Dual Extended Kalman Filter Under Minimum Error Entropy With Fiducial Points

The multivariate autoregressive (MVAR) model is widely used in describing the dynamics of nonlinear systems, in which the estimates of model parameters and underlying states can be achieved by dual extended Kalman filter (DEKF). However, when the measurements are corrupted by complicated non-Gaussian noises, the DEKF based on the minimum mean-square error (MMSE) criterion may provide biased estimates. In the present article, we develop a novel dual Kalman-type filter, referred to as DEKF under minimum error entropy (MEE) with fiducial points (MEEFs-DEKF) to deal with the non-Gaussian noises. First, the equivalent state-space model and parameter-space model are presented based on the MVAR model. Then, an optimality criterion based on MEE with fiducial points (MEEFs) is applied in the batch-mode regression equation to improve the robustness. Finally, a fixed-point iteration algorithm gives the posterior estimates of state and parameter. Simulation results confirm that the proposed MEEF-DEKF can achieve excellent performance in various noises with different distributions, especially in heavy-tailed and multimodal noises.