A robust Cubature Kalman filter for nonlinear systems subject to randomly occurring measurement anomalies without a priori statistic

• Published in: ISA transactions Vol. 139; pp. 122 - 134
• Main Authors: Fu, Hongpo, Li, Zhenwei, Huang, Wei, Cheng, Yongmei, Zhang, Tianyi
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.08.2023
• Subjects: Cubature Kalman filter; Measurement anomaly; Nonlinear system; Variational Bayesian inference; Cubature Kalman filter; Measurement anomaly; Nonlinear system; Variational Bayesian inference
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2023.03.043

In this work, we investigate the problem of state estimation for a class of nonlinear systems subjected to randomly occurring measurement anomalies (ROMAs) without a priori statistic. To address the problem, first, a novel measurement model is constructed, in which the anomalous measurements and anomaly probability are modeled as Gaussian mixture distribution (GMD) and Beta distribution, respectively. Different from the existing researches assuming that the statistical information of anomalous measurements is known in advance, the model does not require a priori statistical knowledge of anomalous measurements. Moreover, by adaptive learning of the anomaly probability, the measurement model is identical with the classical cubature Kalman filter (CKF) in the absence of measurement anomalies. Then, the variational Bayesian inference (VBI) is employed to approximately calculate the joint posterior distribution of the system state and unknown parameters, and a robust filter is derived. Finally, the effectiveness of our filter is demonstrated by the numerical simulation. •To resist the ROMAs without a priori statistic, a novel measurement model is designed. Utilizing the VBI method, a new RCKF is designed.•In the absence of measurement anomalies, the proposed filter is consistent with standard CKF by adaptive learning of the anomaly probability.•Different from the existing results, the proposed filter is more accordant with the practical situation where the measurement anomaly is unknown.