Stability analysis of distributed Kalman filtering algorithm for stochastic regression model
Siyu Xie
Die Gan
Zhixin Liu
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.
Keywords：Distributed Kalman filtering algorithmStochastic cooperative information conditionSensor networksLp-exponential stabilityStochastic regression model
Publication Date：2025-05-30
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：15( 161-175 )