Probability Hypothesis Density Filter Based on Gaussian-Hermite Numerical Integration

Abstract

This work addresses the multi-target tracking problem in the nonlinear Gaussian system. One probability hypothesis density filtering algorithm based on Gaussian-Hermite numerical integration is proposed. In order to calculate integrations in the Gaussian mixture probability hypothesis density filter, the Gaussian-Hermite numerical integration method is used to approximate the integration. In the filtering stages of prediction and update, we calculate the corresponding Gaussian-Hermite integral points and weights, employ the method of numerical accumulation to approximate the integrations of the Gaussian mixture probability hypothesis density filter. Then the corresponding Gaussian items are calculated and the recursions of Gaussian mixture are implemented. The new algorithm can estimate not only the state vector effectively but also the number of targets accurately. Moreover, its time complexity increases in a low level. The simulation results show that the new algorithm can improve the accuracy of target tracking, and its time complexity keeps the same order of magnitude as the extended Kalman Gaussian mixture probability hypothesis density filter.