conventional nonlinear programming algorithm simultaneously estimates the target states (position and velocity). This partitioning is justified by examining the structure of the bearings-only tracking problem under clairvoyant associations; It is shown that the norm squared of the target state error vector is a Lyapunov function for a gradient descent differential equation. As a consequence, an idealized nonlinear programming algorithm (steepest descent with infinitesimal step size) is globally convergent. A practical algorithm is then developed for identification of the number of targets, which combines simulated annealing for associations, and the Gauss-Newton algorithm for target state estimation. Simulation results are presented which compare the tracking performance of the MDL and AUTI algorithms.