Adaptive noise variance identification for probability hypothesis density-based multi-target filter by variational Bayesian approximations

A new extended probability hypothesis density (PHD) filter is proposed for joint estimation of the time-varying number of targets and their states without the measurement noise variance. The extended PHD filter can adaptively learn the unknown noise parameters at each scan time by using the received measurements. With the decomposition of the posterior intensity separated into Gaussian and Inverse-Gamma components, the closed-form solutions to the extended PHD filter are derived by using the variational Bayesian approximations, which have been proved as a simple, analytically tractable method to approximate the posterior intensity of multi-target states and time-varying noise variances. Simulation results show that the proposed filter can accommodate the unknown measurement variances effectively, and improve the estimation accuracy of both the number of targets and their states.