摘要
近二十年来，随着多尺度技术在信号处理领域的广泛应用，多尺度系统理论日趋成熟。目前，一般将多尺度系统分为两大类：SMS(统计多尺度系统，Statistical Multiscale System)和DMS(动态多尺度系统，Dynamic Multiscale System)。SMS主要研究的是统计信号的多尺度处理方法，DMS要解决的问题是动态多尺度系统状态的实时估计，其研究成果远不如SMS丰富，具体实现方法和系统结构也还很不完备，本文针对DMS中的尺度算子和非线性等问题展开研究，主要工作如下：
1．对多尺度系统理论的应用背景和发展现状做了系统的概述，着重讨论了多尺度系统理论的两种基本类型：静态多尺度系统(SMS)和动态多尺度系统理论(DMS)的基本框架，对两种系统理论进行了分析和比较；
2．针对动态多尺度系统理论中的核心——投影算子的实现问题，给出了一种基于最小二乘法的投影算子估计算法及其仿真，根据算法推导过程和仿真结果，得到一些有关算法实用性和原动态多尺度建模理论本身的一些结论，得出原理论框架中一个新的约束条件，进一步完善了原系统理论；
3．将多尺度研究范畴扩展到非线性领域，建立非线性多尺度系统模型，讨论了非线性多尺度系统两种类型，提出了基于非线性Unscented Kalman Filter(UKF)的多尺度融合算法，该算法结合序贯式滤波对多个量测的分散处理，能有效降低计算量，同时具有UKF算法处理系统状态或量测方程强非线性情况的能力，并在二维非线性目标跟踪中显示了其比基于单一尺度的跟踪算法的优越性。
In the last two decades, multiscale system theory has been developed quickly with the broad application of multiscale techniques in signal processing. Multiscale systems can be divided into two categories: SMS (Statistical Multiscale System) and DMS (Dynamic Multiscale System). SMS theory is to discuss the multiscale processing techniques of stochastic signals. DMS theory is to get the real time estimation of the states of the dynamic systems. Now its research efforts can not be compared with that of SMS. The detailed implement method and its system frame are rather incomplete. This thesis is focused on these problems to do some extended research of dynamic multiscale system theory. The main contributions are as follows:
1. It is introduced that what the main application background of multiscale system theory is and how it has developed recently. Next, the two frames of
multiscale system--Static Multiscale System and dynamic multiscale system are
presented detailedly and compared.
2. A new approach is present to estimate the multiscale projection operator by using the Linear least square estimation (LLSE). For application, A recursive edition of this algorithm is also present. Computer simulation results are presented to show the effectiveness of the algorithm. According to the estimation procedure and the simulation result, we get an additional key restriction that is not included in the original theory. This nuclear restriction is that as long as the observation matrixes of all scales (expect the finest scale) are full column rank, the operator's estimation algorithm will always be efficient.
3. We extend the multiscale research to a nonlinear field. Firstly, a nonlinear multiscale model is established. Secondly, we discussed two types of the nonlinear multiscale system, and a set of nonlinear multiscale fusion algorithms based on Unscented Kalman Filter (UKF) and sequential estimation method is presented. Simulation results show that this new algorithm is superior to single scale tracking algorithm.
引文
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