本文關(guān)鍵詞： 隨機(jī)時(shí)滯 測量丟失 噪聲 最優(yōu)濾波 一致濾波　出處：《哈爾濱理工大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：本文研究了具有時(shí)滯和測量丟失的離散隨機(jī)系統(tǒng)的最優(yōu)濾波問題。在實(shí)際系統(tǒng)中,時(shí)滯與測量丟失是最常見的問題之一。為了可以更準(zhǔn)確地對系統(tǒng)的狀態(tài)進(jìn)行估計(jì),我們研究一類具有時(shí)滯和測量丟失的系統(tǒng)是很有理論和實(shí)際意義的。首先,研究具有乘性噪聲和一步隨機(jī)傳感器時(shí)滯的離散隨機(jī)時(shí)滯系統(tǒng)的最優(yōu)濾波問題,系統(tǒng)的過程噪聲與測量噪聲是不相關(guān)的白噪聲。利用新息分析方法以及遞推射影公式,設(shè)計(jì)出了在均方意義下濾波誤差最小的線性最優(yōu)濾波器,并給出數(shù)值算例來驗(yàn)證濾波器的有效性與可行性。隨后,將問題推廣到一般情況,即研究具有一步隨機(jī)多傳感器時(shí)滯的離散隨機(jī)時(shí)滯系統(tǒng)的最優(yōu)濾波問題,為簡化問題不考慮系統(tǒng)的乘性噪聲。類似地,得到了該系統(tǒng)的線性最優(yōu)濾波器,并通過一組數(shù)值算例來驗(yàn)證濾波器的可行性和有效性。其次,研究具有乘性噪聲、有限步自相關(guān)過程噪聲、一步隨機(jī)傳感器時(shí)滯和測量丟失的離散隨機(jī)系統(tǒng)的最優(yōu)濾波問題,系統(tǒng)的測量噪聲是不相關(guān)的白噪聲。我們基于均方誤差最小(minimum mean square error(MMSE))的準(zhǔn)則,設(shè)計(jì)出了估值誤差最小的線性最優(yōu)濾波器,并通過一組數(shù)值算例對濾波器的有效性和可行性進(jìn)行了驗(yàn)證。最后,研究了具有測量丟失的非線性離散隨機(jī)系統(tǒng)基于分布式無損(無跡)卡爾曼濾波(Distributed Unscented Kalman Filtering(DUKF))的一致算法,系統(tǒng)的過程噪聲與測量噪聲是不相關(guān)的白噪聲。通過無損(無跡)變換(Unscented Transformation(UT))的方法設(shè)計(jì)出具有測量丟失的非線性離散隨機(jī)系統(tǒng)的DUKF,根據(jù)一致信息(Consensus on Information(CI))的方法可以得到基于DUKF的一致算法,通過數(shù)值算例說明所設(shè)計(jì)濾波算法的一致性。
[Abstract]:In this paper, the optimal filtering problem for discrete stochastic systems with time delay and measurement loss is studied. Time delay and measurement loss are one of the most common problems. In order to estimate the state of the system more accurately, it is of great theoretical and practical significance to study a class of systems with time delay and measurement loss. The optimal filtering problem for discrete stochastic time-delay systems with multiplicative noise and one-step stochastic sensor delays is studied. The process noise and measurement noise of the system are white noise which is irrelevant. Using innovation analysis method and recursive projective formula, a linear optimal filter with minimum filtering error in the sense of mean square is designed. Numerical examples are given to verify the validity and feasibility of the filter. Then, the problem is extended to the general situation, that is, the optimal filtering problem for discrete stochastic time-delay systems with one-step stochastic multi-sensor delay is studied. In order to simplify the problem without considering the multiplicative noise of the system, the linear optimal filter of the system is obtained, and the feasibility and validity of the filter are verified by a set of numerical examples. The optimal filtering problem for discrete stochastic systems with multiplicative noise, finite step autocorrelation process noise, one-step stochastic sensor delay and measurement loss is studied. The measurement noise of the system is an irrelevant white noise. We base on the criterion of minimum mean square error (MMSE) with minimum mean square error (MSE). A linear optimal filter with minimum estimation error is designed, and the validity and feasibility of the filter are verified by a set of numerical examples. The distributed lossless (unscented) Kalman filter for nonlinear discrete stochastic systems with measurement loss is studied. Distributed Unscented Kalman filtering algorithm. The process noise and the measurement noise of the system are white noises which are irrelevant. Unscented Transformation by Lossless (Unscented Transformation). The DUKF of nonlinear discrete stochastic system with measurement loss is designed. A consistent algorithm based on DUKF can be obtained based on consensus information. A numerical example is given to illustrate the consistency of the proposed filtering algorithm.
【學(xué)位授予單位】：哈爾濱理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN713

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本文編號：1490715