| 摘要: |
| The work proposes a distributed Kalman filtering (KF) algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way. We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions, which implies that the theoretical results are able to be applied to stochastic feedback systems. Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation. We employ analysis techniques such as stochastic Lyapunov function, stability theory of stochastic systems, and algebraic graph theory to deal with the above issue. The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal, the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way. At last, we illustrate the property of the proposed distributed KF algorithm by a simulation example. |
| 关键词: Distributed Kalman filtering algorithm · Stochastic cooperative information condition · Sensor networks ·
L p-exponential stability · Stochastic regression model |
| DOI：https://doi.org/10.1007/s11768-025-00253-x |
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| 基金项目:This work was supported in part by Sichuan Science and Technology
Program under Grant No. 2025ZNSFSC151, in part by the Strategic
Priority Research Program of Chinese Academy of Sciences under
Grant No. XDA27030201, and the Natural Science Foundation of
China under Grant No. U21B6001, in part by the Natural Science
Foundation of Tianjin under Grant No. 24JCQNJC01930 |
|
| Stability analysis of distributed Kalman filtering algorithm for stochastic regression model |
| Die Gan |
| (College of Artificial Intelligence, Nankai University, Tianjin, 300350, China) |
| Abstract: |
| The work proposes a distributed Kalman filtering (KF) algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way. We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions, which implies that the theoretical results are able to be applied to stochastic feedback systems. Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation. We employ analysis techniques such as stochastic Lyapunov function, stability theory of stochastic systems, and algebraic graph theory to deal with the above issue. The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal, the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way. At last, we illustrate the property of the proposed distributed KF algorithm by a simulation example. |
| Key words: Distributed Kalman filtering algorithm · Stochastic cooperative information condition · Sensor networks ·
L p-exponential stability · Stochastic regression model |
