A Novel Outlier-Robust Kalman Filtering Framework Based on Statistical Similarity Measure

• Published in: IEEE transactions on automatic control Vol. 66; no. 6; pp. 2677 - 2692
• Main Authors: Huang, Yulong, Zhang, Yonggang, Zhao, Yuxin, Shi, Peng, Chambers, Jonathon A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Covariance matrices; Estimation; Heavy-tailed noise; Iterative algorithms; Iterative methods; Kalman filter; Kalman filters; Noise measurement; outliers; Outliers (statistics); Pollution measurement; Robustness; separate iterative algorithm; Similarity; Similarity measures; Stability analysis; statistical similarity measure
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3011443

In this article, a statistical similarity measure is introduced to quantify the similarity between two random vectors. The measure is, then, employed to develop a novel outlier-robust Kalman filtering framework. The approximation errors and the stability of the proposed filter are analyzed and discussed. To implement the filter, a fixed-point iterative algorithm and a separate iterative algorithm are given, and their local convergent conditions are also provided, and their comparisons have been made. In addition, selection of the similarity function is considered, and four exemplary similarity functions are established, from which the relations between our new method and existing outlier-robust Kalman filters are revealed. Simulation examples are used to illustrate the effectiveness and potential of the new filtering scheme.