随机过程--滤波、估计与检测
通信专业经典外文教材，中文版！里面有随机过程、kalman滤波等相关课题，非常好的教材！国外电子信息科学经典教材系列随机过程滤波、估计与检测Random Processes: Filtering, Estimation, and Detection[美] Lonnie c. Ludeman著邱天爽李婷毕英伟等译電子工業出版社Publishing House of Electronics Industry北京· BEDING内容筒介书全面介绍了随机过程理论中经典的线性与非线性系统分析技术和假设检验技术,详细阐述了最优伟匚方法、用亍分类的最优决〔规则,描述了件能评价的准则和评佔方法、此外:本书还深入研究了噪声中随机过稈竹滤波、佔计和检测问题全共分为10章,包括概率空间与概率、随札变星、随机变星佔计、随机过难、随机过程通过线性系統、随巩过烓通过非饯性系统、最优线性维纠滤波器、最优线性卡尔曼滤波器、离散观测信号的检测理论以及连縷森测信号的检测理论等内容,本书在围绕主题进行深入分析的同时,给出了许多应用实例和习题,足本容易理解的适用性较强的书本书既可以作为研究生和大学本科高年级学生的教材,也可以供相关领域的工程技术人员自学参考未纤许可,不得以任何方式复制或抄袭本书之部分或全部内容。版叹所有,侵权必究。图书在版编目(C|P)数据随机过程:滤波、计与检测/(美)賡徳曼( LEderman,L,C)著邱天爽,李婷,毕英伟等译.一北京电子业出版社,2005,2(国外电子信息科学经典教材系列书名原文: Random processes: Filtering, Estimation, and detectionISBN7121·0866-1L.随…1.①路…②邱灬⑧李…④毕…Ⅲ.随机过程-教材IV.O2116中国版本图书馆CIP数据核字(205)第002845号责仁编辑:许楷印刷:北京胂义兴许卬刷「出版发行:电厂E业出版社京海淀区万考路173信箱邮编100036经销:2地新华书店廾本;787X192116印张:2875字数:736千字印次:2005年2月第1次印刷印数:500册定价:3900元凡购买电业版社的图书,如有缺损问题,请向购买书店调换。若书店售缺,请与本社发行部联系联系电话:(010)6829077。质量投诉请发邮件至zlts@phej.com.cn,盜版侵杈举报请发邮件至dbqgo phei com.cn译者前言随札过程理论是现代信号处理的基础理沦之一,在诸如通信、计算机视觉、振动及雷达卢肭等应用领域,面临大量的随机信号分析与处理的问题,因此对于随机过程理论的深入理解是非常熏要的。此外,在通信系统和信号处理算法屮,对含噪过程的滤波、估计与检测是必不可少的重要任务。尽管国内外已经出版了不少关于随机过程及其工程应用的著作和教材,但是本书仍然以其独特的风格引起了国内外读者的注意,成为随机信号分析与处理领域一部非常重要且具有特色的著作。夲书的作者朗尼C·略德曼博土是因际数字信号处理领域的著名教授。他于1968年获得美国亚利桑那州立大学博土学位,现为新墨西哥州立大学电子与计算机工稈学院教授,并于1993年在希萨洛尼卡的亚里斯多德大学获得富布赖特基金奖,朗尼C·路德曼博士的另一部著作 Fundamentals of Digital Signal Pπ cessES,在出版当年获得 choice杂志射杰出工程图书奖本书仝面介绍了随机过程理论中经典的线性与非线性系统分析技术和假设检验技术,详细阐述了最优估计方法、用于分类的最优决策规则,描述了性能评价的准则和评估方法。此外,本书还深入研究了噪声中随机过程的滤波、估计和检测问题。本书的内容基本上可以分为四个互相关联的部分,即概率论和随机变量与随机过程的特征,随机过程通过线性与非线性系统的规律,以维纳滤波和卡尔曼滤波为主的最优估计理论,离散时间和连续时间信号的检测理论。本书在圄绕主题进行深入分析的同时,给出了许多应用实例和习题,是一本容易理解的适用性较强的书,既可以作为研究生和大学本科高年级学生的核心教材,也可以供相关领域的工程技术人员自学参考。本书由大连理工大学电子与信息⊥程学院邱大爽教授等完成翻详工作。具体分工为:李婷(第]章、第2章),毕英伟(第3章、第10章),邱天爽(前言、第4章、第5章),唐洪(第6章、第章),初孟〔第8章、第9章),郑效来(附录及图表等)。全书山邱天爽统稿。译者感谢芙文版原书作者朗尼C·路德曼博士和英文版原书出版社 John Wiley and Sons,Inc及电子工业出版杜对本书翻译工作的支持,感谢大连理工大学电子与信息工程学院对本书翻泽工作的支持。于译者水平所限,加之时间比较仓促,翻译中难免存在不妥和错误之处,恳请读者批评指。译者2005年1月于大连理厂大学作者前言每天我们都会遇到这样的信号,我们既不能用解析式来表示它们,也不能以确定的方法夹准确地对其建模,如常规的诰音信号、音乐信号、地震信号、生物信号、被动声呐信号记呆舶温度信号和通信信号等。表小相同内容的语音词句,如果H许多不同的人讲出来,或者是由同一个人在不同的时间讲出来,都会具有定的相似性和差异性。对于这种相似性或差异性,我们很难利用确定性的模型来表不。那么我们怎样表示这类信号呢?事实上,这类信号可以根据数学原理严格地表示为随机过程。而随机信号与可以用解析式表示的信号不同,它们只能根据概率来表示。例如,“在给定的时刻,某随机过程大于给定值的概率为025”就是一种概率表示。玍电气和订算机工程领域,尤其是在通信理论、计算机视觉、数字信号处理以及机械工程中振动理论和强度分析等领域,随机过程是个基本的概念。随机信号的数字处理对于高性能通信系统是非常重要的,而非线性信号处理方法则是有用的处理工具。这些随机信号常作为线性或非线性系统的输入信号。例如,语音信号经由传声器和放大器而到达扬声器输出。我们怎样评价这种系统的输出呢?实际上,系统的输出也可以认为是随机过程。那么,我们自然而然地会提出下面的问题:如果我们已知输入过程的统计特征,那么输出过程的统计特征又如何呢?在许多情况下,随机信号往往受到外来噪声的干扰,并且噪声通常也是随机的。如果这两种随机过程可以用各自的统计特征来表示,则我们可以找到从噪声中提取信号的方法,或者说找到在噪声中估计、滤波或预澳信号过程的方法。我们有许多针对确定性信号的线性和非线忤处理技术,然而,对于随机信号的处理不能直接使用确定性信号处理方法和模型。那么我们如何进行处理以及如何确定最优系统呢?假设我们有一个样本,已知其可能来自几个随机过程中的一个,需要确定该样本究竞属于哪个随过稈。例如,假设有一段语音信号,需要确定该语音信号表示的是五个元音中的哪一个,如何描述确定元音的过程?什么是最合理的性能测度?本书的目的是把随机过程的基础理论、线性及非线性系统分析技术与假设检验技术结合起来,从而给出信号的估计技术、确定最优的估计方法、提供用于分类的最优决策规则,并给山性能评估的方法作者撰写本书的一个主要目标是介绍随机变量和随机过程及其与线性、非线性系统的相作用,它们的估计方法及估计性能,以及噪声中随机过程的检测等本书的内容适合电气、计算机、地球物理以及机械工程等专业的高年级本科生和一年级研究生学习木书的内容可以分为四个主要的且互相关联的部分:概率论和随机变量与随机过程的特征,以随机过程作为输入的线性与非线性系统,包括维纳滤波和卡尔曼滤波的最优估计理论,离散和连续时间信号的检测理论根据不同的课程体系及要求,本书可以适用于几种不同的教育层次。例如,对于基础概率论及随杌过程导论这样的课程,本书适合四年级本科生或一年级研究生使用。如果课程包I括随机过程的波、估计和检测,则本书的内容可以供电气和计算机⊥程专业的一午级研究生使用。本书也可以作为高年级研究生关于检测和佔计理论的教材。对于高年级本科生或硏究,事先了解关概率和随机变量的知识是有帮助的。然而,对于研究生层次的课程,则需荽关于工程概率和基本系统理论的先修课程。由于本书通过大量的铡题介绍了许多基本概,因此本书也可以作为自学读物。在过去的15年寸,本书几乎所有的内容都在教学中使用过。作者在教学中采用了三种不问的形式:关于概率、随机变量和随机过程的概念和理论,使用书的第1~3章内容,并选用第4~6章的部分内容。●关于随机过程滤波及估计概念和理论的介绍,使月本书的第4~6章内容,并选用第7章和第8章的部分内容。关于检测与估计理论,使用本书的第3章、第7~10章内容本书的现打版本已经针对其最初的版本进行了较多的修改,并且吸取了学生们关于内容选取和总体样式的意见和建议。与本书配套的录像资料已经在新墨西哥州立大学( HollomanAFB),白沙导弹射击场( Kirtland AFB), Kwangju理工学院,南 Dakota矿业学院和RCA( larez. Mexico)的电气与计算机工程、物理学和其他工程专业广泛仗用,并且还作为上述学校以及印度科学学院( Bangalore)的标准课程教材。根据不同的听众和不同的课程要求,封次讲课的形式都可能有所不同,其目的是为学生提供容易理解的有用知识本书还给了许多习题,用于强调相关的概念。通过这些习题,学生们可以进一步加强对基本概念的理解,并且,由于习题的数量较多,每年开设这门课程时习题的重复性比较小。大部分习题是供课堂上练习或课后考试用的,用于加强对课堂上讲授的基本概念的理解。少数比较复杂的习题,需要下些功夫才能得到结果。许多习题要求得到完整的解析解是比较困难的,因此需要一些基本的计算技巧。分清哪些习题需要利用计算杋求解,哪些习题可以得到解析解,这种能力正在学生中逐渐培养并成熟起来。作者非常感谢上面提到的学生和有关机构,感谢他们对本书提出的有价值的建议和批评,感谢他们对本书的支持和所做出的努力本书的总体风格主要受到两部著作的影响第一部是 Athanasios Papoulis的经典著作《概奭机变量与随机过程》,第二部是 Harry L. Van trees的里程碑式的著作《检测、佔计和调制(第-“部分)》。我一直认为,本书在论述的方式、完备性和所覆盖的内容等方面很难与上述两部不朽的著作相提并论。本书的写作的不是为了与上述两本著作相竞争,实际上也没有这个必要。我的写作思路是选择这两本著作中的基本内容,并且以稍微低一些层次的数学要求来编写,给出较多的详细说明和例子,但不破坏数学摧述的完整性。关于本书的内容,基本上是根据上述两本著作来选择的,并且受到其他许多作者、教育工作者和学者的启发最后,最重要的是作者永远珍视作者家庭和朋友们对作者的仝面支持和鼓励朗尼C·路德曼目录第1章概率空间与概率………………11概率空间的定义……11.]样本空间平:·界号_.:自日:.即L1,2波莱尔域……11,3概率测度I2联合概率空间…………1………:…412.1两个概率空间的笛卡尔积12,2个概率空间的笛卡尔积…123计数概率空间……PTP=上→1.24联合概率空间的选择…………F+lI+131.3条件概率…1413.1全概率定理…1.32贝叶斯定理……………卡+·+十女d号甲+1千日十目r卡号14随机点………l中国中用里14.1区间中均匀分布的随机点t&142区间中非均匀分布的随机点■m1.5小结………20习题……参考文献25第2章随机变量……2621随机变量的定义2.1.1累积分布函数(CDF)…日·P血:如:721.2概率密度函数…………………………28213局部特征………………………………21.4条件紧积分布函数33215特征恿数……………t上td上2.6高斯随机变量的高阶原点矩…3622常见的连续随机变量…a↓L……3723常见的离散随机变量39元随机变量的变换……40241一元随机变量的变换……………………………-I242累积分布函数…卩,F■!目,,q卩寻↓。■罪品十日十■星·十Pl4dh,·+寻↓4IdaJ4■b+d5期望值的计算4726二元随机变量………………………卜中dp垂4FL4DL用山■山目日国国E目261联合累积分布函数26,2联合慨率度两数50263局部特征……264联合止态随机变量薯■rT了■nT■加1『1m日r“■TDT道十■TLT■"■■T■T5527二元随机变量的两个函数271概率密度函数(离散随机变量……………572.72概率密度函数连续随机变量和连续数}………………273分布函数(连续、离散或混合6128:元随机变量的个函数………………6328,1离散随机变量的概率密度函数………6328,2连续随机变量的概率密衰函数…………………………………6429E(Xy)的计算210多随机变量…692.10.1全局特t,·692.10.2月部特征………………………………和q上中■《+b中:b◆411每d■↓;4abh4画h213高斯随机矢量…1742.11N个随机变量的M个函数…212小结参考文献……第3章随机变量估计…3.1变量估计…………9731随机变量估计的基本公式中■中■1中,中日目■……………97312贝叶斯性能测度++4…97313数据的统计特征……32线性最小均方误差(MMSE)估计32]随机变量的营数估计………通日骨目P十虚加十98322由一个随机变量估计另一个随想变量的线性估计……323由N个随机变量估计一个随机变量的线性估计33非线性最小均方误差(MMSE)估计…107331由一个施机变量估计另一个随机变量的非线性估计…+7332由N个随机变量估计一个随机变量的非线性计11123高斯随机变量的非线性估計.:函.F·dP香P日aa日1124随机变量估计的性质11335贝叶斯估计…1335.!贝叶斯伟计……114352贝叶斯佔计举例11636非随机参量的估计■ptt由口ht面明.·+卩+F119361极大似然估计20362极大似然佔计举例…12037小结习题…1「rT日·」参考文献…128第4章随机过程………1304.1骓机过程的定义……42随机过程的特征13142.1随机过程的全局特征……………13242.2随机过程的阶概率密度中自中14中E4山中中丽………"1324.2.3随机过程的均值………………4.24随机过程的方差…32425随机过程的二阶概率密度133426随机过程的自相关函数和自协力差函数133427随机过程的功率谱密度…134428高阶矩429髙阶谱…………………1354210N阶密度…………“a13543随机过程的平稳性■■!中冒:14中4自L135431广义平稿殖机过程4.3.2广义平稳随机过程的性质…13644随机过程举例平导P中IM3644l自线过程…PP中目-d日++...·...,中·136442半随机二进制传输过程39443随机二进制传输过程…l41444半随机电报过程…………143445随机电报过程………·1464.6随机正弦信号L46447随机游动过程喻,..一14845随机过程的定积分152456随机过程的联合特征153461—阶联合密度Rd46.2互相关晰数十“十1r15446.3互协方差函数……464联合平稳………………465互功率谱密度15547高斯随机过程………155
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NGSIM使用手册（1）
美国NGSIM系统的使用手册，方便读者高效的利用NGSIM进行数据下载，完成交通领域的研究Technical Report Documentation Page1. Report No2. Government Accession no3. Recipients Catalog NoFHWA-HOP-06-0124. Title and subtitle5. Report DateNext Generation Simulation(NGSIM) Data Format Planly20046. Performing Organization Code7. Author(s8. Performing Organization report noVijay Kovvali, richard margiotta, Robert franc, vassiliAlexiadis9. Performing Organization Name and Address10. Work Unit NoCAMBRIDGE SYSTEMATIC INC150 CAMBRIDGE PARK DRIVE SUITE 400011. Contract or grant noCAMBRIDGE MA 02140DTFH61-02-C-0003612. Sponsoring Agency Name and Address13. Type of Report and Period CoveredDepartment of transportationFinal reportFederal Highway AdministrationJuly 2003-july 2004Office of Acquisition Management14. Sponsoring Agency Code400 Seventh Street SW, RM 4410Washington, DC 2059015. Supplementary notesFHWA COTR: John Halkias, Office of Operations, and James Colyar, Office of Operations r&d16. AbstractThe Next Generation Simulation Program(NGSIM) Data Format Plan was developed to define thestructure, documentation, and transfer requirements for data that will be collected for estimationcalibration, and validation of core behavioral algorithms. The development of the data Format Plan isbased on existing formats that are relevant to ngsim and augmented to fill in gaps. to this end, a reviewof existing data formats was undertaken and their relevance to NGSiM was assessed. The review includeddata standards developed for intelligent transportation systems(ITS), data formats developed specificallyfor traffic simulation models, and data formats developed for broader transportation applications. Thespecified data formats were developed with the objective of promoting efficient research by maintainingonsistency between data collection and research, and providing consistent storage and transmittalprotocols. On the other hand, this plan intentionally avoids over specification of data formats, so as tominimize unnecessary limitations to research. This document specifies the conceptual data model by meansof Unified Modeling Language UMl class diagrams; the data dictionary in the data standard prescribed bP1489-1999 format developed by the Institute of Electrical and Electronics Engineers(IEEE); the dataexchange structure for data transfer from user to user or from the database/repository to users; and theNGSIM metadata17. Key words1 8. Distribution StatementNext generation simulation, NGSIM, trafficNo restrictions. This document is available to thesimulation, high-level plan, traffic data collection, public through the National Technical Informationvehicle trajectory dataService, Springfield, VA2216119. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of Pages22. PriceUnclassifiedUnclassifiedForm dot e1700.7(8-72)Reproduction of completed pages authorizedTABLE OF CONTENTSEXECUTIVE SUMMARY1.0 INTRODUCTION1.1High- Level plan context……垂垂垂垂·着垂垂垂垂非垂·非垂垂看垂音非非;·垂垂音看垂看垂1.2 Background1.3 Data Collection Types……1344581. 4 Data Conversion1.5 Data Formats·····.···············.··.···.·;···..·.··..·.···2.0 NGSIM DATA REQUIREMENTS22 Microsimulation Software Data format,…………172.1 NGSIM Data…192.3 Rcquirements for NgsiM data Collection..................193.0 RECOMMENDED NGSIM DATA FORMATS..m. 233.1 NGSIM Data model233.2 NGSIM Data Dictionary……………243.3 NGSIM Metadata.............................253.4 NGSIM Data Exchange Format273.5 File and Directory Naming Convention……293.6 Summary30REFERENCES31APPENDIX A-REVIEW OF EXISTING TRANSPORTATION DATA FORMATS3APPENDIX B-ACCURACY REQUIREMENTS FOR NGSIM DATACOLLECTION,45APPENDIX C-DATA MODEL∴….,,53APPENdIXD-DATA DICTIONARY.APPENDIX E-METADATA. ...........................................................................................99APPENdIX F-SYSTEM-STATE DATA看香音看音香n117List of FiguresFigure 1 Diagram. NGSIM task interdependencies4Figure2. Diagran. Data format classification relevant to ngsim1………Figure 3. Diagram. Top level data model of general traffic simulation55Figure4. Diagram. Influencing factors database packages………………56Figure 5. Diagram. Behavioral models packages57Figure6. Diagran. Facility type generalization…………18Figure 7. Diagram. Traffic management systems generalization......59Figure 8. Diagram. Transit management systems generalizationFigure9. Diagran. nvironment generalization.………………………0Figure 10. Diagram NTCIP Controller class diagram61Figure 11 Diagram Actuated traffic signal controller generalization2Figure12 Diagram. Generalized microsimulation data model………………63Figure 13 Diagram Data concept components and constructs(IEEE Std 1489-1999)66List of tablesTable 1. Example validation data by algorithm categoryTable 2. Summary of NGSiM categorizations for data formatsTable 3. Accuracy requirements for vehicle trajectory data. ..45Table 4. Accuracy requirements for instrumented vehicle data.........46Table 5. Accuracy requirements for wide-area detector data......... 47Table 6. Accuracy requirements for nctwork-rclated data48Table 7. Accuracy requirements for representative transportation managementsystems data52Table 8. Terminology for UMLmodeler54Table 9. Data dictionary for NgSim.67Table 10 processing documentation metadata for ngsimwwwwwm116Table1l. Requisite vehicle trajectory data…………………………117Table 12. requisite wide-area detector data requirements……118EXECUTIVE SUMMARYThe Next Generation Simulation Program(NGsim) Data Format plan was developed todefine the structure, documentation, and transfer requirements for data that will be col-lected for estimation, calibration, and validation of core behavioral algorithms. Thedevelopment of the data format plan is based on existing formats that are relevant toNGSIM and augmented to fill in gaps. To this end, a review of existing data formats wasundertaken and their relevance to ngsim was assessed. The review included data standards developed for intelligent transportation systems (ITS), data formats developed spe-cifically for traffic simulation models and data formats developed for broader transporta-tion applications. The specified data formats were developed with the objective of pro-moting efficient research by maintaining consistency between data collection andresearch, and providing consistent storage and transmittal protocols. On the other handthis plan intentionally avoids overspecification of data formats, so as to minimize unnecessary limitations to researchFour data format components were specified in this document, including: 1)data model,2)data dictionary, 3 )metadata, and 4) data exchange formatNGSIM Data Model- The conceptual data model for NGSIM data formats is pre-sented by means of Unified Modeling Language() class diagrams. Used in con-junction with the data dictionary, the data model allows for construction of a formaldatabase/repository for NGSIM validation dataNGSIM Data Dictionary This provides definition of individual data elementsrequired by NGsim. It follows the data standard prescribed by P1489-1999 formatdeveloped by the Institutc of Elcctrical and Electronics Engineers(ieee)NGSIM Data Exchange Format- The data cxchange structure dcfincs how datashould be transferred from user to user or from the database /repository to users. Thisdocument specifies the framework for developing data exchange formats by providingthe data model and the data dictionary; it also provides clear guidance on the formatstandards with which the data exchange format should conform Currently it doesnot provide specific schema for the data exchange formatsNGSIM Metadata- This includes both traditional metadata(definitions, specificationsand valid value lists for data elements and general information about the dataset andits availability); and processing metadata(what has happened to the data from data col-lection to data archival). Administrative metadata formats were adapted fromContent Standard for Digital Geospatial Metadata(FGDC-STD-001-1998), developedby the Federal Geographic Data Committee(FGDC). Recommendations for NGSiMprocessing metadata are based on the guidance provided in ASTM E2259-03, devel-oped by the American Society for Testing and Materials(ASTm)1.0 INTRODUCTIONThe objectives of the NGsim program include the followingDevelopment of a core set of open behavioral algorithms in support of traffic simulation with a primary focus on microscopic modelingCollection of extensive data that will be used for estimation calibration and validationof the core behavioral algorithms; and storing the data in a repository that can be uni-versally accessedThe High-Level Plan for DatasetsTask E3)identified different kinds of traffic data col-lection methods and technologies and recommended three kinds of data collection effortsfor ngsim, including vehicle trajectory data wide area detector data and instrumentedvehicle dataThis report Task F)presents the documentation, format structure, and transfer requirements for the ngsim data formats for these data collection efforts identified in task e3This report is organized as followsExecutive Summary -Provides an executive summary of this documentSection1.0-Provides an overview and introduction to this report, including the con-text of the data format plan within NGsIM, information on NGsim data collection anddata types, information on data conversion, general information on data formats, anda summary of available transportation data formats and their relevance for ngsimSection 2.0-Presents definitions and categorization for different data types, and pro-vides ngsim data requirementsSection 3.0-Presents data format recommendations for the NGsim program,including a data model, data elements for the data dictionary, metadata to describe thedata collection effort and data exchange formatsReferences-Presents references used in developing this data format planAppendix a-Presents a review of existing transportation data formatsAppendix B-Presents accuracy requirements for NGSiM data collectionAppendix C- Presents a UML representation of the ngsim data modelAppendix D-Presents a high-level NGSIM data dictionaryAppendix E- Presents metadata categories, dictionary, and recommended metadataformats for ngsim1.1 HIGH-LEVEL PLAN CONTEXTInterdependencies among NGSIM tasks are shown in figure 1. The High-Level Plan forDatasets(Task E. 3) presents an assessment of existing datasets of potential use for NGSIM,and makes recommendations on the focus for nGsim data collection methodologies. Thisreport on the data Format Plan task f) provides recommendations on the data exchangeformat(s) for NGSIM data collection efforts. The data formats are also influenced by theHigh-Level Verification and Validation Plan(task e 2)Task E 1-1Core algorithmAssessmentTask e,3Task e.1-2Task e2High-LevelCore AlgorithmHigh-Level Verificationlan for DatasetsPlanandⅤ alidation planTask eData format planFigure 1 Diagram. NGSIM task interdependencies.1.2 BACKGROUNDThe NGSiM field data collection effort pursues data required for developing, estimating,calibrating and validating traffic behavioral algorithms. Tactical route execution, opera-tional driving, and en-route strategic traveler behaviors were identified as the focus of theNGSIM core behavioral algorithm research in the identification and prioritization of coreAlgorithms Task D)report. The High-Level Verification and Validation Plan(task e2)provides an example of the data collection datasets for each algorithm category as shownin table 1. the table illustrates the extent over which data must be collected for each levelof algorithm. For example, for operational driving algorithms, a single stretch of roadwayon a freeway will likely be sufficient, while, for development of tactical driving algo-rithms, the data collection effort should be expanded to include the freeway section andmultiple entry and exit ramps that feed the freeway. The data formats developed in thisplan address the data, both static and dynamic, that are pertinent to the data collectionefforts necessary for developing and validating all three categories of driver behavioralalgorithms4
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