Vardiational Bayesian Hybrid Multi-Bernoulli and CPHD Filters for Superpositional Sensors

Abstract

This paper addresses the problem of multi-target tracking with superpositional sensors, while the covariance matrices of measurement noise are not known. The proposed method is based on the hybrid multi-Bernoulli cardinalized probability hypothesis density (HMB-CPHD) filter, which has been developed for superpositional sensors-based multi-target tracking with known measurement noises. Specifically, we firstly propose the Gaussian mixture (GM) implementation of the HMB-CPHD filter, and then the covariance matrices of measurement noises are augmented into the target state vector, resulting in the Gaussian and inverse Wishart mixture (GIWM) representation of the augmented state. Then the variational Bayesian (VB) method is exploited to approximate the posterior distribution so that it maintains the same form as the prior distribution. A remarkable feature of the proposed method is that it can jointly perform multi-target tracking and measurement noise covariance estimation. The performance of the proposed algorithm is demonstrated via simulations.