Variational Bayesian Filter for Nonlinear System with Gaussian-Skew T Mixture Noise

In the actual application scenario of target tracking and positioning, the target is affected by maneuvering interference, measurement outliers, and abnormal values, and system noise and measurement noise may obey non-Gaussian heavy-tailed and skew distribution. In this case, the traditional Kalman filter based on Gaussian noise modeling fails to obtain the satisfying estimation performance. Aiming at non-Gaussian thick-tailed noise, this paper proposes a hierarchical multivariate Gaussian-Skew T mixture model. Using the variational Bayesian theory, the estimation of the state probability density function is converted into two probability density functions of the unknown noise and the nonlinear state. Using Bayesian inference, an iterative algorithm for joint estimation of state and unknown noise is proposed. And the effectiveness of the algorithm is verified in the target tracking simulation experiment and UWB positioning experiment.