A new Kalman filter algorithm based on the interval process model

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

doi:10.1088/3050-2454/ae16a8

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A new Kalman filter algorithm based on the interval process model

Papers | 更新时间：2026-02-13

- A new Kalman filter algorithm based on the interval process model
- 基于区间过程模型的新型卡尔曼滤波算法
- Journal of Reliability Science and Engineering Issue 4, Pages: 1-17(2025)
- 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
  CLC：
- Received：04 June 2025，
  
  Revised：2025-10-16，
  
  Accepted：20 October 2025，
  
  Online First：14 November 2025，
  
  Published：2025
- 稿件说明：
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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：

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

references

Wiener N 1949 Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications ( MIT Press )

Kalman R E 1960 A new approach to linear filtering and prediction problems J. Basic Eng. 82 35 – 45

Kalman R E and Bucy R S 1961 New results in linear filtering and prediction theory J. Basic Eng. 83 95 – 108

Zakai M 1959 On a property of Wiener filters IRE Trans. Inf. Theory 5 15 – 17

Khodarahmi M and Maihami V 2023 A review on Kalman filter models Arch. Comput. Methods Eng. 30 727 – 47

Li X , Liang J , Huang G , Ma S and Li H 2024 Adaptive invariant extended Kalman filter-based tightly-coupled SINS/RTK-integrated positioning for rotor unmanned aerial vehicle IEEE Trans. Instrum. Meas. 73 1 – 17

Jafari H and Poshtan J 2021 Event-triggered robust fault diagnosis Kalman filter for stochastic systems IEEE Sens. J. 21 11031 – 9

Su Y , Han J , Ma C , Wu J , Wang X , Zhu Q and Shen J 2024 Adaptive Kalman filter based on online ARW estimation for compensating low-frequency error of MHD ARS IEEE Trans. Instrum. Meas. 73 1 – 10

Diaz M , Charbonnel P É and Chamoin L 2023 A new Kalman filter approach for structural parameter tracking: application to the monitoring of damaging structures tested on shaking-tables Mech. Syst. Signal Process 182 109529

Fahmy H M , Hasanien H M , Alharbi M and Ji H 2025 Hybrid extended Kalman filter with Newton Raphson method for lifetime prediction of lithium-ion batteries Sci. Rep. 15 14592

Afrasiabi A , Faramarzi A , Chapman D and Keshavarzi A 2025 Optimising ground penetrating radar data interpretation: a hybrid approach with AI-assisted Kalman filter and wavelet transform for detecting and locating buried utilities J. Appl. Geophys. 232 105567

Guo M , Hao Y , Lu Y and Sun L 2025 Long-short term memory modeling and performance analysis of extended-state Kalman filter-based energy-saving model predictive control for supercritical unit Appl. Therm. Eng. 272 126202

Gao G , Yi Y , Zhong Y , Liang S , Hu G and Gao B 2025 A robust Kalman filter based on kernel density estimation for system state estimation against measurement outliers IEEE Trans. Instrum. Meas. 74 1 – 12

Elliott A J , Nakhaeezadeh Gutierrez A , Felicetti L and Zanotti Fragonara L 2025 In-orbit system identification of a flexible satellite with variable mass using dual unscented Kalman filters Acta Astronaut. 226 71 – 86

Gu H , Li Y , Jiang L and Luo Z 2025 A generalized approach for remaining useful life prediction considering the multi-source uncertainty of mechanical systems J. Reliab. Sci. Eng. 1 025301

Huang Y , Zhang Y , Xu B , Wu Z and Chambers J A 2018 A new adaptive extended Kalman filter for cooperative localization IEEE Trans. Aerosp. Electron. Syst. 54 353 – 68

Davari N and Gholami A 2019 Variational Bayesian adaptive Kalman filter for asynchronous multirate multi-sensor integrated navigation system Ocean Eng. 174 108 – 16

Shan C , Zhou W , Yang Y and Jiang Z 2021 Multi-fading factor and updated monitoring strategy adaptive Kalman filter-based variational Bayesian Sensors 21 198

Fu H and Cheng Y 2022 A novel maximum likelihood and moving weighted average based adaptive Kalman filter J. Instrum. 17 08036

Assa A and Plataniotis K N 2017 Adaptive Kalman filtering by covariance sampling IEEE Signal Process Lett. 24 1288 – 92

Wang H , Deng Z , Feng B , Ma H and Xia Y 2017 An adaptive Kalman filter estimating process noise covariance Neurocomputing 223 12 – 17

Hu J and Shi X 2021 Refined alignment method for single-axis rotary inertial navigation based on fuzzy adaptive filtering J. Sys. Simul. 33 315 – 23

Pan Z , Yi X , Zhang Y , Jeon B and Kwong S 2020 Efficient in-loop filtering based on enhanced deep convolutional neural networks for HEVC IEEE Trans. Image Process 29 5352 – 66

Assa A , Janabi-Sharifi F an d Plataniotis K N 2019 Sample-based adaptive Kalman filtering for accurate camera pose tracking Neurocomputing 333 307 – 18

Liu Y , Fan X , Lv C , Wu J , Li L and Ding D 2018 An innovative information fusion method with adaptive Kalman filter for integrated INS/GPS navigation of autonomous vehicles Mech. Syst. Signal Process. 100 605 – 16

Zhou W , Li X , Yi J and He H 2019 A novel UKF-RBF method based on adaptive noise factor for fault diagnosis in pumping unit IEEE Trans. Ind. Inf. 15 1415 – 24

Ge Q , Li H and Wen C 2019 Deep analysis of Kalman filtering theory for engineering applications J. Command Control 5 167 – 80

Ge Q , Li Y , Wang Y , Hu X , Li H and Sun C 2024 Adaptive Kalman filtering based on model parameter ratios IEEE Trans. Autom. Control 69 6230 – 7

Etter D , Hicks M and Cho K 1982 Recursive adaptive filter design using an adaptive genetic algorithm ICASSP’82. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing pp 635 – 8

Sarkka S and Nummenmaa A 2009 Recursive noise adaptive Kalman filtering by variational Bayesian approximations IEEE Trans. Autom. Control 54 596 – 600

Zhang D , Zhang H , Zhou P , Li X-A , Wang F and Han X 2025 Time-variant system reliability analysis via stochastic process discretization and most probable point trajectory approximation J. Reliab. Sci. Eng. 1 025001

Ge Q , Shao T , Chen S and Wen C 2017 Carrier tracking estimation analysis by using the extended strong tracking filtering IEEE Trans. Ind. Electron 64 1415 – 24

Ge Q , Shao T , Duan Z and Wen C 2016 Performance analysis of the Kalman filter with mismatched noise covariances IEEE Trans. Autom. Control 61 4014 – 9

Chen G , Wang J and Shieh L S 1997 Interval Kalman filtering IEEE Trans. Aerosp. Electron. Syst. 33 250 – 9

Jun X , Carine J , Louise T-M and Françoise L G 2013 Fault detection using interval Kalman filtering enhanced by constraint propagation 52nd IEEE Conf. on Decision and Control pp 490 – 5

Andrew A M 2002 Applied interval analysis: with examples in parameter and state estimation, robust control and robotics Kybernetes 31 1

Tran T A , Jauberthie C , Gall F L and Travé-Massuyès L 2017 Interval Kalman filter enhanced by positive definite upper bounds IFAC-PapersOnLine 50 1595 – 600

Lu Q-H , Fergani S , Jauberthie C and Le Gall F 2019 Optimally bounded interval Kalman filter 2019 IEEE 58th Conf. on Decision and Control (CDC) pp 379 – 84

Lu Q-H , Fergani S and Jauberthie C 2021 A new scheme for fault detection based on optimal upper bounded interval Kalman filter IFAC-PapersOnLine 54 292 – 7

Lu Q-H , Fergani S and Jauberthie C 2024 Analytical bounds for an interval Kalman filter IEEE Trans. Autom. Control 69 449 – 54

Li X , Wang X , Qian J and Jiang G-P 2024 Improving interval Kalman filtering through interval optimization strategy Proc. 2023 7th Chinese Conf. on Swarm Intelligence and Cooperative Control pp 310 – 21

Jiang C , Ni B Y , Han X and Tao Y R 2014 Non-probabilistic convex model process: a new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems Comput. Methods Appl. Mech. Eng. 268 656 – 76

Jiang C , Ni B Y , Liu N Y , Han X and Liu J 2016 Interval process model and non-random vibration analysis J. Sound. Vib. 373 104 – 31

Catlin D E 1989 Estimation, Control, and the Discrete Kalman Filter ( Springer )

Grewal M S and Andrews A P 2014 Kalman Filtering: Theory and Practice with MATLAB ( Wiley )

Jiang C , Li J W , Ni B Y and Fang T 2019 Some significant improvements for interval process model and non-random vibration analysis method Comput. Methods Appl. Mech. Eng. 357 112565

Resnick S I 2013 Adventures in Stochastic Processes ( Springer )

Elishakoff I , Elisseeff P and Glegg S A 1994 Nonprobabilistic, convex-theoretic modeling of scatter in material properties AIAA J. 32 843 – 9

Wu J L , Zhang Y Q , Chen L P and Luo Z 2013 A Chebyshev interval method for nonlinear dynamic systems under uncertainty Appl. Math. Model. 37 4578 – 91

Kang Z and Zhang W B 2016 Construction and application of an ellipsoidal convex model using a semi-definite programming formulation from measured data Comput. Methods Appl. Mech. Eng. 300 461 – 89

Qiu Z P and Wang X J 2003 Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach Int. J. Solids Struct. 40 5423 – 39

Ponce Campuzano J C , Matthews K E and Adams P 2018 On the use of history of mathematics: an introduction to Galileo’s study of free fall motion Int. J. Math. Educ. Sci. Technol. 49 517 – 29

Lin X Y , Luo H Z and Fan W Q 2010 An improved GPS dynamic positioning filtering method J. Nav. Aer. Eng. Coll. 25 361 – 4

Britting K R 2010 Inertial Navigation Systems Analysis ( Wiley )

Chang L , Li J and Chen S 2014 Initial alignment by attitude estimation for strapdown inertial navigation systems IEEE Trans. Instrum. Meas. 64 784 – 94

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