Fundamentals of Optimal Estimation Theory - 副本
服从指数分布的极大似然估计的实际例子
服从指数分布的极大似然估计的实际例子1.统计学家使用极大似然估计来估计指数分布的参数。
Statisticians use maximum likelihood estimation toestimate the parameters of the exponential distribution.2.通过估计参数λ，我们可以更好地了解指数分布中事件发生的方式。
By estimating the parameter λ, we can gain a better understanding of how events occur in an exponential distribution.3.极大似然估计是一种常用的统计方法，可用于估计各种类型的分布。
Maximum likelihood estimation is a commonly usedstatistical method that can be used to estimate various types of distributions.4.我们可以使用极大似然估计来估计指数分布的中位数或平均值。
We can use maximum likelihood estimation to estimate the median or mean of the exponential distribution.5.估计出的参数可以用于预测未来事件的发生情况。
The estimated parameters can be used to predict the occurrence of future events.6.极大似然估计需要收集一定数量的数据来进行计算。
Maximum likelihood estimation requires collecting a sufficient amount of data for computation.7.通过比较不同参数值下的似然函数，我们可以找到最可能的参数值。
《系统分析和设计》 教学大纲 英语
《系统分析和设计》教学大纲课程编号： MIS363课程类型：□通识教育必修课□通识教育选修课√专业必修课□专业选修课□□学科基础课总学时：54 学时讲课学时：36 实验（上机）学时：18学分：3适用对象：信管专业大三学生I.Course IntroductionManagement Information Systems (MIS) continues to be an eclectic mix of ideas, theories, and research methodologies. No other academic unit of the university studies the development of informationsystems, at least not from the particular perspective you find in MIS programs. While it is true that computer science departments are involved in building computer systems, computer sciencedevelopment is largely void of context. No one else in theuniversity, and for that matter in business organizations, has the combination of technical knowledge and organizational contextthat informs the systems development perspective of MIS.Accordingly, students will learn all about the particular MIS perspective on systems development in this course. Students will learn about the systems development life cycle and follow it from the birth of a new information system to the system's death and replacement. Along the way, students will learn about the tools, techniques, and methodologies used by systems analysts to develop information systems in organizations.II.Learning ObjectivesUpon completion of this course, students should be able to: •Demonstrate in-depth knowledge of the systems development lifecycleand the ability to explain the role of information systems within organizations•Demonstrate the ability to think critically and manage risk and reward when applying the systems development lifecycle •Demonstrate the ability to use analysis and design methods competently and effectively•Understand and articulate the roles of the system analyst in modern organizations and how the SA functions in each phase of the systems development life cycle. Competence is tested through written exams and by solving group cases.•Use Hypercase, a hypertext-based program to simulate organizational systems problems and develop solutions to them.•Demonstrate the ability to communicate effectively, orally and in writing, individually and in teamsIII.Connection between Teaching Content and Graduation Requirement MIS Undergraduate Program Learning Goals and Outcomes1. Knowledge: Our graduates will have in-depth disciplinary knowledge applicable in local and global contexts. You should be able to select and apply disciplinary knowledge to business situations in a local and global environment.2. Critical thinking and problem solving: Our graduates will be critical thinkers and effective problem solvers. You should be able to identify and research issues in business situations, analyze the issues, and propose appropriate and well-justified solutions.3. Communication: Our graduates will be effective professional communicators. You should be able to:a. Prepare written documents that are clear and concise, usingappropriate style and presentation for the intended audience,purpose and context.b. Prepare and deliver oral presentations that are clear,focused, well-structured, and delivered in a professional manner.4. Teamwork: Our graduates will be effective team participants. You should be able to participate collaboratively and responsibly in teams, and reflect on your own teamwork, and on the team’s processes an d ability to achieve outcomes.5. Ethical, social and environmental responsibility: Our graduates will have a sound awareness of the ethical, social, cultural and environmental implications of business practice. You should be able to:a. Identify and assess ethical, environmental and/orsustainability considerations in business decision-making andpractice.b. Identify social and cultural implications of businesssituations.The following table shows how the Course Learning Outcomes relate to the overall Program Learning Goals and Outcomes, and indicates where these are assessed:IV.Teaching methodsThis course consists of lectures, labs, discussions, research paper, group assignments and group presentations. Students must beprepared to discuss the assigned papers or cases before class. V.Topical Course OutlineVI.Course Content HighlightsThe course content is divided into five major parts: Systems AnalysisFundamentals (Part I), Information Requirements Analysis (Part II), The Analysis Process (Part III), The Essentials of Design (Part IV), and Quality Assurance and Implementation (Part V).错误!未找到引用源。
SPE外文翻译
在低渗透砂岩层气藏中现场预测克林肯伯格渗透率的新方法Mehdi Tadayoni ，National Iranian Oil Company and Mina Valadkhani ，Sepah Bank摘要油藏的沉积作用和成岩作用使得低渗透性气藏趋于不均质状态，这给地质研究员的分析研究带来了很大困难。
对于静态和动态的储量模型来说，岩石的物理特性是非常重要的。
本文是一篇关于借用人工神经网络的方法、综合的测井曲线和岩心分析数据的方法，来预测位于美国西部一个盆地的克林肯伯格渗透率。
克林肯伯格模型是一个关于气相渗透率和平均岩心压力倒数的近似线性关系式。
克林肯伯格方法是一个与正在开发的以单根数据点为基础的计算岩心样本的渗透率方法相一致的基础方法。
在低渗透性气藏中，随着天然气滑脱现象（克林肯伯格效应）的不断增加导致了孔隙喉管的减小和渗透性参数逐渐降低。
有一些方法可以测定现场的克林肯伯格渗透率——通过测量常规的空气渗透率和克林肯伯格参数，例如在1997年和2003年伯恩的计算，但是这些方法侧重于以岩心的渗透率为计算核心，这就需要很多的岩心塞，所以我们不得不在这方面花很多的时间和费用。
这项研究的目的是，通过使用总纲发展蓝图的方法和反传播的方法(人工神经网络)来描述在三个不同的阶段(培训，确认，应用)的三个不同的井，用适当的岩心校准现场的克林肯伯格渗透率，来研究关于岩心克林肯伯格渗透率和综合测井曲线 (伽玛射线，密度，中子，地层电阻率等等)的关系。
为了两口井能在这里进行非常好的岩心校准，在培训和应用过程中，第二口井（R2）的半径要超过0.7。
非均质性低渗透性强的气藏评价的重要的一项是通过应用人工神经网络和常规的测井曲线来实现的。
这将花费更少的费用和时间，而且最终可获得更精确的克林肯伯格渗透率。
绪论低渗透气藏被定义为底层的渗透率要少于0.1毫达西。
在致密储集层中的油气储量在天然气资源中占有一个非常重要的百分数。
低渗透气藏常常展现出异常的特性，这需要对低渗透气藏有更多的研究。
信道估计的书 -回复
信道估计的书-回复以下是一些关于信道估计的书籍推荐：1. "Wireless Communications: Principles and Practice" by Theodore S. Rappaport - 这本书全面涵盖了无线通信的各个方面，其中包括信道估计的理论和实践。
2. "Digital Communication over Fading Channels" by Marvin K. Simon, Michael M. Sadler, and Mark A. Neifeld - 这本书深入探讨了在衰落信道中进行数字通信的问题，包括信道估计和均衡技术。
3. "Channel Estimation for Wireless Communications" by Hien Quoc Ngo, Trung Q. Duong, and H. Vincent Poor - 这本书专门针对无线通信中的信道估计问题，详细介绍了各种信道估计算法和应用。
4. "Spatial Channel Modeling and Estimation for Wireless Communication Systems" by Jia-Shin Lin and Hsiao-Lu Wu - 这本书主要关注空间信道模型和估计技术，包括MIMO系统中的信道估计。
5. "Fundamentals of Statistical Signal Processing: Estimation Theory" by Steven M. Kay - 虽然这本书不是专门针对信道估计的，但它提供了统计信号处理和估计理论的基础知识，这对于理解和应用信道估计技术非常有帮助。
以上书籍都是在信道估计领域具有较高影响力的著作，可以根据自己的需求和背景选择适合的书籍进行学习。
金融学研究生必读书
应用金融硕士研究生精读书目陈雨露、张杰、瞿强联合推荐2004-12-71、《经济学原理》N·格里高利·曼昆（N.Gregory Mankiw），中国人民大学出版社。
2、《应用经济计量学》拉姆·拉玛纳山（Ramu Ramanathan），机械工业出版社。
3、《货币金融学》弗雷德里克·S·米什金（Fredcric S.Mishkin），中国人民大学出版社。
4、《金融学》兹维·博迪、罗伯特·默顿，中国人民大学出版社。
5、《公司理财》斯蒂芬·A·罗斯，机械工业出版社。
6、《投资学精要》兹维·博迪，中国人民大学出版社。
7、《国际金融管理》Jeff.Madura，北京大学出版社。
8、《固定收入证券市场及其衍生产品》Suresh.M.Sundaresan，北京大学出版社。
9、《银行管理——教程与案例》（第五版），乔治·H·汉普尔，中国人民大学出版社。
10、《投资组合管理：理论及应用》小詹姆斯·法雷尔，机械工业出版社。
11、《衍生金融工具与风险管理》唐·M·钱斯（Don.M.Chanc），中信出版社攻读博士学位预备生精读书目陈雨露、张杰、瞿强联合推荐2004-12-71、《经济学原理》N·格里高利·曼昆（N.Gregory Mankiw），中国人民大学出版社。
2、《应用经济计量学》拉姆·拉玛纳山（Ramu Ramanathan），机械工业出版社。
3、《金融经济学》（德）于尔根·艾希贝格尔，西南财经大学出版社。
4、《货币金融学》弗雷德里克·S·米什金（Fredcric S.Mishkin），中国人民大学出版社。
5、《金融学》兹维·博迪、罗伯特·默顿，中国人民大学出版社。
6、《国际经济学》（美）保罗·克鲁德曼，中国人民大学出版社。
群体药物动力学解析
加和型误差(Additive type error)：是观测值与拟合值 之间的差 Additive type error : subtraction between predictions and observations .
Obs Pred
误差的存在独立于观测值的大小，属于绝对误差。 Additive errors are absolute error, independent on the observations .
比例型误差(proportional errors)：公式
Obs Pr ed • (1 )
误差的大小与拟合值成比例的变化，属于相对误差。
proportional errors are relative error, proportionate to the predictions.
指数型误差(exponential errors)：公式
Random effects factors cannot be observed. Such as some unknown physiological and pathological states, biological chemistry or pathology difference that cannot be measured ,deviation and so on.
群体药物动力学的特点
Characteristics of population pharmacokinetics
1
对于数据组与稀疏数据组均可以进行分析
Userful either for rich or spaese data set
应用的外推于临床前的群体数据分析以及种属之间
2
概率与测度论经典专著
概率与测度论;数理统计;随机过程微积分金融经典教材专著下面的当然不可能都看，Some books on the list of references might be to your taste. 每个方向认真看1,2本就行，其他的只是做参考，看看一些章节就行。
本书单中为什么要列出各种语言的书，只看中文书或者英文书行吗？（答：例如陈景润为了能直接阅读外国资料，掌握最新信息，在继续学习英语的同时，又攻读了俄语、德语、法语、日语、意大利语和西班牙语。
）非数学专业本科生概率统计随机过程概率论与数理统计(第4版) 盛骤考研必备概率论与数理统计教程(第2版) 茆诗松概率论与数理统计陈希孺概率论基础教程(第8版) 罗斯、郑忠国译（已经出第9版，也是最后一版）第7版答案/p-109941348.html概率论与数理统计(第3版改编版) 德格奥特、谢尔维斯概率统计(英文版第4版）德格鲁特、舍维什概率与统计(英文版)Ronald E.Walpole;Raymond H.Myers;Sharon L.Myers;Keying Ye概率论(英文版) 皮特曼应用随机过程:概率模型导论(第10版) 罗斯、龚光鲁译概率、统计与随机过程(第4版)(英文版) 亨利斯塔克(Henry Stark)、Schaum's Outlines - Probability, Random Variables And Random ProcessesSchaum's Easy Outline of Probability and Statistics.Schaum's Outline of Beginning Statistics, 2 EditionSchaum's Outlines - Elements of Statistics I - Descriptive Statistics and Probability Schaum's Outlines - Elements of Statistics II - Inferential StatisticsApplied Multivariate Statistical Analysis (6th Ed)RICHARD A. JOHNSONMultivariate Data Analysis (7th Edition) Joseph F. Hair, William C. Black, Barry J. Babin, Rolph E. AndersonA Modern Introduction to Probability and Statistics_Understanding Why and How Dekking Chris Spatz, "Basic Statistics: Tales of Distributions (10th edition)"Basic Concepts of Probability and Statistics (Classics in Applied Mathematics) by J. L. Hodges Jr and E. L. Lehmann (Jan 11, 2005)Modern Mathematical Statistics with Applications (Springer Texts in Statistics) by Jay L. Devore and Kenneth N. Berk (8 Dec 2011)A Course in Mathematical Statistics, Third Edition, Third Edition by George G. Roussas (Feb 15, 2014)辅导书概率论与数理统计教程:习题与解答(第2版) 茆诗松概率论与数理统计习题全解指南(浙大•第4版) 盛骤Schaum's Outline of Theory and Problems of Probability and Statistics应用统计学Elements of Statistics 6ed，Arthur L Bowley 世界上第一本统计学教材 1911统计学，David Freedman等著，魏宗舒，施锡铨等译中国统计出版社（据说是统计思想讲得最好的一本书，读了部分章节，受益很多。
Wooldridge计量经济学答案
PREFACE
iii
SUGGESTED COURSE OUTLINES
iv
Chapter 1 The Nature of Econometrics and Economic Data
1
Chapter 2 The Simple Regression Model
5
Chapter 3 Multiple Regression Analysis: Estimation
15
Chapter 4 Multiple Regression Analysis: Inference
28
Chapter 5 Multiple Regression Analysis: OLS Asymptotics
39
Chapter 6 Multiple Regression Analysis: Further Issues
The solutions to the computer exercises were obtained using Stata, starting with version 4.0 and running through version 7.0. Nevertheless, almost all of the estimation methods covered in the text have been standardized, and different econometrics or statistical packages should give the same answers. There can be differences when applying more advanced techniques, as conventions sometimes differ on how to choose or estimate auxiliary parameters. (Examples include heteroskedasticity-robust standard errors, estimates of a random effects model, and corrections for sample selection bias.)
合成孔径声纳重叠相位中心与惯性导航系统联合估计运动误差算法
第42卷第3期兵工学报Vol.42No.3 2021年3月ACTA ARMAMENTARII Mar.2021合成孔径声纳重叠相位中心与惯性导航系统联合估计运动误差算法张羽W,王朋^2,刘纪元钟荣兴匚吊,韦琳哲^2,迟骋^2(1.中国科学院声学研究所，北京100190；2.中国科学院先进水下信息技术重点实验室，北京100190；3.中国科学院大学，北京100049)摘要：为降低运动测量系统复杂度、提高运动误差估计精度，使用回波数据与惯性导航系统(INS)数据两种数据源联合估计合成孔径声纳的运动误差，形成一种基于重叠相位中心(DPC)算法和INS的DPC联合INS算法。
利用回波的多子阵空间互相关矩阵估计声纳的前向速度，结合INS姿态角解算出DPC方法下的三向速度，采用卡尔曼滤波算法融合DPC算法的三向速度与INS 的三向加速度，输出声纳速度的最优值，从而计算运动误差。
湖试数据处理结果表明：DPC与INS 联合算法相比于传统的DPC算法，融合了INS的加速度数据，使速度曲线变得更加陡峭，增加了细节信息，提高了声纳速度估计的准确性；经过运动补偿后，图像质量得到提高，目标散焦和重影的现象均得到改善。
关键词：合成孔径声纳；运动误差；重叠相位中心；惯性导航系统；卡尔曼滤波算法中图分类号：U666.73文献标志码：A文章编号：1000-1093(2021)03-0588-10DOI：10.3969/j.issn.1000-1093.2021.03.015Motion Error Estimation Algorithm Based on DPC andINS for Synthetic Aperture SonarZHANG Yu1，2,3,WANG Peng1，2,LIU Jiyuan1，2,ZHONG Rongxing1，2,3,WEI Linzhe1，2,CHI Cheng1，2(1.Institute of Acoustics,Chinese Academy of Sciences,Beijing100190,China；2.Key Laboratory of Science and Technology on Advanced Underwater Acoustic Signal Processing,Chinese Academy of Sciences,Beijing100190,China；3.University of Chinese Academy of Sciences,Beijing100049,China)Abstract：A displaced phase center(DPC)aided inertial navigation system(INS)combination method is proposed to reduce the complexity of motion measurement system and improve the estimation accuracy of motion error of synthetic aperture sonar.A multiple-receiver spatial mutual correlation matrix is built to estimate the forward velocity of sonar in reference to DPC method,and then three-dimensional velocity can be calculated with the attitude angle from INS.Kalman filter is applied to fuse data from DPC and INS,which outputs the optimal estimation of the velocity.Finally,the motion error is calculated with the integral of the velocity.The field experimental results show that DPC aided INS combination method,in comparison to DPC algorithm,increases more motion details that the velocity curve gets sharper,which收稿日期：2020-04-13基金项目：中国科学院声学研究所青年英才计划项目(QNYC201803)；中国科学院青年创新促进会项目(2019023)作者简介：张羽(1994—),男，博士研究生。
The development and comparison of robust methods for estimating the fundamental matrix
1. Introduction
In most computer vision algorithms it is assumed that a least squares framework is su cient to deal with data corrupted by noise. However, in many applications, visual data are not only noisy, but also contain outliers, data that are in gross disagreement with a postulated model. Outliers, which are inevitably included in an initial t, can so distort a tting process that the tted parameters become arbitrary. This is particularly severe when the veridical data are themselves degenerate or near-degenerate with respect to the model, for then outliers can appear to break the degeneracy. In such circumstances, the deployment of robust estimation methods is essential. Robust methods continue to recover meaningful descriptions of a
statistical population even when the data contain outlying elements belonging to a di erent population. They are also able to perform when other assumptions underlying the estimation, say the noise model, are not wholly satis ed. Amongst the earliest to draw the value of such methods to the attention of computer vision researchers were Fischler and Bolles (1981). Figure 1 shows a table of x; y data from their paper which contains a gross outlier (Point 7). Fit 1 is the result of applying least squares, Fit 2 is the result of applying least squares after one robust method has removed the outlier, and the solid line is the result of applying their fully robust RANSAC algorithm to the data. The data set can also be used to demonstrate the failings of na ve heuristics to remove outliers. For example, discarding
数字信号处理书籍介绍
转自:研学论坛作者: xuefei (半粒电子@学飞) 站内: SP1、《Linear Systems and Signals》——thi这本书个人觉得很不错，是一本线性系统和信号的入门好书。
可以适用于通信、电路、控制等专业。
虽说是入门的好书，但是本书的编排是内容由浅入深，讲述可是深入浅出。
我通读全书后，觉得深有体会，看这本书就像在看小说一般，对于一个话题的介绍，往往从其历史发展说起，让你知道其来龙去脉。
不像国内的书，一上来就是定理、定律。
同时，书中每讲完一个知识点，都会有适当的例题让你加深理解。
本书给我的一种感觉就是，作者将一种菜吃透了，消化了，而且掌握了作者这种菜的方法，然后把这种做法告诉你，然你自己去做菜，做出来的菜可能不一样，但是方法你是掌握了。
最根本的你掌握了，做什么菜是你自己的发挥了。
不像国内的教科书，就要你做出一样的菜才是学会了做菜。
这本书讲述了线性系统的一般原理，信号的分析处理，例Fourier变换、Laplace变换、z变换、Hilbert变换等等。
从连续信号说到离散信号，总之是一气呵成，中间似乎看不出什么突变。
对于初学者，这是一本很好的入门书，对于深入者，这又是一本极好的参考书。
极力推荐。
实话说，Lathi的书每看一回都会有新的感觉，常看常新。
2、《Fundamentals of Statistical Signal Processing,V olume I: Estimation Theory》——Steven M. Kay3、《Fundamentals of Statistical Signal Processing,V olume II: Detection Theory》——Steven M. Kay这两本书是Kay的成名作。
我只读过第一卷，因为图书馆只有第一卷:p这两本书比Van Trees的书成书要晚，所以内容比较新。
作者的作风很严谨，书中的推导极其严密。
不失为一位严谨的学者的作风！虽说推导严密，但是本书也不只是单纯讲数学的，与工程应用也很贴近。
convex_optimizationpdf：convex_optimizationpdf
CALL FOR PAPERSIEEE S IGNAL P ROCESSING M AGAZINESpecial Issue on Convex Optimization for Signal ProcessingIn recent years, we have witnessed technical breakthroughs in a wide variety of topics where the key to success is the use of convex optimization. In fact, convex optimization has now emerged as a major signal processing technique and has made significant impact on numerous problems previously considered intractable. Today, innovative applications of convex optimization in signal processing range from those in adaptive filtering, detection and estimation, sensor array processing, MIMO communications, sensor networks, sampling theory, and more recently, image processing, speech processing and cognitive radios - and the scope of its applications is still expanding. Considering the foundational nature and potential impact of convex optimization in signal processing, there appears to be a clear need for a special issue that introduces convex optimization to the broad signal processing community, gives insights into how convex optimization can make a di erence, and showcases some notable successes. This special issue aims to solicit papers that provide tutorials of convex optimization techniques (including available software) and various successful signal processing applications. Also welcome are tutorial papers that deal with emerging, meaningful applications; or that give friendly overviews of certain theoretically advanced convex optimization techniques relevant to signal processing.To enhance readability and appeal for a broad signal processing audience, prospective authors are encouraged to use an intuitive approach in their presentation; e.g., by using simple instructive examples, considering special cases that show insights into the ideas, and using illustrations to the extent possible. Examples of topics that will be addressed in this special issue include, but are not limited to: Adaptive filteringBeamformingConvex optimization fundamentals including relaxation techniques and software toolboxesImage processing applications, including denoising, MRI image processing, phase unwrappingCompressed sensingDetection and estimationMIMO communicationsSensor networksCognitive radiosSpeech applicationsSubmission Procedure:Prospective authors should submit their white papers through the web submission system at/spm. The white paper should be no more than 6 pages in the IEEE double-space one-column 11-point format.Schedule (all deadlines are firm no exceptions)White paper due:May 5, 2009Invitation notification:June 1, 2009Manuscript submission:September 1, 2009Notification of acceptance:December 1, 2009Final manuscript decision:January 15, 2010Publication date:May, 2010Guest Editors:Yonina Eldar Zhi-Quan Luo Wing-Kin (Ken)Daniel Palomar NikosTechnion, Israel Institute of Technologyyonina@ee.technion.ac.il University of Minnesotaluozq@umn.edluozq@MaThe Chinese University ofHong Kongwkma@.hkHong Kong Universityof Science andTechnologypalomar@ust.hkSidiropoulosTechnical University ofCretenikos@telecom.tuc.gr。
大地测量学与测量工程(081601)
大地测量学与测量工程（081601）学科门类：工学（08）一级学科：测绘科学与技术（0816）大地测量学与测量工程是地球科学的一门分支学科，它既是一门测绘科学与技术的基础学科，又是一门工程应用学科。
本学科以精密工程测量、变形监测理论与方法、空间信息测量学理论与应用和多系统定位信息融合理论与方法为主要特色和研究方向，研究和解决各种有特殊精度要求的测量技术和测量方法，建立大型工程测控理论与监测技术；研究各种安全监控模型和监测系统的网络化理论，建立安全监控信息管理系统及专家评判系统；研究卫星导航和精密定位技术，建立多系统定位信息融合模型与方法等。
本学科现有教学及科研人员约30人，其中教授6人，副教授及高工11人。
近年来本学科承担了包括国家自然科学基金、国家重大工程在内的众多科研项目，平均科研经费超过300万元/年。
在大型建筑物安全监控、监测数据的分析处理、高精度测量控制网的建立和数据处理、精密三角高程测量理论与应用、卫星导航与定位等方面的研究取得了显著成果，获得10多项国家和省部级奖励，发表论文200余篇，其中多篇论文被SCI和EI检索。
一、培养目标培养测绘领域的高层次人才，能够胜任高等教学、科学研究或大型工程技术研发与管理等方面工作。
要求具有数学、计算机应用方面的基础理论知识，具有坚实而深厚的大地测量学与测量工程的基础理论，深入地了解近代大地测量学与测量工程的进展与动态。
熟练掌握大地测量学、测量工程的数据采集、资料综合分析与处理的理论和方法。
至少掌握一门外语，能熟练阅读本专业的外文资料，具有一定的写作能力和进行国际学术交流的能力。
能主持科研工作和组织工程生产的技术设计、规划和实施，并能熟练进行大地测量学与测量工程的信息加工与处理，具有从事与相关学科交叉的科学研究能力，能够从事学科前沿的创新研究工作。
二、主要研究方向1、现代大地测量理论与方法2、精密工程测量理论与技术3、安全监控理论与技术4、卫星导航与定位5、多系统定位信息融合理论与方法三、课程设置。
国外关于有限元方面的书籍
Ainsworth, M. and Oden, J. T., A Posterior Error Estimation in Finite Element Analysis , 2000
Backstrom, G., Fields of Physics on the PC by Finite Element Analysis, 1994
Backstrom, G., Fields of Physics by Finite Element Analysis, An Introduction, 1998
Baldwin, K., ed., Modern Methods for Automating Finite Element Mesh Generation, 1986, CP
Baran, N. M., Finite Element Analysis on Microcomputers, 1988
Argyris, J. H. and Mlejnek, H. P. Computerdynamik der Tragwerke, Band III Die Methode der Finiten Elemente, 1996
Ashwell, D. G. and Gallagher, R. H., eds. Finite Elements for Thin Shells and Curved Members, 1976
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随机信号分析第五版教学设计
随机信号分析第五版教学设计课程简介本课程是一门讲授随机信号分析基本概念和常见分析方法的课程。
课程从概率论入手，通过讲解常用的随机过程模型、功率谱密度和相关函数等内容，深入探讨了随机信号在实际应用中的原理和方法。
课程目标通过本课程的学习，学生将掌握以下技能和知识：1.掌握随机信号概率统计基础知识；2.理解随机过程及其相关数学描述；3.掌握常见随机过程模型及其性质；4.熟练掌握常用功率谱密度计算方法；5.能够实际应用以上知识解决实际工程问题。
课程大纲第一章概率论基础本章主要内容包括：概率论基本概念、随机变量、概率密度函数、分布函数、矩、期望和方差等知识。
第二章随机过程本章主要讲述：随机过程的概念、常用描述方法、随机过程的性质、二阶矩及相关函数等知识。
第三章常见随机过程模型本章主要内容包括：高斯过程，泊松过程，Markov过程等随机过程模型及其性质分析。
第四章随机过程的功率谱密度本章主要内容包括：随机过程的功率谱密度的概念、性质、功率谱密度实例计算等。
第五章随机过程的相关函数本章主要内容包括：随机过程的相关函数概念、性质、互相关函数实例计算等。
第六章信噪比及噪声本章主要内容包括：信噪比的定义和计算、噪声模型及其功率谱密度分析。
教学方法本课程采用讲授+练习的方式进行教学。
在讲授过程中，教师将采用举例、演示，图表展示等方式，使学生更好地理解和掌握相关概念和方法；在练习环节中，教师将会提供一定数量的习题，帮助学生巩固和练习课程中所学知识，同时也可以提高学生的思维能力、解决实际工程问题的能力。
教学评价针对本课程的教学评价，考核方式主要包括平时小测验、课堂互动、实验报告、期末考试等形式。
其中平时小测验和课堂互动主要考察学生对课程内容的理解情况；实验报告主要考察学生解决实际工程问题的能力；期末考试则主要考察学生对课程所学内容的综合应用能力。
参考教材1.刘硕. 随机信号分析. 清华大学出版社, 2020.2.Papoulis A. Probability, Random Variables, and StochasticProcesses. McGraw-Hill, 2002.3.Kay SM. Fundamentals of Statistical Signal Processing,Volume 1: Estimation Theory. Prentice Hall, 1993.结束语以上是本课程的教学设计，旨在通过系统化的教学内容和灵活多样的教学方式，提高学生的随机信号分析能力和工程问题解决能力，为学生的应用型人才培养奠定坚实的基础。
信号检测与估计理论
信号检测与估计理论介绍信号检测与估计理论是数字通信和统计信号处理中的一个重要领域。
它研究的是如何准确地检测到信号的存在以及对信号进行估计。
该理论在许多实际应用中具有重要意义，包括雷达系统、通信系统、生物医学信号处理等。
信号检测在信号检测中，我们的目标是从观测到的信号中确定是否存在某个特定的信号。
通常情况下，我们将信号检测问题建模为一个假设检验问题，其中有两个假设：零假设H0表示没有信号存在，备择假设H1表示信号存在。
在信号检测中，我们通过设计一个检测器来根据观测到的信号样本进行决策。
常用的检测器包括最大似然检测器、贝叶斯检测器等。
这些检测器利用观测到的信号样本的统计特性，通过最大化某个准则函数（如似然比）来做出决策。
信号估计信号估计是根据观测到的信号样本，估计出信号的参数或者信号本身的过程。
信号估计有多种方法，包括参数估计和非参数估计。
在参数估计中，我们假设信号遵循某个已知的参数化模型，并通过观测到的信号样本去估计这些参数。
常用的参数估计方法有极大似然估计、最小二乘估计等。
这些方法基于最优准则来选择最优参数估计。
非参数估计不需要对信号满足某个特定的参数化模型的假设，它们通常利用样本的统计特性来进行估计。
常用的非参数估计方法有最小二乘法、核方法等。
检测与估计的性能评价在信号检测与估计中，我们需要对检测与估计的性能进行评价。
通常情况下，我们使用概率误差、均方误差等作为评价指标。
在信号检测中，我们常用的评价指标有误报概率和漏报概率。
误报概率指当信号不存在时，检测器判定信号存在的概率；漏报概率指当信号存在时，检测器未能正确判定信号存在的概率。
在信号估计中，我们常用的评价指标有均方误差和偏差方差平衡等。
均方误差指估计值和真实值之间的平均平方误差；偏差方差平衡则是指在估计和真实值之间平衡偏差和方差。
应用领域信号检测与估计理论在许多领域都有广泛的应用。
其中，雷达系统是一个重要的应用领域。
在雷达系统中，我们需要通过检测和估计来实现目标检测、目标定位等功能。
fundamentalsofmu...
Chapter 15International Portfolio Theory and DiversificationT QuestionsDiversification benefits1. How does the diversification of a portfolio change its expected returns and expected risks? Is this inprinciple any different for internationally diversified portfolios?The diversification of a portfolio results primarily in the reduction of risk. For a domestic portfolio, the diversification of the portfolio results in a weighted average expected return, but a reduction in risk as the returns of individual securities will be less than perfectly correlated.This principle also applies to international diversification, but the definition of the “market” isexpanded with many new securities with their respective risks, returns, and correlations being added.The other added component of international diversification is the introduction of currency risk.Risk reduction2. What types of risk are present in a diversified portfolio? Which type of risk remains after theportfolio has been diversified?A diversified portfolio has systematic risk and unsystematic risk. Systematic risk is the risk of themarket itself. Unsystematic risk is the risk of individual securities within the market and the portfolio.Increasing the number of securities in the portfolio reduces and ultimately eliminates theunsystematic risk—the risk of the individual securities—leaving only the risk of the market, the systematic risk.Measurement of risk3. How, according to portfolio theory, is the risk of the portfolio measured exactly?If we assume a portfolio consists of two assets, asset 1 and asset 2, The weights of investment in thetwo assets are w1 and w2respectively, and w1+ w2= 1. The risk of the portfolio (σp), usuallyexpressed in terms of the standard deviation of the portfolio’s expected return, is given by the following equation:pσ=where σ12and σ22 are the variances of the expected returns of risky assets 1 and 2, respectively. σ1andσ2are their respective standard deviations. ρ12is the correlation coefficient between the two assets’returns.Chapter 15 International Portfolio Theory and Diversification 281Market risk4. If all national markets have market risk, is all market risk the same?All market risk is not the same because all markets, like individual assets, are not perfectly correlated in their returns. The addition of additional markets to the potential portfolio of the investor reduces the overall market risk below that of any individual market.Currency risk5. The currency risk associated with international diversification is a serious concern for portfoliomanagers. Is it possible for currency risk ever to benefit the portfolio’s return?Currency risk for a portfolio, like currency risk for a firm or a currency speculator, can be positive or negative. If an individual investors buys a security denominated in a currency, which then appreciates against the home currency of the investor, it increases the expected returns of the investor in home currency terms. Different international portfolios and portfolio managers deal with this concern very differently. Some international portfolios wish to hedge the currency risk as much as possible,focusing on the expected returns and risks of the individual assets for their portfolio goals. Other managers, however, use the currency of denomination of the asset as part of the expected returns and risks from which the manager is trying to profit.Optimal domestic portfolio6. Define in words (without graphics) how the optimal domestic portfolio is constructed.An investor may choose any portfolio of assets which lie within the domestic portfolio opportunity set. In order to maximize expected return while minimizing expected risk, the investor will find a combination of the risk-free asset available in the market with some portfolio of risky assets as found in the domestic portfolio opportunity set. The optimal domestic portfolio is then found as thatportfolio which provides the highest expected return when combined with the riskless asset and the lowest possible expected portfolio risk.Minimum risk portfolios7. If the primary benefit of portfolio diversification is risk reduction, is the investor always better offchoosing the portfolio with the lowest expected risk?The portfolio with the lowest expected risk is not the same thing as the optimal portfolio. Theportfolio with minimum risk is measured only on that basis—risk—and does not consider the relative amount of expected return per unit of expected risk. Modern portfolio theory assumes that investors are risk averse, but are in search of the highest expected return per unit of risk which they canachieve.International risk8. Many portfolio managers, when asked why they do not internationally diversify their portfolios,answer that “the risks are not worth the expected returns.” Using the theory of internationaldiversification, how would you evaluate this statement?This means that, at least from their perspective, they do not expect that international diversification will result in any net reduction in the potential portfolio opportunity set’s risk. This is equivalent to saying that internationally diversifying the portfolio does not cause an inward shift of the portfolio opportunity set as illustrated in Exhibits 19.4 and 19.5.282 Moffett • Fundamentals of Multinational Finance, Second EditionCorrelation coefficients9. The benefits of portfolio construction, domestically or internationally, arise from the lack ofcorrelation among assets and markets. The increasing globalization of business is expected to change these correlations over time. How do you believe they will change and why?Many experts have expected the correlations between markets to slowly but steadily increase over time as the world “globalizes.” There are, however, many political and institutional frictions and barriers which may cause this to be a very, very long process.One important development over the past decade complicates this process. While more and more countries have opened their markets to foreign investors and firms, more and more of the world’s publicly traded firms are listing and trading in the world’s primary equity markets of London and New York in addition to their individual domestic equity markets. This reduces market segmentation, increases correlation, and increases liquidity.Relative risk and return10. Conceptually, how do the Sharpe and Treynor performance measures define risk differently? Whichdo you believe is a more useful measure in an internationally diversified portfolio?The Sharpe measure (SHP) defines risk as the standard deviation of the returns of the portfolio. The Treynor measure (TRN) uses a measure of risk which measures the systematic risk of the portfolio versus the world market portfolio. If a portfolio is poorly diversified, it is possible for it to show a high ranking on the basis of the Treynor measure, but a lower ranking on the basis of the Sharpe measure. The two measures provide different information, but are useful in their own ways when evaluating portfolios which are not always adequately diversified.International equities and currencies11. As the newest member of the asset allocation team in your firm, you constantly find yourself beingquizzed by your fellow group members. The topic this morning is international diversification. One analyst asks you the following question:Security prices are driven by a variety of factors, but corporate earnings are clearly one of theprimary drivers. And corporate earnings—on average—follow business cycles. Exchange rates, as they taught you back in college, reflect the market’s assessment of the growth prospects forthe economy behind the currency. So if securities go up with the business cycle, and currenciesgo up with the business cycle, why do we see currencies and securities prices across the globenot going up and down together?Answer her questionWhat sounds so simple at first glance is not. First, exchange rate values change as a result of many factors (as described in earlier chapters of this book), not just business cycles. Expected changes in inflation, real interest rates, political and country risk, current account balances, to name a few, all influence the movement of exchange rates. Secondly, even if business cycles were a primary driver of currency values, business cycles are not perfectly correlated globally. In fact, one way to appreciate this phenomenon is to consider that in 2001–2002 most of the major industrial economies were either in recession or near-recession, but currencies still fluctuated widely. For example, the Japanese yen first depreciated against the dollar in the early part of 2002, but still appreciated significantly by mid-year.Chapter 15 International Portfolio Theory and Diversification 283Are MNEs global investments?12. Firms with operations and assets across the globe, true MNEs, are in many ways as international incomposition as the most internationally diversified portfolio of unrelated securities. Why do investors not simply invest in MNEs traded on their local exchanges and forego the complexity of purchasing securities traded on foreign exchanges?Actually, many investors do consider ownership in the securities of a MNE listed on their localexchange as a substitute for international diversification. Although generating its earnings partially in different countries and currencies, its results are reported in the home currency of the parentcompany. The MNE bears the currency risk of ‘international diversification’ internally, rather than the investor bearing the explicit risk of international diversification.ADRs versus direct holdings13. When you are constructing your portfolio, you know you want to include Cementos de Mexico(Mexico) in it, but you cannot decide whether you wish to hold it in the form of ADRs traded on the NYSE or directly through purchases on the Mexico City Bolsa.(a) Does it make any difference in regard to currency risk? The currency risk is the same.(b) List the pros and cons of ADRs and direct purchases. ADRs convey certain technical advantagesto U.S. shareholders. Dividends paid by a foreign firm are passed to its custodial bank and then to the bank that issued the ADR. The issuing bank exchanges the foreign currency dividends forU.S. dollars and sends the dollar dividend to the ADR holders. ADRs are in registered form,rather than in bearer form. Transfer of ownership is facilitated because it is done in the UnitedStates in accordance with U.S. laws and procedures. In the event of death of a shareholder, theestate need not to go through probate in a foreign court system. Normally, trading costs are lower than when buying or selling the underlying shares in their home market. Settlement is usuallyfaster in the United States. Withholding taxes are simpler because they’re handled by thedepositary bank.(c) What would you recommend if you were an asset investor for a corporation with no internationaloperations or internationally diversified holdings? Discussion question.T Mini-Case: Strategic Hedging1. According to Exhibit 1, were there a significant number of portfolio managers able to add value tointernational portfolios through active (selective) currency management consistently over the time period studied?The top 25th percentile were consistently able to outperform the median and mean significantly with respect to active return. However, this does not show the risk that needed to be acquired or accepted to achieve those returns, at least not in exhibit 1.2. According to Exhibit 2, would the international investor in an Australia portfolio be better off, onaverage, with a completely hedged or unhedged portfolio?It is not possible to determine if an international investor would be better off being hedged orunhedged. An Australian-only investor would have had a higher return unhedged (4.44% versus3.30%), but a higher level of risk (15.60% versus 14.10%). However, an international investor wouldbe able to reduce they Australian equities’ risk, both hedged and unhedged, through international portfolio diversification.284 Moffett • Fundamentals of Multinational Finance, Second Edition3. If you were Sean, what would you conclude from this specific study?Sean may have learned a number of different things. First, that although a portfolio is internationally diversified, that is not the same thing as ‘hedged.’ Secondly, that hedging does not—at least on the basis of the data provided—guarantee any better or worse returns over time. In fact, Sean might come to the same conclusion that traditional corporate treasurers have for many years, that selectivehedging may protect the firm or the portfolio from significant losses in value from unforseenexchange rate changes, but that in the long run, the risks and returns to hedging do appear to average out.Chapter 15 International Portfolio Theory and Diversification 285 T ProblemsWhat is the return on this investment in foreign securities?Jan 1st Dec 31stElement Purchase Sale DistributionsShare price, euros P135.00 P157.60 P15.00Exchange rate, US$/euro $1.0660 $1.1250Gain inLocal Currency Percentagea. Return on the security in local currency termsCapital appreciation 22.60 16.74%Dividend distribution 15.00 11.11%Total return 37.60 27.85%b. Return on the security in US$ termsInitial investment in US$ $100,000.00Converted to euros P93,808.63Purchases shares at initial price P135.00Holding this number of shares 694.88Which earn this dividend per share P15.00Total dividend income P10,423.18Ending share price P157.60Total euro proceeds, Dec 31 P119,936.07End of period exchange rate, US$/euro $1.1250End of period proceeds, US$ $134,928.08Rate of return in US$ terms 34.93%(ending/beginning) −1c. Although both returns appear to be very good for a one year period, the relative returnon an individual security should always be compared to that of the market as a whole(or some index of the market).286 Moffett • Fundamentals of Multinational Finance, Second EditionAssumptions Expected Return Expected Risk (σ) Correlation (ρ) Boeing (US) 18.60% 22.80% 0.60 Unilever (UK) 16.00% 24.00%PORTFOLIO ANALYSISWeight of Weight of Expected ExpectedBoeing in Unilever in Risk ReturnPortfolio Portfolio (percent) (percent)1.00 0.00 22.80% 18.60%0.95 0.05 22.40% 18.47%0.90 0.10 22.04% 18.34%0.85 0.15 21.73% 18.21%0.80 0.20 21.47% 18.08%0.75 0.25 21.25% 17.95%0.70 0.30 21.08% 17.82%0.65 0.35 20.97% 17.69%0.60 0.40 20.90% 17.56%0.55 0.45 20.89% 17.43%0.50 0.50 20.93% 17.30%0.45 0.55 21.02% 17.17%0.40 0.60 21.17% 17.04%0.35 0.65 21.36% 16.91%0.30 0.70 21.61% 16.78%0.25 0.75 21.90% 16.65%0.20 0.80 22.24% 16.52%0.15 0.85 22.62% 16.39%0.10 0.90 23.04% 16.26%0.05 0.95 23.50% 16.13%0.00 1.00 24.00% 16.00%Expected Return Expected Risk Correlationa. Equally weighted 17.30% 20.93% +0.6portfolio hasb. 70% Boeing & 17.82% 21.08% +0.630% Unileverc. Optimal portfolio 17.43% 20.89% +0.655% Boeing, 45% Unilever(assume ‘optimal’ is minimum risk)292 Moffett •Fundamentals of Multinational Finance, Second EditionWhat were the returns on the Brazilian diversification?April 10, 2002 April 10, 2003 Element Purchase SaleShare price of SPYDERS (US dollars) $112.60 $87.50Exchange rate (Reais/$) 2.27 3.22Index Price Percentagea. Return on the security in US dollar termsInitial price 112.60Ending price 87.50Total change in price (25.10) −22.29%b. Return on the security in Brazilian reais termsInitial investment in Brazilian reais R$ 500,000Initial exchange rate (R$/$) 2.27Converted to dollars $220,264.32Purchases shares at initial price $112.60Holding this number of shares 1,956.17Ending share price $87.50Ending proceeds in US$ $171,164.54End of period exchange rate, R$/$ 3.22End of period proceeds, R$ R$ 551,149.83Rate of return in Brazilian reais 10.23%(ending/beginning) −1c. The Brazilian investor did indeed make a positive return on its investment. However,the return was positive only because of the fall in the value of the Brazilian real, as the SPYDERS themselves lost more than 22% of their value over this period of the bearmarket. If the Brazilian investors could have invested its R$500,000 in an interestbearing deposit in Brazil and earn 12%, it would have actually made a higher return(12% > 10.23%), but there would have been no up-side potential as offered by the USequity market possessed (but didn’t deliver).。
Optimal Control and Estimation
Optimal Control and Estimation Optimal control and estimation are crucial aspects of engineering and technology that play a significant role in various fields such as aerospace, robotics, automotive systems, and many more. These techniques are used to design control systems that optimize the performance of a given system while considering the uncertainties and disturbances that may affect it. In this response, I will delve into the importance of optimal control and estimation, their applications, challenges, and future prospects. One of the fundamental aspects of optimalcontrol and estimation is their ability to improve the performance of systems. By utilizing mathematical models and algorithms, engineers can design control systems that minimize costs, energy consumption, or any other performance metric while ensuring stability and robustness. This is particularly important in fields suchas aerospace and automotive systems, where efficiency and safety are of utmost importance. For example, in aerospace, optimal control and estimation techniques are used to design autopilot systems that ensure the stability and safety of an aircraft, while minimizing fuel consumption and maximizing passenger comfort. Moreover, optimal control and estimation techniques are also essential for the advancement of robotics and autonomous systems. These techniques enable robots to navigate complex environments, manipulate objects with precision, and adapt to changing conditions. For instance, in industrial automation, optimal control and estimation are used to design robotic arms that can perform tasks with high accuracy and efficiency, leading to increased productivity and cost savings for companies. Despite their numerous advantages, optimal control and estimation techniques also present several challenges. One of the main challenges is the need for accurate and reliable models of the system being controlled. In many real-world applications, the dynamics of the system may not be fully known or may be subject to uncertainties and disturbances. This can lead to suboptimal performance or even instability of the control system. Therefore, developing robust estimation techniques and adaptive control algorithms is crucial to address these challenges. Furthermore, the implementation of optimal control and estimation techniques inreal-world systems often requires sophisticated sensors, actuators, and computing resources. This can significantly increase the cost and complexity of the controlsystem, making it less accessible for small-scale applications or industries with limited resources. Therefore, there is a need to develop cost-effective and efficient hardware and software solutions that can facilitate the implementation of optimal control and estimation techniques in a wide range of applications. Looking ahead, the future prospects of optimal control and estimation are promising, thanks to advancements in various fields such as artificial intelligence, machine learning, and data-driven control. These advancements have the potential to revolutionize the way control systems are designed and implemented. For example, machine learning algorithms can be used to learn the dynamics of a system from data, enabling the design of control systems without the need for accurate mathematical models. This data-driven approach to control design has the potential to make optimal control and estimation more accessible and effective for a wider range of applications. In conclusion, optimal control and estimation are indispensable tools for designing control systems that optimize the performance of various engineering systems. Their applications span across a wide range of industries, from aerospace and automotive systems to robotics and industrial automation. However, they also present challenges such as the need for accurate models and the complexity of implementation. Looking ahead, advancements in artificial intelligence and data-driven control have the potential to address these challenges and open up new possibilities for the use of optimal control and estimation in diverse applications.。
基于ADM1模型的沼气生产过程的模型参数选择和辨识
基于ADM1模型的沼气生产过程的模型参数选择和辨识林斌;薛蕾;徐庆贤【摘要】国际水协IWA提出的ADM1模型可以较好地描述厌氧发酵过程，但其大量的模型参数使其在实际应用中存在困难。
针对ADM1模型，在分析了各可变参数的可辨识性和灵敏度后，确定六种参数对于整个动态过程影响较大。
因此，可以对这六种参数进行辨识，从而得到一个较好的ADM1模型。
以此为基础，针对ADM1具体实施条件进行了仿真建模，利用标准仿真软件STOAT生成数据，通过求解一个非线性最优化问题得到参数的最优估计值，进而通过辨识后的模型进行仿真比较，验证了本文的结论。
%The process of anaerobic digestion(AD) can be described well by ADM1 developed by International Water Associa-tion(IWA).However, the complexity of our model contributes a large number of parameters,which make the model difficult to apply in practical. After analyzing the identification and sensitivity of variable parameters, six important parameters have been proved to have significant impact on the whole process. So these six parameters are identified to obtain a better model to simulate the process. Based on this, simulation model for specific cases was built, producing a set of real data by using the standard simula-tion software STOAT. Through solving a problem of nonlinear constrained optimization, the parameters’ optimal estimation was obtained. From comparison between output of identified model and real data, the conclusion was verified.【期刊名称】《微型电脑应用》【年(卷),期】2014(000)010【总页数】5页(P23-27)【关键词】沼气生产;参数选择;参数辨识;建模仿真【作者】林斌;薛蕾;徐庆贤【作者单位】福建省农科院农业工程技术研究所;上海交通大学自动化系;福建省农科院农业工程技术研究所【正文语种】中文【中图分类】TP311厌氧消化是对有机废物进行有效处理和利用的环保工艺技术。
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不同估计方法的比较
• 最小二乘估计：仅适用于对静态系统的状态进行估计，不需 要使用被估计量的动态信息和统计信息。算法简单，但估计 精度不高 • 极大似然估计和极大后验估计：需要被估值和观测值的条件 概率密度信息，并且计算复杂 • 最小方差估计：需要被估值和观测值的条件概率密度，应用 范围较窄 • 线性最小方差估计：需要知道被估值和观测值的一阶矩和二 阶矩，仅适用于平稳过程 • 卡尔曼滤波：线性最小方差估计的一种，由于采用递推算法 并利用了系统的动态特性因此应用比较广泛
最小二乘估计
最小二乘估计H矩阵源自Z向量加权最小二乘估计加权最小二乘估计
最小二乘估计
传统的最小二乘估计算法需要知道所有测量值信息，为了避免 计算机储存所有测量值发展出了递推的最小二乘估计，由于公 式较为复杂在此省略 最小二乘估计的特点： • 只能估计常值向量，无法估计动态向量，因此最小二乘估计 只能应用于对静态系统的估计 • 最小二乘的指标只能保证估计均方误差之和最小，而这往往 不能保证被估计量的估计误差是最小的，所以估计精度不高 • 最小二乘估计不需要关于测量误差的先验知识，是只针对测 量结果的估计方法
经典滤波器和现代滤波器的比较
经典滤波器：假定信号中有用成分和噪声各自占有不同的频带， 当信号通过一个线性系统（即滤波器）可将噪声有效去除 • 从功能上分类包括低通、高通、带通、带阻滤波器 • 根据实现方式分为IIR（无限冲激响应）滤波器和FIR（有限 冲激响应滤波器） • 经典滤波器不考虑系统的动态特性，仅根据信号的频率特性 本身来进行信号的降噪 现代滤波器：将信号和噪声都视为随机信号，利用它们的统计 特征导出一套最佳的估值算法 • 包括维纳滤波器、卡尔曼滤波器、线性预测器和自适应滤波 器等 • 强调对状态的预测和估计，往往需要知道系统的动态特性 （状态空间方程）
Fundamentals of Optimal Estimation Theory
最优估计理论基础
估计问题的提出
估计问题的分类
离散系统的估计问题根据观测值与估计值的时间关系进行分类 • 用过去和当前的数据估计当前的信号值，称为滤波问题 • 用过去的数据估计过去的信号值，称为平滑（内插）问题 • 用过去和当前的数据估计以后的信号值，称为预测（外推） 问题 滤波
平滑 预测
T
最优估计方法
不同最优估计方法基于指标函数的选择 • 最小二乘估计：残差平方和达到最小，不需要任何先验知识 • 最小方差估计：估计误差的方差阵达到最小，需要被估值 X(t)和观测值Z(t)的条件概率密度和联合概率密度 • 极大似然估计：使条件概率密度p(z|x)达到极大，需要知道 条件概率密度p(z|x) • 极大后验估计：使条件概率密度p(x|z)达到极大，需要知道 条件概率密度p(x|z) • 线性最小方差估计：最小方差估计的特殊形式 • 维纳滤波：线性最小方差估计的一种 • 卡尔曼滤波：线性最小方差估计的一种
最小方差估计
正态随机向量的最小方差估计
线性最小方差估计
与正态分布下的最小方差估计表达式一样
离散随机线性系统的卡尔曼滤波
离散随机线性系统的卡尔曼滤波
白噪声：功率谱密 度为常数的信号
离散随机线性系统的卡尔曼滤波
用k-1时刻的状态估 计来预测k时刻状态
利用预测值和观测 值对状态估计进行 更新
对预测的质量优劣 进行定量描述
参考资料
• 董景新 吴秋平 《现代控制理论与方法概论》 • 胡广书 《数字信号处理》（第二版）
Thanks
以上即卡尔曼滤波五大基本方程，卡尔曼滤波被证明可以实现最小均方误差
卡尔曼滤波的特点
• 是一种时域滤波方法 • 算法是递推的，不需要占用太多内存 • 采用了状态方程来描述被估计量的动态变化规律，被估计量 可以是平稳的也可以是非平稳的 以上卡尔曼滤波方程要求系统是离散线性的，对于连续系统有 连续的卡尔曼滤波方程，对于非线性系统发明了扩展卡尔曼滤 波（EKF）方法