Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise. Based on the cubature Kalman filter, we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise. The system states and the statistics of skew t noise distribution, including the shape matrix, the scale matrix, and the degree of freedom (DOF) are estimated jointly by employing variational Bayesian (VB) inference. The proposed method is validated in a target tracking example. Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Automated summary

This paper introduces a new nonlinear filtering algorithm using skew t distribution to deal with asymmetry of measurement noise. The joint estimation of system states and statistics of skew t noise distribution is conducted using variational Bayesian inference. Simulation results show that the proposed nonlinear filter performs well even when facing unknown statistics of measurement noise, outperforming existing state-of-the-art nonlinear filters.