Kalman Filter Based on Multiple Scaled Multivariate Skew Normal Variance Mean Mixture Distributions With Application to Target Tracking

Abstract

In this brief, we first propose a multiple scaled multivariate skew normal variance-mean mixture (MSMSNVMM) distribution to model heavy-tailed and/or skew measurement noises (HTSMN) whose each dimension has different tail and skewness behaviors. The MSMSNVMM distribution has more flexible tail behaviors and richer skewness features than Gaussian scale mixture (GScM) distribution, generalized Gaussian scale mixture (GGScM) distribution and scale mixtures of skew normal (SMSN) distribution. Furthermore, we derive a robust Kalman filter based on variational Bayesian (VB) method. The superiority of the new filter is demonstrated in a maneuvering target tracking example.