带乘性噪声的观测时滞系统估计研究
发布时间：2018-07-15 17:51
【摘要】：近年来,带乘性噪声观测时滞系统估计问题得到了众多学者的关注,因为这些问题广泛应用于石油勘探、网络通信工程、图像处理等实际应用领域。通常情况下学者们会用标量来表示乘性噪声。然而,本文用一个多维随机对角矩阵表示乘性噪声,同时给出了两种估计算法,分别是最优估计算法和限定记忆最优滤波算法。本文主要研究工作包括如下几点:(1)针对含有乘性噪声的观测时滞系统,根据卡尔曼滤波原理提出了有限时间最优估计器算法。首先利用新息重组理论将带时滞系统转化为无时滞系统,然后根据正交投影定理和卡尔曼滤波算法,通过计算两个和原使系统具有相同维数的黎卡提差分方程和李雅普诺夫方程求出所需要的最优状态估计器。在计算过程中,介绍并使用了矩阵Hadamard积(⊙)乘法。(2)进而,在系统矩阵稳定的条件下设计了稳态估计器。最后针对含有乘性噪声的观测时滞系统做了最优反褶积估计研究,其研究过程同样是根据卡尔曼滤波和投影定理进行的。(3)随着估计误差的积累,过“老”的观测值不能准确地用来估计新的状态值。与最优估计算法相比,限定记忆最优滤波的好处在于只利用当前时刻以前固定数量的测量数据,这样就可以减小计算量。针对观测时滞系统,本文提供了有效的方法求得限定记忆最优滤波的初始值,再根据投影定理和卡尔曼滤波得出限定记忆最优滤波器。(4)用Matlab进行了大量仿真研究并给出了数值例子,分别证明了这两种滤波算法是有效的。
[Abstract]:In recent years, the estimation of time-delay systems with multiplicative noise observations has attracted many scholars' attention, because these problems are widely used in oil exploration, network communication engineering, image processing and other practical applications. In general, scholars will use scalars to represent multiplicative noise. However, the multiplicative noise is represented by a multi-dimensional random diagonal matrix, and two estimation algorithms are presented, which are optimal estimation algorithm and constrained memory optimal filtering algorithm. The main work of this paper is as follows: (1) for time-delay systems with multiplicative noise, a finite-time optimal estimator algorithm is proposed according to the Kalman filter principle. Firstly, the time-delay system is transformed into a delay-free system by using the innovation recombination theory. Then, according to the orthogonal projection theorem and the Kalman filter algorithm, By calculating two Rikati difference equations and Lyapunov equations with the same dimension, the optimal state estimators are obtained. In the process of calculation, matrix Hadamard product multiplication is introduced and used. (2) A steady state estimator is designed under the condition that the system matrix is stable. Finally, the optimal deconvolution estimation is studied for observational time-delay systems with multiplicative noise. The research process is also based on Kalman filtering and projection theorem. (3) with the accumulation of estimation errors, Over-the-old observations cannot be used accurately to estimate new state values. Compared with the optimal estimation algorithm, the advantage of constrained memory optimal filtering is that only a fixed number of measurement data before the current moment is used, which can reduce the computational complexity. For observational time-delay systems, this paper provides an effective method to obtain the initial value of the constrained memory optimal filtering. According to the projection theorem and Kalman filter, the optimal filter with limited memory is obtained. (4) A large number of simulation studies are carried out with Matlab and numerical examples are given, respectively, to prove that these two filtering algorithms are effective.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713
本文编号：2124881
[Abstract]:In recent years, the estimation of time-delay systems with multiplicative noise observations has attracted many scholars' attention, because these problems are widely used in oil exploration, network communication engineering, image processing and other practical applications. In general, scholars will use scalars to represent multiplicative noise. However, the multiplicative noise is represented by a multi-dimensional random diagonal matrix, and two estimation algorithms are presented, which are optimal estimation algorithm and constrained memory optimal filtering algorithm. The main work of this paper is as follows: (1) for time-delay systems with multiplicative noise, a finite-time optimal estimator algorithm is proposed according to the Kalman filter principle. Firstly, the time-delay system is transformed into a delay-free system by using the innovation recombination theory. Then, according to the orthogonal projection theorem and the Kalman filter algorithm, By calculating two Rikati difference equations and Lyapunov equations with the same dimension, the optimal state estimators are obtained. In the process of calculation, matrix Hadamard product multiplication is introduced and used. (2) A steady state estimator is designed under the condition that the system matrix is stable. Finally, the optimal deconvolution estimation is studied for observational time-delay systems with multiplicative noise. The research process is also based on Kalman filtering and projection theorem. (3) with the accumulation of estimation errors, Over-the-old observations cannot be used accurately to estimate new state values. Compared with the optimal estimation algorithm, the advantage of constrained memory optimal filtering is that only a fixed number of measurement data before the current moment is used, which can reduce the computational complexity. For observational time-delay systems, this paper provides an effective method to obtain the initial value of the constrained memory optimal filtering. According to the projection theorem and Kalman filter, the optimal filter with limited memory is obtained. (4) A large number of simulation studies are carried out with Matlab and numerical examples are given, respectively, to prove that these two filtering algorithms are effective.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713
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