Robust selection of the degrees of freedom in the Student's t distribution through Multiple Model Adaptive Estimation

A robust Multiple Model Adaptive Estimation (MMAE) framework of parallel extended Student's t filters (ESTFs) with different degrees of freedom (dof) is proposed. Compared with the conventional extended Kalman filter (EKF) based on a Gaussian distributed noise assumption, the Student's t based filtering algorithms show a better robustness against outliers existing in process and measurement noises. In a Student's t based filter, the dof which determines the tail behavior of the noise density plays a significant role in the performance of the filter. However, there is currently no appropriate selection criterion for the dof for the Student's t based filters, because it is related to the properties of the outliers which are usually time-varying and unpredictable. In this paper, the extended Student's t filtering algorithm is derived, and three typical dof values which represent extreme and intermediate heavy tailed distributed noise together with approximated Gaussian distributed noise are chosen. The state estimation is the weighted summation of all three extended Student's t filters, and the effect of each dof value is automatically and dynamically adjusted via the MMAE framework. Simulation results show the efficiency and superiority of the proposed MMAE framework for the extended Student's t filters as compared with the conventional EKF, conventional UKF, and the extended Student's t filter and unscented Student's t filter with a fixed dof value.