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Volume 10 Issue 1
Jan.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Q. B. Ge, X. M. Hu, Y. Y. Li, H. L. He, and  Z. H. Song,  “A novel adaptive Kalman filter based on credibility measure,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 103–120, Jan. 2023. doi: 10.1109/JAS.2023.123012
Citation: Q. B. Ge, X. M. Hu, Y. Y. Li, H. L. He, and  Z. H. Song,  “A novel adaptive Kalman filter based on credibility measure,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 103–120, Jan. 2023. doi: 10.1109/JAS.2023.123012

A Novel Adaptive Kalman Filter Based on Credibility Measure

doi: 10.1109/JAS.2023.123012
Funds:  This work was supported by the National Natural Science Foundation of China (62033010) and Aeronautical Science Foundation of China (2019460T5001)
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  • It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent,  while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modified to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation maximization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.


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    • A trust factor, which evaluated online, is designed to express the creditable degree of the Kalman filter. Exactly, it also indicates the closeness of true mean square errors (TMSE) and filter calculated mean square errors (FMSE) matching degree of the used system model
    • The necessary and sufficient condition for accurate noise estimation is Pzkf = Pzkm, Pzkf - Pzkm is presented for noise covariances estimation. Where Pzkf and Pzkm, represents the filter FMSE and the TMSE , respectively. It also indicates the relationship between TMSE and FMSE. Under this case, the equivalence between the filter TMSE and FMSE becomes a necessary and sufficient condition for noise covariances estimation
    • The directly numerical solving way is presented to estimate the noise covariances, meanwhile, the Sage-Husa technology is also introduced to estimate the trust factor. Afterward, the evaluation of the trust factor is also discussed for the case with two unknown noise covariances. When the directly numerical solving way is used to solve this problem, it is found that the method is unavailable to deal with two unknown covariances
    • The optimization method proposed in this paper is successfully used to deal with the estimation with two unknown noise covariances. the optimization solution is proposed to synchronously estimate the two noise covariances. The corresponding optimization model is constructed, and the particle swarm optimization method is introduced to solve the optimization problem. The results show that the estimation accuracy and the convergence can be improved


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