Adaptive probability hypothesis density filter based on variational Bayesian approximation for multi‐target tracking

Probability hypothesis density (PHD) filter has been demonstrated a promising algorithm for tracking an unknown number of targets in real time. However, this method can only be used in the multi‐target tracking systems with known measurement noise variances; otherwise, the tracking performance will decline greatly. To solve this problem, an adaptive PHD filter algorithm is proposed based on the variational Bayesian approximation technique to recursively estimate the joint PHDs of the multi‐target states and the time‐varying measurement noise variances. First, the variational calculus method is employed to derive the multi‐target estimate recursions, and then the Gaussian and the inverse Gamma distributions are introduced to approximate the joint posterior PHD, and achieve a closed‐form solution. Simulation results show that the proposed algorithm can effectively estimate the unknown measurement noise variances and has a good performance of multi‐target tracking with a strong robustness.