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Volume 11 Issue 5
May  2024

IEEE/CAA Journal of Automatica Sinica

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K. Li, S. Zhao, B. Huang, and  F. Liu,  “Bayesian filtering for high-dimensional state-space models with state partition and error compensation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1239–1249, May 2024. doi: 10.1109/JAS.2023.124137
Citation: K. Li, S. Zhao, B. Huang, and  F. Liu,  “Bayesian filtering for high-dimensional state-space models with state partition and error compensation,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 5, pp. 1239–1249, May 2024. doi: 10.1109/JAS.2023.124137

Bayesian Filtering for High-Dimensional State-Space Models With State Partition and Error Compensation

doi: 10.1109/JAS.2023.124137
Funds:  This work was supported in part by the National Key R&D Program of China (2022YFC3401303), the Natural Science Foundation of Jiangsu Province (BK20211528), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KFCX22_2300)
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  • In the era of exponential growth of data availability, the architecture of systems has a trend toward high dimensionality, and directly exploiting holistic information for state inference is not always computationally affordable. This paper proposes a novel Bayesian filtering algorithm that considers algorithmic computational cost and estimation accuracy for high-dimensional linear systems. The high-dimensional state vector is divided into several blocks to save computation resources by avoiding the calculation of error covariance with immense dimensions. After that, two sequential states are estimated simultaneously by introducing an auxiliary variable in the new probability space, mitigating the performance degradation caused by state segmentation. Moreover, the computational cost and error covariance of the proposed algorithm are analyzed analytically to show its distinct features compared with several existing methods. Simulation results illustrate that the proposed Bayesian filtering can maintain a higher estimation accuracy with reasonable computational cost when applied to high-dimensional linear systems.

     

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    Highlights

    • In order to reduce the computational cost, the high-dimensional state vector is partitioned into multiple interrelated state blocks so that the complex operations on covariance matrices of immense dimensions can be avoided
    • To mitigate the error caused by the use of blocks, an auxiliary variable is introduced in the new probability space, which can adjust the predicted covariance of the divided state. The joint probability density function under the original probability space is mapped to a new probability space to realize the real-time estimation of the state and the auxiliary variable by minimizing the difference between the two
    • The performance of the proposed algorithm and the method of directly splitting into multiple independent subsystems is analyzed. At the same time, the computational cost of the algorithm is described with flops and analytically compared with several existing methods. By doing this, the resulting filter maintains the property that state segmentation reduces computational cost while considerably enhancing estimation accuracy

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