PHD filter for multi-target tracking by variational Bayesian approximation

In this paper, we address the problem of multi-target tracking with unknown measurement noise variance parameters by the probability hypothesis density (PHD) filter. Based on the concept of conjugate prior distributions for noise statistics, the inverse-Gamma distributions are employed to describe the dynamics of the noise variance parameters and a novel implementation to the PHD recursion is developed by representing the predicted and the posterior intensities as mixtures of Gaussian-inverse-Gamma terms. As the target state and the noise variance parameters are coupled in the likelihood functions, the variational Bayesian approximation approach is applied so that the posterior is derived in the same form as the prior and the resulting algorithm is recursive. A numerical example is provided to illustrate the effectiveness of the proposed filter.