PHD filter for multi-target tracking with glint noise

• A PHD filter is proposed for multi-target tracking with glint noise.
• The extended PHD filter is derived by augmenting the target state and the noise parameters.
• A closed-form expression to the extended PHD filter is developed by variational Bayesian approach.

This paper studies the problem of multi-target tracking with glint noise in the formulation of random finite set theory. By using the Student's t-distribution to describe the glint noise statistics, the probability hypothesis density (PHD) filter is extended via augmenting the target state and the noise parameters. To derive a closed-form expression for the extended PHD filter, the prior Gamma distribution for the noise parameters is adopted so that the predicted and the updated intensities can be represented by mixtures of Gaussian–Gamma terms. As the target state and the noise parameters are coupled in the likelihood functions, the variational Bayesian approach is applied to derive approximated distributions so that the updated intensity is represented in the same form as the predicted intensity and the resulting algorithm is recursive. Simulation results are provided via a numerical example to illustrate the effectiveness of the proposed filter.