【作者】 赵巍；

【导师】 潘泉； 戴冠中； 张洪才；

【作者基本信息】 西北工业大学 ， 控制理论与控制工程， 2000， 博士

【摘要】 多尺度系统理论的提出和发展，为更全面、更精确地描述复杂大系统提供了新的思想和方法。本文将多尺度分析方法与动态系统的卡尔曼滤波、线性系统理论相结合，提出了一套体系较为完整的多尺度系统建模、估计与融合方法。在此基础上得到的实时算法可以给出多个层次（尺度）观测数据的最优综合，或在任一层次（尺度）上利用全局信息对局部信号进行最优估计。论文的主要贡献如下：1．以小波逆变换为基础在无限网格上建立了多尺度模型，网格被严格定义为二 叉树形式，用移动算子来表示尺度之间的递推关系。这样建立的多尺度模型 已经不只局限在小波变换的范畴，而是具有更广泛的意义，它可以描述信号 在某一尺度上的一般随机过程特征；2．将时间离散随机过程的马尔可夫性推广到多尺度随机系统，提出了多尺度树 上的马尔可夫性这一新概念。研究了多尺度模型的内部实现和外部实现方法， 给出了选取内部矩阵的基本原则，并着重分析了为马尔可夫自由场建立内部 模型的方法；3．将Kalman滤波和Rauch-Tung-Striebel平滑算法推广到多尺度状态空间，给出 了多尺度估计与融合算法。这个算法具有很好的并行计算特性，扩展到2-D 数据时计算复杂度增加不多；4．提出了一种多尺度动态递归估计算法，将尺度动态方程与时间动态方程相结 合，建立了尺度框架下的动态系统。与传统的动态估计方法比较，在解决大 型系统的估计问题时，计算量大大减少；5．与时间动态系统的状态空间分析相对照，定义了多尺度状态空间的能达性、 能控性、能观性和可重构性，并给出了各自的相应条件。分析了最优多尺度 估计算法的误差协方差特性，研究了误差的动态方程和黎卡提方程的稳定性 和渐近稳定性。6．提出了一种与前面形式不同的动态系统多尺度估计和融合新算法，它无需建 立多尺度模型，在最小估计误差方差意义下具有最优性。随后，进一步对算 法的实时性进行了改进。特别是给出了在某些尺度观测数据残缺的情况下， 构造等效观测方程和等效观测值的方法，使该算法更具实用价值。更多还原

【Abstract】 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.更多还原