Fuzzy Methods for the Gaussian Mixture Probability Hypothesis Density Filter

The Gaussian mature probability hypothesis density (GM-PHD) filter method is presented, which is closed-form solution to the probability hypothesis density (PHD) recursion. The approach involves applying the Kalman filter to predict and update the probability hypothesis density (PHD), which is a first order statistic of the random finite set of targets. The GM-PHD not only has a good tracking performance, but also greatly reduces the computational complexity, compares with the probability hypothesis density particle filter (PF-PHD). However the GM-PHD filter does not provide identities of individual target state estimates, which are needed to construct tracks of individual targets. In this paper we propose a new fuzzy method involving initiating, propagating and terminating tracks based on the GM-PHD,filter, which gives the trajectory of each target and filters out unwanted clutter point over time. Various issues regarding initiating, propagating and terminating tracks are discussed. Finally, simulation results validate the proposed method can effectively estimate multi-target track in complex background and this method also can improve the tracking accuracy.