Minimax Robust Kalman Filtering under Multistep Random Measurement Delays and Packet Dropouts

YANG Chunshan; ZHAO Ying; LIU Zheng; QIU Yuan; JING Benqin

doi:10.11999/JEIT250741

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YANG Chunshan, ZHAO Ying, LIU Zheng, QIU Yuan, JING Benqin. Minimax Robust Kalman Filtering under Multistep Random Measurement Delays and Packet Dropouts[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250741

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YANG Chunshan, ZHAO Ying, LIU Zheng, QIU Yuan, JING Benqin. Minimax Robust Kalman Filtering under Multistep Random Measurement Delays and Packet Dropouts[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250741

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Minimax Robust Kalman Filtering under Multistep Random Measurement Delays and Packet Dropouts

doi: 10.11999/JEIT250741 cstr: 32379.14.JEIT250741

School of Artificial Intelligence, Guilin University of Aerospace Technology, Guilin, 541004, China

Funds: The National Natural Science Foundation of China (62263009), Guangxi Natural Science Foundation (GXNSFAA069941 and GXNSFAA069180), GUAT Special Research Project on the Strategic Development of Distinctive Interdisciplinary Fields (TS2024241)

Received Date: 2025-08-12
Accepted Date: 2025-11-03
Rev Recd Date: 2025-11-03

Available Online: 2025-11-12

Abstract

Abstract

Objective The networked control system (NCS) offer many advantages including flexibility in installation and maintenance, lower cost, but also introduce more complexities that include the random measurement delays and packet dropouts due to the unreliability of the communication network and the limited bandwidth. Meanwhile, the system noise variance may fluctuate significantly under the environment of strong electromagnetic interference. The time delay is random and uncertain in NCS. When a group of Bernoulli distributed random variables are used to describe multi-step random measurement delays and packet dropouts, the fictitious noise method in the current research work will lead to the autocorrelation between different components, which make it hard to compute the fictitious noise variances, and hard to prove the robustness. This research offers the solution to minimax robust Kalman filtering for system with uncertain noise variance, multistep random measurement delay and packet dropouts. Methods The main difficulties lie in model transformation and proof of robustness. When a group of Bernoulli distributed random variables are used to describe multi-step random measurement delays and packet dropouts, a series of approaches have been adopted to address the minimax robust Kalman filtering problem. Firstly, a new model transformation method is presented based on the flexibility of Hadamard product in multi-dimensional data processing, and then the robust time-varying Kalman estimator is designed in a unified form based on the minimax robust filtering principle. Secondly, the matrix elementary transformation, strict diagonal-dominance matrix, Gerŝgorin circle theorem and Hadamard product theorem are used to prove the robustness based on the generalized Lyapunov equation method. Additionally, the Hadamard product is converted into matrix product by using matrix factorization method, a sufficient condition for the existence of the steady-state estimator is obtained, then the robust steady-state Kalman estimator is designed. Results and Discussions The proposed minimax robust Kalman filter extended the robust Kalman filtering method and provided new theoretical support for solving the robust fusion filtering problem of complex NCS. The curves (Fig. 5) give the actual accuracy ${\text{tr}}{{\mathbf{\bar P}}^l}(N)$, $l = a,b,c,d$ versus $ 0.1 \le {\alpha _0},{\alpha _1},{\alpha _2} \le 1 $. It can be seen that the situation (a) has the highest robust accuracy, followed by situation (b) and situation (c), and the situation (d) has worse actual accuracy. That is because the measurements received by estimators in situations (a) have one-step random delay, and situation (d) has higher packet loss rate. The curves (Fig. 5) show the reasonability and effectiveness of the proposed method. Another simulation is considered for mass–spring–damper system. The comparisons between the proposed method and optimal robust filtering method (Tab. 2, Fig. 7), it can be seen that although the proposed method can guarantee that the actual prediction error variance has the minimum upper bound, however, the actual accuracy is slightly lower than the optimal prediction accuracy. Conclusions The minimax robust Kalman filtering problem is addressed for system with uncertain noise variance, multistep random measurement delay and packet dropouts. The system noise variance is uncertain but with known conservative upper bounds, and a group of Bernoulli distributed random variables with known probability are used to describe the multistep random measurement delay and packet dropouts from sensor to estimator. The Hadamard product is used to improve the model transformation method, and then the minimax robust time-varying Kalman estimator are designed. The robustness is proved by matrix elementary transformation, Gerŝgorin circle theorem, Hadamard product theorem, matrix factorization and Lyapunov equation method. A sufficient condition that the time-vary generalized Lyapunov equation has steady-state unique positive semi-definite solution is given, and then robust steady-state estimator is designed. The convergence in a realization between the time-varying and steady state estimator is proved. Two simulation examples show the effectiveness of the proposed results. The proposed methods overcome the limitation of existing methods, and provide theoretical support for solving the robust fusion filtering problem of complex NCS.
- Multistep random measurement delays,
- Packet dropouts,
- Hadamard product,
- Ger$\hat s $gorin circle theorem,
- Minimax robust filtering

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References(20)

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