Multi-Prior Mixture Distribution and Arithmetic Average Fusion-Based Student’s t Filter

In this paper, a multi-prior mixture (MPM) distribution and arithmetic average (AA) fusion-based Student’s t filter (MPMAASTF) is proposed for the problem of non-stationary heavy-tailed noises filtering with only rough prior information available. Firstly, a MPM distribution is proposed to model the joint probability density function (PDF) for one-step prediction and measure likelihood, then the Kullback-Leibler Divergence (KLD) minimization technique and Jensen’s inequality are used to derive approximate posterior PDFs for states and parameters. A finite number of Student’s t PDF fusion algorithm based on AA fusion is developed to guarantee the closure of the filtering posterior PDF, and finally existing high precision moment matching technique is embedded. The proposed filter improves the filtering accuracy of non-stationary heavy-tailed noises by adaptive learning of the degrees of freedom (dof), the one-step prediction error scale matrix and the measurement noise scale matrix. Simulations validate the effectiveness and superiority of the proposed method.