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Volume 12 Issue 1
Jan.  2025

IEEE/CAA Journal of Automatica Sinica

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J. Cheng, H. Chen, Z. Xue, Y. Huang, and  Y. Zhang,  “An online exploratory maximum likelihood estimation approach to adaptive Kalman filtering,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 1, pp. 228–254, Jan. 2025. doi: 10.1109/JAS.2024.125001
Citation: J. Cheng, H. Chen, Z. Xue, Y. Huang, and  Y. Zhang,  “An online exploratory maximum likelihood estimation approach to adaptive Kalman filtering,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 1, pp. 228–254, Jan. 2025. doi: 10.1109/JAS.2024.125001

An Online Exploratory Maximum Likelihood Estimation Approach to Adaptive Kalman Filtering

doi: 10.1109/JAS.2024.125001
Funds:  This work was supported in part by the National Key Research and Development Program of China (2023YFB3906403), the National Natural Science Foundation of China (62373118, 62173105), and the Natural Science Foundation of Heilongjiang Province of China (ZD2023F002)
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  • Over the past few decades, numerous adaptive Kalman filters (AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation (MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation. Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation, which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy, and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.

     

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  • Jiajun Cheng and Haonan Chen and Zhirui Xue contributed equally to this work.
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    Highlights

    • A one-time step exploratory coordinate descent method is proposed, which not only sidesteps presenting analytical expressions for the complex maximum likelihood cost function and solving it, but also adequately utilizes historical measurement information to improve estimation accuracy
    • An underlying mechanism by which the mean of the minimum point of the maximum likelihood cost function is equal to the true NCMs is revealed. Based on this theoretical result, the maximum likelihood cost function is simplified with fewer and simpler terms which are selected in a mini-batch and calculated in a backtracking way to reduce the calculation load for online NCM estimation
    • A novel mini-batch coordinate descent NCM estimation framework is developed, which can achieve AKFs with fast convergence speed and high estimation accuracy
    • Under the mini-batch coordinate descent NCMs estimation framework, four specific algorithms are derived to meet the different practical requirements in terms of convergence speed, convergence accuracy and calculation load

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