基于区间过程模型的新型卡尔曼滤波算法

Jinyang Li; Jinwu Li; Chengkai Shen; Chao Jiang; Bingyu Ni

doi:10.1088/3050-2454/ae16a8

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基于区间过程模型的新型卡尔曼滤波算法

Papers | 更新时间：2026-02-13

- 基于区间过程模型的新型卡尔曼滤波算法
- A new Kalman filter algorithm based on the interval process model
- 可靠性科学与工程学报（英文） 2025年第4期页码：1-17
- 作者机构：
  
  State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, People’s Republic of China
  School of Mechanical Engineering, Dongguan University of Technology, Dongguan 523808, People’s Republic of China
- 作者简介：
  
  [ "Jinyang Li, PhD candidate at Hunan University. His research interests include reliability analysis and uncertainty propagation analysis." ]
  [ "Jinwu Li, received his PhD degree in Mechanical Engineering from Hunan University, People's Republic of China, in 2020. His research interests include uncertainty quantification, intelligent design, and reliability design." ]
  [ "Chengkai Shen, received an MS degree in Mechanical Engineering from Hunan University, Changsha, People's Republic of China, in 2022. His research interests include Kalman filter and uncertainty quantification." ]
  [ "Chao Jiang, PhD, is currently a professor at the College of Mechanical and Vehicle Engineering and vice president of Hunan University. His academic research is mainly focused on mechanical design, with particular interests in the scientific issues of uncertainty quantification and analysis, structural reliability, optimization design, and fracture and fatigue." ]
  [ "Bingyu Ni, associate professor, received a PhD degree in Mechanical Engineering from Hunan University in 2017. His main research interests include uncertainty analysis in structural dynamics, spatial uncertainty quantification and propagation, and structural interval finite element analysis, etc." ]
- 基金信息：
- DOI：10.1088/3050-2454/ae16a8
  中图分类号：
- 收稿：2025-06-04，
  
  修回：2025-10-16，
  
  录用：2025-10-20，
  
  网络首发：2025-11-14，
  
  纸质出版：2025
- 稿件说明：
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Jinyang Li, Jinwu Li, Chengkai Shen, 等. 基于区间过程模型的新型卡尔曼滤波算法[J]. 可靠性科学与工程学报（英文）, 2025,(4):1-17.

Jinyang Li, Jinwu Li, Chengkai Shen, et al. A new Kalman filter algorithm based on the interval process model[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-17.
Jinyang Li, Jinwu Li, Chengkai Shen, 等. 基于区间过程模型的新型卡尔曼滤波算法[J]. 可靠性科学与工程学报（英文）, 2025,(4):1-17. DOI： 10.1088/3050-2454/ae16a8.

Jinyang Li, Jinwu Li, Chengkai Shen, et al. A new Kalman filter algorithm based on the interval process model[J]. Journal of Reliability Science and Engineering, 2025, (4): 1-17. DOI： 10.1088/3050-2454/ae16a8.

摘要

在传统卡尔曼滤波分析中，通常需要准确的噪声统计特性以获得参数的最优估计。然而，在许多实际工程应用中，受试验条件或经费成本等因素的限制，往往难以获取足够的样本来构建精确的噪声统计模型，从而导致分析精度下降，甚至出现结果发散的问题。针对上述不足，本文引入区间过程模型来表征噪声不确定性，提出了一种新的卡尔曼滤波算法。在滤波过程中仅需给定噪声的上下界信息，无需预先假定其精确的概率分布。首先，采用区间过程模型对噪声不确定性进行刻画，并建立相应的状态空间方程；其次，针对一维与多维线性离散系统，构建了一种新的卡尔曼滤波算法，并以滤波误差方差表征滤波估计波动程度；最后，通过三个数值算例对所提出算法的有效性进行了验证。

Abstract

In the traditional Kalman filter analysis

accurate noise statistics are typically required to achieve optimal estimations of parameters. However

in many practical engineering scenarios

the acquisition of sufficient samples to construct precise noise statistics is frequently constrained by limitations in testing conditions or financial considerations

which will lead to reduced precision or even divergence in the analysis results. In this paper

a novel Kalman filter algorithm is developed using an interval process model to represent noise uncertainty

only the upper and lower bounds of the noise are required during the filtering process

eliminating the need for precise probability distributions. Firstly

the uncertainty in the noise is characterized using the interval process model

and the corresponding state space equations are formulated. Secondly

a new Kalman filter algorithm is developed for both one- and multi-dimensional linear discrete systems

where the filter error variance is utilized to indicate the degree of filter estimation fluctuation. Finally

three numerical examples are investigated to validate the efficacy of the proposed algorithm.

关键词

Keywords

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