The Dirac Weighted-sum Probability Hypothesis Density Filter

To solve the problem for multi-target tracking in the presence of clutter, an unknown covariance of the process noise, and an unknown and variable number of targets, we propose a Dirac weighted-sum probability hypothesis density (PHD) filter for a linear system model. The proposed filter expresses the posterior intensity as the weighted sum of Dirac delta functions. Similar to the Gaussian mixture PHD filter, this filter propagates the posterior intensity of multiple targets in filter recursion. Unlike the Gaussian mixture PHD filter that uses the Kalman filter to obtain the updated posterior intensity of multiple targets, this filter employs α-β filter with variable gain to obtain the updated posterior intensity of multiple targets. Meanwhile, we also present a method for determining parametersαandβ in the α-β filter with variable gain. The simulation results demonstrate that the proposed filter provides an efficient method for the multi-target tracking problem in the presence of clutter, an unknown covariance of the process noise, and an unknown and variable number of targets, and its average performing time is smaller than that of the Gaussian mixture PHD filter, so that it will have good engineering application prospects.