张贤达的《高阶统计量信号处理方法》
高阶统计量分析方法是一种重要的非高斯信号分析方法，在此上传张贤达的这本书，希望对大家的学习有所帮助专题内容概述高阶统计量的定义、性质和估计155()高阶矩、高阶累积量及其谱·*·····“········““··“·(二)高阶累积量与高阶谱的性质三)高阶累积量与高阶谱的估计…......19、非最小相位系统的辨识21(一)基本问题21(二)MA系统的辨识.25(三)ARMA系统的辨识…135四、谐波恢复42()基本问题42()谐波恢复的高阶累积量方法……………·………43五、空间窄带信号源的波达方向估计()基本问题46(二)基于二阶统计量的DOA估计方法及其不足.147(三)基于高阶统计量的DOA估计方法53、概述高阶统计量( (Higher-order Statistics)是指比二阶统计量更高阶的随机变量或随机过程的统计量。二阶统计量有:〉随机变量(矢量):方差、协方差(相关矩)、二阶矩。随机过程:自相关函数、功率谱、互相关函数、互功率谱、自协方差函数等高阶统计量有:随机变量(矢量):高阶矩( Higher-order Moment),高阶累积量(Higher-order Cumulant)随机过程:高阶矩、高阶累积量、高阶谱( Higher- order Spectra,Polyspectra)。从统计学的角度,对正态分布的随机变量(矢量),用一阶和二阶统计量就可以完备地表示其统计特征。如对一个高斯分布的随机矢量,知道了其数学期望和协方差矩阵,就可以知道它的联合概率密度函数。对一个高斯随机过程,知道了均值和自相关函数(或自协方差函数),就可以知道它的概率结构,即知道它的整个统计特征。但是,对不服从髙斯分布的随机变量(矢量)或随机过程,一阶和二阶统计量不能完备地表示其统计特征。或者说,信息没有全部包含在一二阶统计量中,更高阶的统计量中也包含了大量有用的信息。高阶统计量信号处理方法,就是从非高斯信号的高阶统计量中提取信号的有用信息,特别是从一、二阶统计量中无法提取的信息的方法。从这个角度来说,高阶统计量方法不仅是对基于相关函数或功率谱的随机信号处理方法的重要补充,而且可以为二阶统计量方法无法解决的许多信号处理问题提供手段。可以亳不夸张地说,凡是使用功率谱或相关函数进行过分析与处理,而又未得到满意结果的任何问题,都值得重新试用高阶统计量方法。高阶统计量的概念于1889年提出。高阶统计量的研究始于六十年代初,主要是数学家和统计学家们在做基础理论的研究,以及针对光学、流体动力学、地球物理、信号处理等领域特定问题的应用研究。直到八十年代中、后期,在信号处理和系统理论领域才掀起了高阶统计量方法的研究热潮。标志性的事件有:1. K. S. Lii. m. rosenblatt "Deconvolution and Estimation of TransferFunction phase and Coefficients for non-Gaussian Linear processes AnnStatistcs, Vol, 10, pp. 1195-1208, 1982首次用高阶统计量解决了非最小相位系统的盲辩识问题。2.C.L. Nikias,M.R. Raghuveer的综述文章“ Bispectrum Estimation:ADigital Signal Processing Framework”在Proc.正EE发表,1987July3.1989、1991、1993、1995、1997、1999年举办了六届关于高阶统计量的信号处理专题研讨会(海军研究办公室,NSF, IEEE Control SystemSociety, IEEE ASSP Society, IEEE Geoscience and Remote sensingSociety4. IEEE Trans.onAC1990年1月专辑5. IEEE Trans, on AssP1990年7月专辑。6.J.M. Mendel的综述文章 Tutorial on Higher- Order statistics( Spectra)inSignal Processing and System Theory: Theoretical Results and SomeApplications”.Proc,正E,1991(主要是关于非最小相位系统辨识)。7.C.L. Nikias&A.P. Petropula的专著 Higher-order Spectral Analysis:ANonlinear Processing Framework,由 Prentice-Hall I1993出版。8. Signal Processing,19944月专辑。9. Circuits, Systems, and Signal Processing,1994.6月专辑。高阶统计量方法已在雷达、声纳、通信、海洋学、电磁学、等离子体物理、结晶学、地球物理、生物医学、故障诊断、振动分析、流体动力学等领域的信号处理问题中获得应用。典型的信号处理应用包括系统辨识与时间序列分析建模、自适应估计与滤波、信号重构、信号检测、谐波恢复、图像处理、阵列信号处理、盲反卷积与盲均衡等。在信号处理中使用高阶统计量的主要动机可以归纳成四点1、抑制未知功率谱的加性有色噪声的影响。2、辨识非最小相位系统或重构非最小相位信号。自相关函数或功率谱是相盲的,即不包含信号或系统的相位信息。仅当系统或信号是最小相位时,二阶统计量的方法才能获得正确的结果。相反,高阶统计量既包含了幅度信息,又保留了信号的相位信息,因而可以用来解决非最小相位系统的辨识或非最小相位信号的重构问题。3、提取由于高斯性偏离带来的各种信息对于非高斯信号,其高阶统计量中也包含了大量的信息。对模式识别、信号检测、分类等问题,有可能从高阶统计量获得信号的显著分类特征,4、检测和表征信号中的非线性以及辨识非线性系统。如用来解决非线性引起的二次、三次相位耦合问题。参考资料:1、张贤达,《时间序列分析一高阶统计量方法》,清华大学出版社,1996。2、沈凤麟等,《生物医学随机信号处理》(第9章),中国科学技术大学出版社,1999。3 J M. Mendel. "Tutorial on Higher-order Statistics(Spectra) in SignalProcessing and Systems Theory: Theoretical Results and SomeApplications. Proc. IEEE, Vol. 79, pp. 278-305, 19914, C. L. Nikias A. P, Petropulu. Higher-order Spectral Analysis: ANonlinear Processing Framework. Prentice-Hall. 19935 C L. Nikias J. M. Mendel.Signal Processing with Higher-orderSpectra. IEEE Signal Processing Magazine, Vol 10, July, pp 10-37, 19936 C. L Nikias M. R Raghuveer." Bispectrum Estimation: A DigitalSignal Processing Firamewoork". Proc. IEEE, Vol. 75, pp. 869-891, 19877 P. A. Delaney d. O. Walsh. " A Bibliography of Higher-Order Spectraand Cumulants". IEEE Signal Processing Magazine, Vol 11 July, pp. 61-7019948、J.A. Cadzow.“ Blind Deconvolution via Cumulant Extrema”.IEEESignal Processing Magazine, Vol 13, No 3, pp 24-42, 1996www.ant,uni-bremen.edu.de/hoshome二、高阶统计量的定义、性质和估计(一)高阶矩、高阶累积量及其谱从随机变量→随机矢量→随机过程)1、随机变量的特征函数与累积量定义:设随机变量x具有概率密度fx),其特征函数定义为(s)=f()edx=Eel其中s为特征函数的参数。(可看作八x)的拉普拉斯变换)特征函数Φ(s)只是参数s的函数。对Φ)求k次导数,可得Φ^(s)=Exe因此(O)=E}=m也就是说)在原点阶导数等孩x阶筹k。因此,Φ(s)也称作矩生成函数(又叫第一特征函数)。矩生成函数可以唯一地、完全地确定一个概率分布。这可由矩生成函数唯一性定理阐明:定理:设F(x)和G(x)是具有相同矩生成函数的分布函数,即:e dF (x)= esdG(x)则F(x)=G(x)由矩生成函数可以定义随机变量κ的累积量生成函数(又叫第二特征函数)及累积量。定义:设随机变量x的矩生成函数为Φ(s),则函数H(s)=nΦ(s)称为x的累积量生成函数,而v()在原点的k阶导数dky(s)ds k0称为x的k阶累积量如果将s)和v展开成 Taylor级数,根据以上定义,就会有①(s)=1+m1S+m2S2+…+,,mkS+…k!(2+4+x12cmk!k1也就是说,x的k阶矩和累积量分别是其矩生成函数和累积量生成函数的Taylor级数展开中s项的系数。2、随机矢量的特征函数与累积量定义:令x=[x,x2,…,x是一随机矢量,且s=s,s2,…,sr,则随机矢量x的矩生成函数定义为Φ(S1SES11+2x2+…+Skxkl52为Ex的累积量生成函数定义为(S1,S2,…,Sk)=lnΦ(s1,x的(vy2…,w)阶矩和累积量分别定义为矩生成函数和累积量生成函数的Iayr级数展开中S1S2…S项的函数,即0Φ(S1,s2;…,s)ExVIS"Y(1521512skas1Os2…ask其中vko对v=V2=…=认=1的特殊情况,记随机矢量x的矩和累积量分别为mom(,,cum(Y1X我们下面将用它们来定义随机过程的高阶矩和累积量。3、随机过程的高阶矩和高阶累积量定义:设{x(n)}为k阶平稳随机过程,则该过程的k阶矩定义为ma(z1,z2,…,k-)=mom{x(n),x(n+),…,x(n+xk-1)}而k阶累积量定义为cs(1,z2,…,k-)=cum{x(m),x(nt+),…,x(n+tk1)}根据这一定义,平稳随机过程的k阶矩和k阶累积量实质上就是取x1=x(n),x2=x(n+a),…,x=x(n+k)之后的随机矢量[(n),x(n+z),…,
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Observers in Control Systems
详细介绍了状态观测器及其在控制系统中的应用。Observers inControl SystemsA Practical guideGeorge ellisDanaher corporation4ACADEMIC PRESSAn imprint of elsevier ScienceAmsterdam Boston London New York Oxford ParisSan Diego San Francisco Singapore Sydney TokyoThis book is printed on acid-free paper ooCopyright 2002, Elsevier Science (USA)All rightsNo part of this publication may be reproduced or transmitted in any form or by anymeans, electronic or mechanical, including photocopy, recording, or any informationstorage and retrieval system, without permission in writing from the publisher. Requestsfor permission to make copies of any part of the work should be mailed to thefollowing address: Permissions Department, Harcourt, Inc, 6277 Sea Harbor DriveOrlando. Florida. 32887-6777.ACADEMIC PRESSAn imprint of Elsevier Science525 B Street, Suite 1900, San Diego, CA 92101-4495, USAhttp://www.academicpress.comAcademic pr84 Theobalds Road. London WCIX 8RR. UKhttp://www.academicpress.comLibrary of congress control Number: 2002104256International Standard book Number: 0-12-237472-XPrinted in the United States of america020304050607MB987654321TO Lee Ann, my loving wife, and our daughter Gretchen, who makes us both proud.Observers in Control Systems■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■Acknowledgments■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■Safety■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■1 Control Systems and the role of observers■■■■■■■■■■■■■■■■1.1 Overviewaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa1.2 Preview of observers21.3 Summary of the book2 Control-System Background52.1 Control-System Structures52.2 Goals of control systems132.3 Visual Model Simulation Environment2. 4 Software Experiments: Introduction to Visual ModelQ182.5 Exercises393 Review of the Frequency Domain.■■■■■■■■■■■■■■■■■■■■■■■■■■■■■3. 1 Overview of the s-domain413.2 Overview of the z-Domain543.3 The Open-Loop Method593.4 A Zone-Based Tuning Procedure623.5 Exercises664 The Luenberger observer: Correcting SensorProblems674. 1 What Is a luenberger observer?674.2 Experiments 4A-4C: Enhancing Stability with an Observer724.3 Predictor-Corrector Form of the Luenberger Observer774. 4 Filter Form of the luenberger observer. ..................................784.5 Designing a Luenberger observer824.6 Introduction to Tuning an observer compensator9047 Exercises955 The Luenberger Observer and Model Inaccuracy... 975.1 Model Inaccuracy.........….……,975.2 Effects of Model Inaccuracy .............................................1005.3 Experimental Evaluation1025.4 Exercises1146 The Luenberger observer and disturbances1156.1 Disturbances1156.2 Disturbance Response1236.3 Disturbance DecouplingIB..-.81296.4 Exercises1387 Noise in the Luenberger Observer…,,,…,,…,…,1417.1 Noise in Control Systems1417.2 Sensor noise and the luenberger observer1457.3 Noise Sensitivity when Using Disturbance Decoupling1567. 4 Reducing Noise Susceptibility in Observer-Based Systems1617.5 Exercises1708 Using the Luenberger Observer in Motion Control1738.1 The Luenberger observers in motion Systems1738.2 Observing Velocity to Reduce Phase Lag1858.3 Using observers to Improve Disturbance Response..... 2028.4 Exercises212Referencesn213A Observer-Based resolver conversion in industrialServo Systems1■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■217B Cures for mechanical resonance in IndustrialServo Systems227Introductionaaa日aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa日aaaaa.aaaaaaaaaaaaaaa日aa227TWo-Part Transfer function228LOW-Frequency Resonance229Velocity Control Law…...8....230Methods of Correction Applied to Low-Frequency Resonance231Conc| usion.…235Acknowledgments235References235C European Symbols for Block Diagrams237Part Linear functions237Part l: nonlinear functions238D Development of the bilinear transformation241Bilinear Transformation241Prewarning242Factoring polynomials243Phase Advancing………………………,243Solutions toChapter 2245Chapter 3245Chapter 4246Chapter 5重口m口m246Chapter 6247Chapter7.….B..8..8..8...248Chapter 8249Index251AcknowledgmentsWriting a book is a large task and requires support from numerous people, and thosepeople deserve thanks. First, I thank LeeAnn, my devoted wife of more than 20 yearsShe has been an unflagging fan, a counselor, and a demanding editor. She taught memuch of what I have managed to learn about how to express a thought in ink. Thanksto my mother who was sure I would grow into someone in whom she would be proudwhen facts should have dissuaded her Thanks also to my father for his insistence thatI obtain a college education; that privilege was denied to him, an intelligent man borninto a family of modest meansI am grateful for the education provided by Virginia Tech Go Hokies. The basicsof electrical engineering imparted to me over my years at school allowed me to graspthe concepts I apply regularly today. I am grateful to Mr. Emory Pace, a toughprofessor who led me through numerous calculus courses and, in doing so, gaveme the confidence on which I would rely throughout my college career and beyondI am especially grateful to Dr Charles Nunnally; having arrived at university froma successful career in industry, he provided my earliest exposure to the practicalapplication of the material I strove to learn. I also thank Dr robert lorenz of theUniversity of Wisconsin at Madison, who introduced me to observers some years agoHis instruction has been enlightening and practical. Several of his university coursesare available in video format and are recommended for those who would like toextend their knowledge of controls. In particular, readers should consider ME 746which presents observers and numerous other subjectsI thank those who reviewed the manuscript for this book. Special thanks goes toDan Carlson for his contributions to almost every chapter contained herein Thanksalso to Eric Berg for his numerous insights. Thanks to the people of KollmorgenCorporation(now, Danaher Corporation), my long-time employer, for their continuing support in writing this book. Finally, thanks to Academic Press, especially to JoelClaypool, my editor, for the opportunity to write this edition and for editing, printing, distributing, and performing the myriad other tasks required to publish a bookX1
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