Target Tracking and Multi-Sensor Fusion with Adaptive Cubature Information Filter

This chapter presents a noise adaptive cubature information filter based on variational Bayesian approximation (VB-ACIF). This filter can jointly estimate the dynamic state and time varying measurement noise for Gaussian nonlinear state space models. In the framework of recursive Bayesian estimation, the noise adaptive information filter propagating the information matrix and information state are derived. The integration of recursive Bayesian estimation is approximated by cubature integration rule. The inverse of measurement noise matrix, which is called measurement information matrix, is modeled as a Wishart distribution. So the joint distribution of posterior state and measurement noise can be approximated by the product of independent Gaussian and Wishart. As the parameters are coupled, the updated equation can be solved by fixed point iteration. The corresponding square root version of VB-ACIF is also derived to improve numerical precision and stability. Simulations are used to verify the performance of the proposed algorithms. Results demonstrate the improved performance of the proposed algorithms over conventional cubature information filter and square root version. When both state function and measurement function are nonlinear, the VB-ASCIF outperforms the VB-ACIF.