The optimal filtering of a class of dynamic multiscale systems

• Published in: Science China. Information sciences Vol. 47; no. 4; pp. 501 - 517
• Main Authors: Pan, Quan, Zhang, Lei, Cui, Peiling, Zhang, Hongcai
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.08.2004; Department of Automatic Control, Northwestern Polytechnical University, Xi'an 710072, China
• Subjects: Algorithms; Controllability; Dynamical systems; Kalman filters; Observability (systems); Sensors; Time invariant systems; Wavelet transforms; 动态多模系统; 卡尔曼滤波; 小波变换; 离散时间模型; dynamic multiscale system; Kalman filtering; wavelet transform
• ISSN: 1009-2757; 1674-733X; 1862-2836; 1869-1919
• DOI: 10.1007/BF02901660

This paper discusses the optimal filtering of a class of dynamic multiscale systems (DMS), which are observed independently by several sensors distributed at different resolution spaces. The system is subject to known dynamic system model. The resolution and sampling frequencies of the sensors are supposed to decrease by a factor of two. By using the Haar wavelet transform to link the state nodes at each of the scales within a time block, a discrete-time model of this class of multiscale systems is given, and the conditions for applying Kalman filtering are proven. Based on the linear time-invariant system, the controllability and observability of the system and the stability of the Kalman filtering is studied, and a theorem is given. It is proved that the Kalman filter is stable if only the system is controllable and observable at the finest scale. Finally, a constant-velocity process is used to obtain insight into the efficiencies offered by our model and alqorithm.