An Outlier-Robust Kalman Filter With Adaptive Selection of Elliptically Contoured Distributions

• Published in: IEEE transactions on signal processing 2022, Vol.70, p.994-1009
• Main Authors: Xue, Chao, Huang, Yulong, Zhu, Fengchi, Zhang, Yonggang, Chambers, Jonathon A.
• Format: Article
• Language: English
• Subjects: Adaptation models; Algorithms; Complexity; Computational modeling; Conditional probability; Contours; Covariance matrices; elliptically contoured distribution; fixed-point iteration; Heuristic methods; interaction multiple model; Kalman filter; Kalman filters; Noise measurement; non-Gaussian heavy-tailed noise; Outliers (statistics); Pollution measurement; Probability density functions; Random variables; Robustness (mathematics); State vectors; Switches
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2022.3151199

In this paper, elliptically contoured (EC) distributions are used to model outlier-contaminated measurement noises. Exploiting a heuristic approach to introduce an unknown parameter, we present an analytical update form of the joint posterior probability density function of the state vector and auxiliary random variable, from which a novel robust EC distributions-based Kalman filtering framework is first derived. To illustrate the effectiveness of the proposed framework, the convergence, robustness, optimality and computational complexity analyses of the proposed method are then given. In addition, to cope with complex noise environments, the interaction multiple model is employed to achieve the adaptive selection of EC distributions such that well-behaved estimation performance can be obtained for different noise cases. Simulation results demonstrate the validity and superiority of the proposed algorithm.