帶乘性噪聲的觀測時滯系統(tǒng)估計研究
發(fā)布時間：2018-07-15 17:51
【摘要】：近年來,帶乘性噪聲觀測時滯系統(tǒng)估計問題得到了眾多學者的關注,因為這些問題廣泛應用于石油勘探、網(wǎng)絡通信工程、圖像處理等實際應用領域。通常情況下學者們會用標量來表示乘性噪聲。然而,本文用一個多維隨機對角矩陣表示乘性噪聲,同時給出了兩種估計算法,分別是最優(yōu)估計算法和限定記憶最優(yōu)濾波算法。本文主要研究工作包括如下幾點:(1)針對含有乘性噪聲的觀測時滯系統(tǒng),根據(jù)卡爾曼濾波原理提出了有限時間最優(yōu)估計器算法。首先利用新息重組理論將帶時滯系統(tǒng)轉化為無時滯系統(tǒng),然后根據(jù)正交投影定理和卡爾曼濾波算法,通過計算兩個和原使系統(tǒng)具有相同維數(shù)的黎卡提差分方程和李雅普諾夫方程求出所需要的最優(yōu)狀態(tài)估計器。在計算過程中,介紹并使用了矩陣Hadamard積(⊙)乘法。(2)進而,在系統(tǒng)矩陣穩(wěn)定的條件下設計了穩(wěn)態(tài)估計器。最后針對含有乘性噪聲的觀測時滯系統(tǒng)做了最優(yōu)反褶積估計研究,其研究過程同樣是根據(jù)卡爾曼濾波和投影定理進行的。(3)隨著估計誤差的積累,過“老”的觀測值不能準確地用來估計新的狀態(tài)值。與最優(yōu)估計算法相比,限定記憶最優(yōu)濾波的好處在于只利用當前時刻以前固定數(shù)量的測量數(shù)據(jù),這樣就可以減小計算量。針對觀測時滯系統(tǒng),本文提供了有效的方法求得限定記憶最優(yōu)濾波的初始值,再根據(jù)投影定理和卡爾曼濾波得出限定記憶最優(yōu)濾波器。(4)用Matlab進行了大量仿真研究并給出了數(shù)值例子,分別證明了這兩種濾波算法是有效的。
[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.
【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN713
本文編號：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.
【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN713
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