A New Heavy-Tailed Robust Kalman Filter with Time-Varying Process Bias

A new heavy-tailed robust Kalman filter is presented to address the issue that the linear stochastic state-space model has heavy-tailed noise with time-varying process bias. The one-step predicted probability density function (PDF) is modeled as the Student's-t-inverse-Wishart distribution, and the likelihood PDF is modeled as the Student's-t distribution. To acquire the approximate joint posterior PDF, the conjugate prior distributions of the state vector and auxiliary variables are set as the Gaussian, the inverse-Wishart, the Gaussian-Gamma, and the Gamma distributions, respectively. A new Gaussian hierarchical state-space model is presented by introducing auxiliary variables. Based on the proposed Gaussian hierarchical state-space model, the parameters of the proposed heavy-tailed robust filter are jointly inferred using the approach of the variational Bayesian. The simulation illustrates that the time-varying process bias is adaptively real-time estimated in this paper. In comparison with the existing cutting-edge filters, the presented heavy-tailed robust filter obtains higher accuracy.