Modeling and estimation of a class of dynamic multiscale systems by general compactly supported wavelet

This paper addresses the problem of dynamic multiscale system (DMS) estimation. Research achievements in the related area have been reported in the literature, but they either rely on the assumption of stationarity of the observed process or are difficult to be implemented. In this paper, a model of DMS that meets the requirements of the standard discrete time Kalman filtering is built and is realized by general compactly supported wavelet. The introduction of the state space projection equation and the augmentation of measurement equation are a major part of the novelty in our work. A theorem on the optimal filtering output at each scale is put forward. Experimental results are given to verify our methods' superior performances.