Robust Kalman Filter and Smoother based on the Student's t Minimum Error Entropy Criterion

Abstract

Error entropy is a potent tool for quantifying the similarity between two random vectors, occupying a significant position in state estimation. However, the Gaussian kernel function lacks flexibility in adjusting the shape of error entropy, thereby restricting its capacity to effectively handle non-Gaussian noise with unknown distribution. To address this issue, by introducing the degree of freedom (dof), this article constructs a student's t minimum error entropy (SMEE) criterion and derives a more robust Kalman filter termed SMEEKF based on this criterion, along with its corresponding Kalman smoother named SMEEKS. Furthermore, we prove the sufficient conditions for fixed-point iteration convergence and compute the floating-point complexity of proposed algorithms. Moreover, we provide algorithm's mean error behavior and mean-square error behavior in detail. In addition, we analyze the sensitivity of dof and kernel bandwidth to the proposed algorithms and validate the effectiveness of the proposed algorithms with complex noise in different scenarios.