A Gaussian–Pearson type VII adaptive mixture distribution-based outlier-robust Kalman filter

Abstract

Considering that existing robust filtering algorithms rely on the selection of initial values of degree of freedom (DOF) parameters in outlier interference environments and cannot effectively cope with unknown non-stationary heavy-tailed measurement noises (HMN), a
Gaussian–Pearson type VII (PTV) adaptive mixture distribution-based outlier-robust Kalman filter (GPTVMAKF) is proposed. In order to determine whether the current measurement is a normal value or an outlier, a judgment factor subject to the Beta-Bernoulli distribution is introduced. PTV distribution is used to model HMN caused by outliers, and two Gamma distributions are used to model the two different DOF parameters, which can make the PTV distribution have the adaptive adjustment ability. By introducing the inverse Wishart distribution as the prior distribution of the measurement noise covariance, which is adaptively estimated to cope with the unknown time-varying measurement noises. The state and parameters are jointly estimated by variational Bayesian. Finally, the simulation experiments verify that the proposed GPTVMAKF can obtain more accurate state estimation than existing filters in the environments with varying degrees of HMN and unknown non-stationary HMN.