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Volume 11 Issue 4
Apr.  2024

IEEE/CAA Journal of Automatica Sinica

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Article Contents
E. Javanfar and  M. Rahmani,  “Data-based filters for non-Gaussian dynamic systems with unknown output noise covariance,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 866–877, Apr. 2024. doi: 10.1109/JAS.2023.124164
Citation: E. Javanfar and  M. Rahmani,  “Data-based filters for non-Gaussian dynamic systems with unknown output noise covariance,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 866–877, Apr. 2024. doi: 10.1109/JAS.2023.124164

Data-Based Filters for Non-Gaussian Dynamic Systems With Unknown Output Noise Covariance

doi: 10.1109/JAS.2023.124164
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  • This paper proposes linear and nonlinear filters for a non-Gaussian dynamic system with an unknown nominal covariance of the output noise. The challenge of designing a suitable filter in the presence of an unknown covariance matrix is addressed by focusing on the output data set of the system. Considering that data generated from a Gaussian distribution exhibit ellipsoidal scattering, we first propose the weighted sum of norms (SON) clustering method that prioritizes nearby points, reduces distant point influence, and lowers computational cost. Then, by introducing the weighted maximum likelihood, we propose a semi-definite program (SDP) to detect outliers and reduce their impacts on each cluster. Detecting these weights paves the way to obtain an appropriate covariance of the output noise. Next, two filtering approaches are presented: a cluster-based robust linear filter using the maximum a posterior (MAP) estimation and a cluster-based robust nonlinear filter assuming that output noise distribution stems from some Gaussian noise resources according to the ellipsoidal clusters. At last, simulation results demonstrate the effectiveness of our proposed filtering approaches.

     

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    Highlights

    • Novel data-based linear and non-linear filters are proposed for linear dynamic systems subjected to non-Gaussian noise
    • These filters address the particular challenges posed by unknown output noise covariance and inaccurate process noise covariance
    • A weighted SON clustering approach is presented to enhance the regularization and improve the performance of the conventional SON clustering
    • To mitigate the impact of outliers within each cluster, a weighted MLE technique is proposed

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