Iterative Mixture Component Pruning Algorithm for Gaussian Mixture PHD Filter

Xiaoxi Yan

doi:10.1155/2014/653259

Abstract

As far as the increasing number of mixture components in the Gaussian mixture PHD filter is concerned, an iterative mixture component pruning algorithm is proposed. The pruning algorithm is based on maximizing the posterior probability density of the mixture weights. The entropy distribution of the mixture weights is adopted as the prior distribution of mixture component parameters. The iterative update formulations of the mixture weights are derived by Lagrange multiplier and LambertWfunction. Mixture components, whose weights become negative during iterative procedure, are pruned by setting corresponding mixture weights to zeros. In addition, multiple mixture components with similar parameters describing the same PHD peak can be merged into one mixture component in the algorithm. Simulation results show that the proposed iterative mixture component pruning algorithm is superior to the typical pruning algorithm based on thresholds.

Highlights

The objective of multitarget tracking is to estimate target number and target states from a sequence of noisy and cluttered measurement sets
Joint probabilistic data association is a generalization of probabilistic data association for multiple target tracking in which association probabilities of all the targets and measurements are described by confirmed matrices [5, 6]
There have been two implementations of probability hypothesis density (PHD) filter, Gaussian mixture implementation [10, 11] and sequential Monte Carlo implementation [12,13,14,15,16], which are suitable for linear Gaussian dynamics and nonlinear nonGaussian dynamics

Summary

Introduction

The objective of multitarget tracking is to estimate target number and target states from a sequence of noisy and cluttered measurement sets. The probability hypothesis density (PHD) filter derived by Mahler based on random finite sets statistics theory is an elegant and tractable approximate solution to the multitarget tracking problem [7, 8]. Another interpretation of the PHD in bin-occupancy view is presented in [9]. The convergence of the Gaussian mixture implementation of extended object probability hypothesis density filter is discussed in [37]. An iterative mixture component pruning algorithm is proposed for the Gaussian mixture PHD filter.

Problem Description

Iterative Pruning Algorithm

Simulation Study

Conclusion