Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions

LIU Xin; HAI Yang; DAI Wei

doi:10.12263/DZXB.20230957

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Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions

PAPERS | 更新时间：2025-12-08

- Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions
- ACTA ELECTRONICA SINICA Vol. 52, Issue 9, Pages: 3052-3064(2024)
- 作者机构：
  
  1.中国矿业大学人工智能研究院，江苏徐州 221116
  2.中国矿业大学信息与控制工程学院，江苏徐州 221116
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62103134;62373361);National Key Research and Development Program of China(2022YFB3304700);China Postdoctoral Science Foundation(2023M743776)
- DOI：10.12263/DZXB.20230957
  CLC： TP27
- Received：16 October 2023，
  
  Revised：2024-02-24，
  
  Published：25 September 2024
- 稿件说明：
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刘鑫, 海洋, 代伟. 基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法[J]. 电子学报, 2024, 52(09): 3052-3064.

LIU Xin, HAI Yang, DAI Wei. Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions[J]. Acta Electronica Sinica, 2024, 52(09): 3052-3064.
刘鑫, 海洋, 代伟. 基于厚尾双学生氏t分布的非线性状态空间系统鲁棒辨识方法[J]. 电子学报, 2024, 52(09): 3052-3064. DOI：10.12263/DZXB.20230957

LIU Xin, HAI Yang, DAI Wei. Robust Identification of Nonlinear State-Space System Based on Dual Heavy-Tailed Noise Distributions[J]. Acta Electronica Sinica, 2024, 52(09): 3052-3064. DOI：10.12263/DZXB.20230957

摘要

状态空间模型作为一种常见且重要的模型结构在自动化领域有着广泛的应用，本文针对异常值干扰下的非线性状态空间系统辨识问题开展研究.与现有的辨识方法不同，本文充分考虑了状态转移过程和输出量测过程均受到异常值干扰的情况，提出了一种更加全面的鲁棒辨识算法.首先利用两个相互独立的学生氏t分布分别对状态噪声和输出噪声进行建模以保障算法的鲁棒性；其次利用粒子平滑算法估计状态变量的后验概率分布以解决状态未知问题；最后利用期望最大化算法实现未知参数估计.在算法实现过程中使用了学生氏t分布表达式的数学分解，这样做的好处是：（1）更加有利于算法的推导和实现；（2）更清晰地解释了算法的鲁棒性能.并且本文通过数值算例和应用算例验证了该方法的有效性.

Abstract

The state space model is a common and important model structure for automation and control. In this paper

the robust identification of nonlinear state-space model corrupted by outliers is investigated. The outliers imposed on both the state transition process and the output measurement process are considered and a more comprehensive and robust identification algorithm is proposed. To ensure the robustness of the proposed algorithm

two independent heavy-tailed Student's t-distributions are used to describe the state noise and the output noise

respectively. Then the particle smoothing method is applied to estimate the posterior distribution of the unknown states. Finally

the expectation maximization algorithm is used to realize the parameter estimation problem. The mathematical decomposition of the Student's t-distribution is employed in the identification process which brings two main advantages: (1) facilitating the derivation and implementation of the proposed algorithm; (2) providing a more clearer explanation of the robustness of the algorithm. The usefulness of the proposed algorithm is demonstrated via the numerical and mechanical examples.

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references

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