Poisson multi‐Bernoulli mixture filters with coloured measurement noise

Abstract

Abstract To solve multitarget tracking (MTT) problems with coloured measurement noise, this study proposes a Poisson multi‐Bernoulli mixture filter with coloured measurement noise (PMBM‐CMN) and a robust PMBM‐CMN filter. By using the measurement differencing method and state augmentation approach, the proposed PMBM‐CMN filter transforms a state estimation problem with coloured measurement noise into a problem with white measurement noise. However, covariances of the true process and measurement noise in the proposed PMBM‐CMN filter are time‐varying and unknown, which may degrade the filtering performance. Therefore, a robust PMBM‐CMN filter is proposed for estimating the augmented state, including the kinematic state, the predicted state covariance, and the white measurement noise covariance. For linear Gaussian systems, the augmented state is modelled as a Gaussian inverse Wishart inverse Wishart (GIWIW) distribution. The variational Bayesian method is also employed to guarantee the conjugacy of the GIWIW density. Simulation results demonstrate the ability of the PMBM‐CMN filter to solve MTT problems with coloured measurement noise and show that the robust PMBM‐CMN filter based on the GIWIW model (GIWIW‐PMBM‐CMN) has the best overall performance in comparison with existing state‐of‐the‐art filters.

Keywords

• coloured measurement noise
• Gaussian inverse Wishart inverse Wishart
• multitarget tracking
• Poisson multi‐Bernoulli mixture
• unknown noise covariances
• variational Bayesian