1. 55 zhongguancun east road, haidian district, Beijing, , Beijing China 100190
2. Wayne State University, 622 W Forest Avenue , Detroit Michigan United States 48202-3489
3. 北京海淀区中关村东路55号 , 北京 China 100190
In this paper, we propose a distributed Kalman Filter (DKF) for the dynamical system with general random coefficients. In the proposed method, each estimator shares local innovation pairs with its neighbors to collectively complete the estimation task. Further, we introduce a collective random observability condition by which the $L_p$-stability of the covariance matrix and the $L_p$-exponential stability of the homogeneous part of the estimation error equation can be established. In contrast, the stringent conditions on the coefficient matrices, such as independency and stationarity are not required. Besides, the stability of the DKF, i.e., the boundedness of the filtering errors, can be established. Finally, from the simulation result, we demonstrate the cooperative effect of the sensors.
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