A Study Of Multiscale System Modeling,Estimation And Fusion

The multiscale system theory provides a new idea and method to describe the complex and large-scale systems more completely and accurately. In this dissertation, a systemic multiscale modeling, estimation and data fusion theory is developed on the basis of multiscale analysis method, Kalman filtering for dynamic systems and linear system theory. The real-time algorithms derived from this theory can obtain the optimal global fusion of multiresolution (multiscale) data, or optimal estimation at a certain scale. The main contributions are as follows: I. Based on wavelet inverse translation, the multiscale models are built on infinite lattice. The infinite lattice is defined as dyadic tree strictly and a scale-to-scale relationship is specified by the shift operator. In this case the multiscale model is more abstract than wavelet transform. It can represent the features of the signal at a certain scale. 2. Markov property of time discrete stochastic systems is generalized to multisale stochastic systems and a new concept桵arkov property of multisale tree is proposed. The internal realization and external models are given. The principle of choosing internal matrix is developed at the same time. It is analyzed how to build internal realization models for Markov random field. 3. By generalizing Kalman filtering and Rauch-Tung-Striebe smoothing algorithm, a multiscale estimation and data fusion algorithm is presented. This algorithm is highly parallelizable and computationally efficient. When the same idea is extended to 2-D data, the computation burden will not increase significantly. 4. A multiscale dynamic recursive estimation algorithm is proposed and the dynamic systems on multiscale frame are built. While modeling and estimating for large-scale system, this method can reduce computations greatly compared with conventional optimal estimation methods. 5. The reachability, controllability, observability and reconstructibilty for multiscale models are defined as compared to their counterparts for ordinary state-space models. The conditions are given under which the system is reachable, controllable and observable. The properties of error covariance for optimal multiscale estimation algorithm, and the stability and asymptotic behavior of the error dynamics and Riccati equation are analyzed. 6. A new multiscale estimation and data fusion algorithm is given. The advantages are that there is no need to build multiscale model and the algorithm is optimal in the sense of linear least square estimation. A proposal to reduce delay time is put forward. It is discussed how to obtain equivalent measurement equation and measurements in the case of no measurement data at some scale.