A Bayesian EM algorithm for optimal tracking of a maneuvering target in clutter

Abstract

The difficulty in tracking a maneuvering target in the presence of false measurements arises from the uncertain origin of the measurements (as a result of the observation/detection process) and the uncertainty in the maneuvering command driving the state of the target. Conditional mean estimates of the target state require a computational cost which is exponential with the number of observations and the levels of the maneuver command. In this paper, we propose an alternative optimal state estimation algorithm. Unlike the conditional mean estimator, which require computational cost exponential in the data length, the proposed iterative algorithm is linear in the data length (per iteration). The proposed iterative off-line algorithm optimally combines a hidden Markov model and a Kalman smoother—the optimality is demonstrated via the expectation maximization algor ithm—to yield the maximum a posteriori trajectory estimate of the target state. The algorithm proposed in this paper, uses probabilistic multi-hypothesis (PMHT) techniques for tracking a single maneuvering target in clutter. The extension of our algorithm to multiple maneuvering target tracking is straightforward and details are omitted. Previous applications of the PMHT technique (IEEE Trans. Automat. Control, submitted) have addressed the problem of tracking multiple non-maneuvering targets. These techniques are extended to address the problem of optimal tracking of a maneuvering target in a cluttered environment.