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宽带信号DOA估计SST算法

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  • matlab 实现线性调频信号以及分析处理
    里面有关于实现matlab的算法以及分析处理山国科技记文在线分布的时频平面作直线积分投影的变换,统称对信号作变换在分布的时频平面里惯用轴的截距和斜率为参数表小直线。因此,当需要沿作直线积分时,可将积分路径(直线)的参数(u,a)替换成()日两对参数之间的关系为:m=-cot,w=! sina。若求信号的变换,并以参数表示积分路径,则有:D.a=PQ线w, (t, wB u-u du∫r(,n)ma(w-mn-m)nh∫m(,w[一(m+motcw lt, wo +mt dt/sinaWo=u/sina上式表明,若是参数为和的信号,则积分值最大;而当参数偏离与或时,积分值迅速减小,即对‘定的信号,其变换会在对应的参数处呈现尖峰。我们自然会想到:多分量的信号的特性在平面里更加突出。即表现为各个尖峰,因而更有利于区别交叉项和噪声。利用变换一定能够获得更好的性能。作为时频分析方法之一,分数阶傅里叶变换ˉ与分布()变换()分别有着一定的数学关系,借助它们的联系,可进一步说明分数阶傅里叶变换的物理意义。信号的分布函数的定义为t+=xtde作为能量型时频表示满足许多期望的数学性质,这里给出其边缘特性X tt wdvXw=wtwat对WD旋转C角度,即对分布实施变换,其结果是RWIW=∫f山国技记文在线而信号的阶分薮阶傅里叶变换X。t的就是将信号的旋转c角度,即对于分数阶傅里叶变换只有旋转不变性,所以有X u= wtP可以看出,对时间轴与频率轴的积分分别是信号在时刻的瞬时功率和信号在频率的谱密度,而信号的对与时间成c角度的轴的积分投影对应着角度为a的分数阶傅里叶变换的幅度平方,这进步从能量的角度说明分数阶傅里叶变换作为广义傅里叶变换的含义。正弦信号在时频平面是一条平行于时间轴的直线,即它的频率不随时间变化,可视为旋转角度为°的完全时间域表示;冲击朕数在时频平面是一条平行于频率轴的直线可视为旋转角度为°的完全频率域表示;信号在时频平面是一条斜率为调频率的直线,当该信号的某一角度的分数阶傅里叶变换与其调频率一致时,在无限长度的理想情况下,表现为幅度为无穷大的冲击,在信号长度有限的情况下,其分数阶傅里卟变换呈现极大值这就是信号在分数阶傅里叶变换域的特点。离散 Chirp fourier变换是最近提出的一种有效的线性调频信号检测技术,它 Fourier变换的一种推广形式,可同时匹配 chirp信号的中心频率和调频率。本文利用修正离散Chirp- Fourie交换( MDCFT)实现干扰信号的检测和参数估计,从而实现对干扰的自适应抑制。分析和仿真表明,该方法可对FM干扰有着极好的抑制效果;同时,由于 Chirp- Fourie变换是维的线性变换,可借助快速傅里叶变换(FFT〕实现,与基于WVD的算法相比,不仅避免了交叉项十扰,而且降低了计算的复杂度,其实现更为简使3.基于Mat1ab的上机仿真过程及结果分析3.1对单分量信号的仿真及结果分析():输入解析信号为x()=eb的分布:40,图单分量信号的分布山国科技论文在线在上述解析信号中加入噪声后,用分布分析其性能图加入噪声的单分量信号的分布由图可以看出实际结果与前面的理论推导致。在实际应用中,信号长度总是有限长的,此时分布呈背鳍状。由图可以得到变换对噪声不太敏感,时频变换后信噪比较高。但当干扰的幅度大到一定程度时,变换的结果会严重变差,甚至分析不出结果。():前两个图是输入解析信号为x(t)=em的变换,后两个图是在这个解析信号中加入噪声以后用变换对其进行的分析:400C501m01501020100150图单分量信号的变换由理论分析可知,当旋转角度与线性调频信号的斜率相這应时,变换将出现一个峰值。这个分析在图中得到了证实。():图前两个图是输入解析信号为x()=e的分数阶傅里叶变换,后两个图是在山国科技论文在线这个解析信号中加入噪声以后用分数阶傅甲叶变换对其进行的分析:分数阶傅甲叶变换变换与变换的紧密联系在图和图的仿真中也可以得到证实HOD50图单分量信号的分数阶傅里叶变换():图的前两个图是输入中心频率是,调频率是的单分量线性调频信号后的Chirp- Fourier变换,后两个图是在这个信号中加入噪声以后用 Chirp-Fourier变换对其进行的分析。通过这个仿真,还将证明一个重要性质: Chirp- Fourier变换可同时匹配线性调频信号的中心频率和调频率的82a图单分量信号的 Chirp fourier变换比较结论:从以上几个仿真图形可以看出,对单分量的信号而言,上述几个变换山国科技论文在线都有非常好的时频聚集性,特别是分布与理论结果完仝一致。在抗噪声方面,对比几个图可知,变换和 Chirp- Fourier变换要比分布和分数阶傅里叶变换吏好。而对于分数阶傅里叶变换和分布,分数阶傅里叶变换的抗噪声性能要好3.2对多分量信号的仿真及结果分析个多分量的线性调频信号的D15020心Dm图多分量信号的一个多分量的线性调频信号的变换50.540多分量信号的变换山国科技论文在线个多分量的线性调频信号的分数阶傅甲叶变换:图多分量信号的分数阶傅里叶变换个多分量的线性调频信号(含两个分量,中心频率和调频率分别为k=)的 Chirp- Fourier变换50299,Q图多分量信号的 Chirp-fourier变换比较结论:从以上四个图可以看出,对于多分量信号,分布由于存在交叉项,时频面模糊不清,而其他三种变换则可以检测到两个信号。从图中还可以看到,Chirp- Fourier变换的效果是最好的。而且我们从图中还可以清楚地看到线性调频信号的中心频率和调频率。4LFM信号的应用线性词频)信号广泛地应用于雷达、声纳和通信等信息系统中。在这类系统中,信号的检测与参数估计是个重要的研究课题,受到特别的关注。下面给出一个基于FRT的MTD雷达信号处理过程的防真实例。假设有一个运动目标,回波信号为Stjn∫t-jwt+nt,其中nt为杂波信号,信号参数为nt是均值为零,方差为的高斯白噪声,信噪比为,观测时间为,采样频率为采样点数为N采用分数阶域的扫描上算法对该冋波信号作计算机仿真,仿真结果如图所从图中可以清楚看到一个LFM信号的存在,而闬目标的峰值非常突出,受杂波的影响相对较小。因此采用FRT的MTD雷达的抗干扰能力较强。另外由于日标的特征非常明显,可以通过适当提高杂波门限的方法来减小虚警概率山国科技论文在线图基于ⅣRFT的MTD雷达信号处理过程的防真5结束语非平稳信号是现代信号处理的主要研究对象之一,对其有很多种理论分析方法。本文介绍的分布,变换,分数阶傅里叶变换,变换是其中比较常用和重要的几种。本文对这几种变换做了初步的介绍,进而对它们进行了一些比较这有助于进一步了解各种变换的性能和作信号分析时选择合适的变换。时频分布之所以受到很多研究人员和信号处理领域的工程人员的重视,是因为它有很多传统傅立叶变换所不具备的性质。由时频分析的定义可知时频表示能给出信号在时域和频域的信息。经过儿年的发展,时频分析理论趋于成熟,并遂渐在实际应用中崭露头角,近年来已在实际的非平稳信号处理中获得了十分广泛的应用。如:信号检测与分类,吋频域滤波,信号综合,系统辩识和谱估计等。在的期刊和国际会议上发表的与采用时频工具处理非平稳干扰有关的论文及研究报告共有余篇,其中以美国大学教授的成果最为显著。时频分析是一个前景很广阔的研究方向,虽然取得了一定的成就,但理论体系尚不十分完备,需要进一步的发展。参考文献[1ˉ张贤达,保铮《非平稳信号分析与处理》[M1998年9月第1版国防工业出版社[2ˉ沈民奋,孙丽莎《现代随机信号与系统分析》M年月第版科学出版社[3丁凤芹,曹家麟《基丁分数阶傅里叶变换的多分量 Chirp信号的检测与参数估计》《语音技术》2004年第1期[4_孙泓波,郭欣,顾红,苏上民,刘国岁《修正 Chirp- Flourier变换及其在SAR运动目标检测中的应用》《电子学报》2003年第1期山国技记文在线[5董永强,陶然,思永,王越《基丁分数阶傅里叶变换的SAR运动目标检测与成像》《兵工学报》1999年第2期L6_陶然,齐林,王越《分数阶 Fourier变奂的原理与应用》LM」2004年8月第1版清华大学出版社[7董永强,陶然,周思永,王越《含未知参数的多分量 chirp信号的分数阶傅里叶分析》《北京理工大学学报》1999年第5期[8ˉ陈辉,王永良《利用离散 Chirp- Flourier变换技术估计调频信号参数》《空军雷达学院学报》2001年第1期[9ˉ齐林,穆晓敏,朱春华《系统中基于 Chirp- Fourier变换的扫频干扰抑制算》《电讯技术》年第期[10]李勇,徐震等《 MATLAB辅助现代工程数字信号处理》[M2002年10月鷥1版西安电子科技人学出版社「111胡昌华,周淘,夏启兵,张伟《基于 MATLAB的系统分析与设计—时频分析》「M12001年7月第1[2]干小宁,许家栋《离散调频-傅里叶变换及其作雷达成像中的应用》《系统工稈与电子技术》2002年第3期
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  • MATLAB在卡尔曼滤波器中应用的理论与实践Kalman
    MATLAB在卡尔曼滤波器中应用的理论与实践KalmanKALMAN FILTERINGTheory and Practice Using MATLABThird editionMOHINDER S GREWALCalifornia State University at FullertonANGUS P. ANDREWSRockwell Science Center (retired)WILEYA JOHN WILEY & SONS, INC. PUBLICATIONCopyright 2008 by John Wiley sons, Inc. All rights reservedPublished by John Wiley sons, InC, Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or byany means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permittedunder Section 107 or 108 of the 1976 United States Copyright Act, without either the prior writtenpermission of the Publisher, or authorization through payment of the appropriate per-copy fee to theCopyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA 01923,(978)750-8400, fax(978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherforpermissionshouldbe addressed to the Permissions Department, John Wiley Sons, Inc, lll River Street, Hoboken, NJ07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissionimit of liability Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability orfitness for a particular purpose. No warranty may be created or extended by sales representatives orwritten sales materials. The advice and strategies contained herein may not be suitable for your situationYou should consult with a professional where appropriate. Neither the publisher nor author shall be liablefor any loss of profit or any other commercial damages, including but not limited to special, incidentalconsequential, or other damagesFor general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at(800)762-2974, outside the United States at(317)572-3993 or fax(317)572-4002Wiley also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic format. For more information about wiley products, visit our web site atwww.wiley.comLibrary of Congress Cataloging- in-Publication DataGrewal. Mohinder sKalman filtering: theory and practice using MATLAB/Mohinder S. GrewalAngus p. andrews. 3rd edIncludes bibliographical references and indexISBN978-0-470-17366-4( cloth)1. Kalman filtering. 2. MATLAB. I. Andrews, Angus P. II. TitleQA402.3.G69520086298312—dc22200803733Printed in the United States of america10987654321CONTENTSPrefaceAcknowledgmentsXIIIList of abbreviationsXV1 General Information1.1 On Kalman Filtering1.2 On Optimal Estimation Methods, 51. 3 On the notation Used In This book 231. 4 Summary, 25Problems. 262 Linear Dvnamic Systems2. 1 Chapter focus, 312.2 Dynamic System Models, 362. 3 Continuous Linear Systems and Their Solutions, 402.4 Discrete Linear Systems and Their Solutions, 532.5 Observability of Linear Dynamic System Models, 552.6 Summary, 61Problems. 643 Random Processes and Stochastic Systems3.1 Chapter Focus, 673.2 Probability and random Variables (rvs), 703.3 Statistical Properties of RVS, 78CONTEN3.4 Statistical Properties of Random Processes(RPs),803.5 Linear rp models. 883.6 Shaping Filters and State Augmentation, 953.7 Mean and Covariance propagation, 993.8 Relationships between Model Parameters, 1053.9 Orthogonality principle 1143.10 Summary, 118Problems. 1214 Linear Optimal Filters and Predictors1314.1 Chapter Focus, 1314.2 Kalman Filter. 1334.3 Kalman-Bucy filter, 1444.4 Optimal Linear Predictors, 1464.5 Correlated noise Sources 1474.6 Relationships between Kalman-Bucy and wiener Filters, 1484.7 Quadratic Loss Functions, 1494.8 Matrix Riccati Differential Equation. 1514.9 Matrix Riccati Equation In Discrete Time, 1654.10 Model equations for Transformed State Variables, 1704.11 Application of Kalman Filters, 1724.12 Summary, 177Problems. 1795 Optimal Smoothers5.1 Chapter Focus, 1835.2 Fixed-Interval Smoothing, 1895.3 Fixed-Lag Smoothing, 2005.4 Fixed-Point Smoothing, 2135.5 Summary, 220Problems. 226 Implementation Methods2256. 1 Chapter Focus, 2256.2 Computer Roundoff, 2276.3 Effects of roundoff errors on Kalman filters 2326.4 Factorization Methods for Square-Root Filtering, 2386. 5 Square-Root and UD Filters, 2616.6 Other Implementation Methods, 2756.7 Summary, 288Problems. 2897 Nonlinear Filtering2937.1 Chapter Focus, 2937.2 Quasilinear Filtering, 296CONTENTS7.3 Sampling Methods for Nonlinear Filtering, 3307.4 Summary, 345Problems. 3508 Practical Considerations3558.1 Chapter Focus. 3558.2 Detecting and Correcting Anomalous behavior, 3568.3 Prefiltering and Data Rejection Methods, 3798.4 Stability of Kalman Filters, 3828. 5 Suboptimal and reduced- Order Filters, 3838.6 Schmidt-Kalman Filtering, 3938.7 Memory, Throughput, and wordlength Requirements, 4038.8 Ways to Reduce Computational requirements 4098.9 Error Budgets and Sensitivity Analysis, 4148.10 Optimizing Measurement Selection Policies, 4198.11 Innovations analysis, 4248.12 Summary, 425Problems. 4269 Applications to Navigation4279.1 Chapter focus, 4279.2 Host vehicle dynamics, 4319.3 Inertial Navigation Systems(INS), 4359. 4 Global Navigation Satellite Systems(GNSS), 4659.5 Kalman Filters for GNSS. 4709.6 Loosely Coupled GNSS/INS Integration, 4889.7 Tightly Coupled GNSS /INS Integration, 4919. 8 Summary, 507Problems. 508Appendix A MATLAB Software511A 1 Notice. 511A 2 General System Requirements, 511A 3 CD Directory Structure, 512A 4 MATLAB Software for Chapter 2, 512A. 5 MATLAB Software for Chapter 3, 512A6 MATLAB Software for Chapter 4, 512A. 7 MATLAB Software for Chapter 5, 513A 8 MATLAB Software for Chapter 6, 513A 9 MATLAB Software for Chapter 7, 514A10 MATLAB Software for Chapter 8, 515A 11 MATLAB Software for Chapter 9, 515A 12 Other Sources of software 516CONTENAppendix b A Matrix Refresher519B. 1 Matrix Forms. 519B 2 Matrix Operations, 523B 3 Block matrix Formulas. 527B 4 Functions of Square Matrices, 531B 5 Norms. 538B6 Cholesky decomposition, 541B7 Orthogonal Decompositions of Matrices, 543B 8 Quadratic Forms, 545B 9 Derivatives of matrices. 546Bibliography549Index565PREFACEThis book is designed to provide familiarity with both the theoretical and practicalaspects of Kalman filtering by including real-world problems in practice as illustrativeexamples. The material includes the essential technical background for Kalman filter-ing and the more practical aspects of implementation: how to represent the problem ina mathematical model, analyze the performance of the estimator as a function ofsystem design parameters, implement the mechanization equations in numericallystable algorithms, assess its computational requirements, test the validity of resultsitor the filteThetant attributes ofthe subject that are often overlooked in theoretical treatments but are necessary forapplication of the theory to real-world problemsIn this third edition, we have included important developments in the implemen-tation and application of Kalman filtering over the past several years, including adaptations for nonlinear filtering, more robust smoothing methods, and develelopingapplications in navigationWe have also incorporated many helpful corrections and suggefrom ourreaders, reviewers, colleagues, and students over the past several years for theoverall improvement of the textbookAll software has been provided in MatLab so that users can take advantage ofits excellent graphing capabilities and a programming interface that is very close tothe mathematical equations used for defining Kalman filtering and its applicationsSee Appendix a for more information on MATLAB softwareThe inclusion of the software is practically a matter of necessity because Kalmanfiltering would not be very useful without computers to implement it. It provides aMATLAB is a registered trademark of The Mathworks, IncEFACEbetter learning experience for the student to discover how the Kalman filter works byobserving it in actionThe implementation of Kalman filtering on computers also illuminates some of thepractical considerations of finite-wordlength arithmetic and the need for alternativealgorithms to preserve the accuracy of the results. If the student wishes to applywhat she or he learns, then it is essential that she or he experience its workingsand failings--and learn to recognize the differenceThe book is organized as a text for an introductory course in stochastic processes atthe senior level and as a first-year graduate-level course in Kalman filtering theory andapplicationIt can also be used for self-instruction or for purposes of review by practi-cing engineers and scientists who are not intimately familiar with the subject. Theorganization of the material is illustrated by the following chapter-level dependencygraph, which shows how the subject of each chapter depends upon material in otherchapters. The arrows in the figure indicate the recommended order of study. Boxesabove another box and connected by arrows indicate that the material represented bythe upper boxes is background material for the subject in the lower boxAPPENDIX B: A MATRIX REFRESHERGENERAL INFORMATION2. LINEAR DYNAMIC SYSTEMSRANDOM PROCESSES AND STOCHASTIC SYSTEMS4. OPTIMAL LINEAR FILTERS AND PREDICTORS5. OPTIMAL SMOOTHERS6. IMPLEMENTATIONMETHODS7. NONLINEAR8. PRACTICAL9. APPLICATIONSFILTERINGCONSIDERATIONSTO NAVIGATIONAPPENDIX A: MATLAB SOFTWAREChapter l provides an informal introduction to the general subject matter by wayof its history of development and application. Chapters 2 and 3 and Appendix b coverthe essential background material on linear systems, probability, stochastic processesand modeling. These chapters could be covered in a senior-level course in electricalcomputer, and systems engineeringChapter 4 covers linear optimal filters and predictors, with detailed examples ofapplications. Chapter 5 is a new tutorial-level treatment of optimal smoothing
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