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. © 2011 IEEE

State Estimation and Smoothing for the Probability Hypothesis Density Filter

Tracking multiple objects is a challenging problem for an automated system, with applications in many domains. Typically the system must be able to represent the posterior distribution of the state of the targets, using a recursive algorithm that takes information from noisy measurements. However, in many important cases the number of targets is also unknown, and has also to be estimated from data. The Probability Hypothesis Density (PHD) filter is an effective approach for this problem. The method uses a first-order moment approximation to develop a recursive algorithm for the optimal Bayesian filter. The PHD recursion can implemented in closed form in some restricted cases, and more generally using Sequential Monte Carlo (SMC) methods. The assumptions made in the PHD filter are appealing for computational reasons in real-time tracking implementations. These are only justifiable when the signal to noise ratio (SNR) of a single target is high enough that remediates the loss of information from the approximation. Although the original derivation of the PHD filter is based on functional expansions of belief-mass functions, it can also be developed by exploiting elementary constructions of Poisson processes. This thesis presents novel strategies for improving the Sequential Monte Carlo implementation of PHD filter using the point process approach. Firstly, we propose a post-processing state estimation step for the PHD filter, using Markov Chain Monte Carlo methods for mixture models. Secondly, we develop recursive Bayesian smoothing algorithms using the approximations of the filter backwards in time. The purpose of both strategies is to overcome the problems arising from the PHD filter assumptions. As a motivating example, we analyze the performance of the methods for the difficult problem of person tracking in crowded environment