Multitarget Tracking using Probability Hypothesis Density Smoothing

In general, for multitarget problems where the number of targets and their states are time varying, the optimal Bayesian multitarget tracking is computationally demanding. The Probability Hypothesis Density (PHD) filter, which is the first-order moment approximation of the optimal one, is a computationally tractable alternative. By evaluating the PHD, the number of targets as well as their individual states can be extracted. Recent sequential Monte Carlo (SMC) implementations of the PHD filter have paved the way to its application to realistic nonlinear non-Gaussian problems. It is observed that the particle implementation of the PHD filter is dependent on current measurements, especially in the case of low observable target problems (i.e., estimates are sensitive to missed detections and false alarms). In this paper a PHD smoothing algorithm is proposed to improve the capability of PHD-based tracking system. It involves forward multitarget filtering using the standard PHD filter recursion followed by backward smoothing recursion using a novel recursive formula. Smoothing, which produces delayed estimates, results in better estimates for target states and a better estimate for the number of targets. Multiple model PHD (MMPHD) smoothing, which is an extension of the proposed technique to maneuvering targets, is also provided. Simulations are performed with the proposed method on a multitarget scenario. Simulation results confirm improved performance of the proposed algorithm.