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《误差理论与测量平差基础》课程教学大纲课程代码：024123 课程负责人：邱卫宁课程中文名称:误差理论与测量平差基础课程英文名称：Error Theory and Foundation of Surveying Adjustment 课程类别：必修课程学分数：3 课程学时数：54 授课对象：第2学年，第4学期测绘专业本科生本课程的前导课程：测绘学概论、数字测图原理、高等数学、线性代数、概率论与数理统计一、教学目的和要求误差理论与测量平差基础是一门专业基础课，以培养学生掌握测量数据处理的基本方法和原理为目的。课程内容包括误差理论和测量平差基础两部分，误差理论主要讲授测量误差的来源、分类、性质、分布、数字特征、传播及主要应用，以误差分布、数字特征及传播律为重点。测量平差基础主要讲授经典测量平差的基本原理、方法、估计理论及精度评定。在教学过程中，这些内容互相联系，互为基础，使学生能掌握误差理论和测量平差的基本知识，处理测量误差的基本理论，数据处理的基本原理和方法。为进一步研究测量数据处理理论和后续课程打下坚实的基础。二、课程内容与学时分配课程内容与学时分配表内容学时第一章、第二章、第三章 16 第四章、第五章、第六章 14 第七章 10 第八章、第九章 6 第十章 8 第一章绪论第一节观测误差内容：测量误差的概念、观测误差来源、分类。第二节测量平差学科的研究对象内容：研究对象。第三节测量平差的简史和发展内容：发展史。第四节本课程的任务和内容内容：主要内容。重点讲授测量误差的概念、测量平差的主要内容等。第二章误差分布与精度指标第一节正态分布内容：测量误差的正态分布。第二节偶然误差的规律性内容：偶然误差的特性及规律性。第三节衡量精度的指标内容：中误差的概念。第四节精度、准确度与精确度内容：精度、准确度与精确度的概念及联系。第五节测量不确定度重点讲授偶然误差的分布、规律性和数字特征。第三章协方差传播律及权第一节数学期望的传播内容：数学期望的概念。第二节协方差传播律内容：协方差传播律。第三节协方差传播律的应用内容：应用。第四节权与定权的常用方法内容：权的定义、常用的定权方法。第五节协因数和协因数传播律内容：协因数传播律。第六节由真误差计算中误差的实际应用内容：应用举例。第七节系统误差的传播重点讲授协方差、协因数的概念、传播律及应用；权的概念及定权的常用方法。第四章平差数学模型与最小二乘原理第一节测量平差概述内容：测量平差的概念。第二节函数模型内容：函数模型的概念。第三节函数模型的线性化内容：函数模型的线性化。第四节测量平差的数学模型内容：随机模型的概念。第五节参数估计与最小二乘原理内容：参数估计与最小二乘原理。重点讲授测量平差的函数模型、随机模型；参数估计及最小二乘原理。第五章条件平差第一节条件平差原理内容：条件平差原理。第二节条件方程内容：条件方程的个数及列立。第三节精度评定内容：条件平差的精度评定。第四节条件平差公式汇编和水准网平差示例内容：公式汇编和水准网平差示例重点讲授条件平差的基本原理、条件方程的列立和精度评定。第六章附有参数的条件平差第一节附有参数的条件平差原理内容：平差原理。第二节精度评定内容：精度评定。第三节公式汇编和示例内容：公式汇编和举例。重点讲授附有参数的条件平差原理。第七章间接平差第一节间接平差原理内容：间接平差原理。第二节误差方程内容：误差方程的列立。第三节精度评定内容：精度评定公式及应用。第四节间接平差公式汇编和水准网平差示例内容：公式汇编和水准网平差示例第五节间接平差特例——直接平差内容：公式汇编和水准网平差。第六节三角网坐标平差内容：测角网坐标平差举例。第七节测边网坐标平差内容：测边网坐标平差举例。第八节导线网坐标平差内容：导线网坐标平差举例。第九节GPS网坐标平差内容：GPS网坐标平差举例。重点讲授间接平差原理、误差方程的列立、精度评定及各类测量控制网坐标平差的示例。第八章附有限制条件的间接平差第一节附有限制条件的间接平差原理内容：测量误差的概念、观测误差来源、分类。第二节精度评定内容：测量误差的概念、观测误差来源、分类。第三节公式汇编和示例内容：测量误差的概念、观测误差来源、分类。重点讲授附有限制条件的间接平差原理。第九章概括平差函数模型第一节基本平差方法的概括函数模型内容：概括函数模型的形式。第二节附有限制条件的条件平差原理内容：平差原理。第三节精度评定内容：精度评定。第四节各种平差方法的共性与特性内容：平差方法的共性。第五节平差结果的统计性质内容：平差结果的统计性质。重点讲授各种平差方法的共性与特性，平差结果的统计性质。第十章误差椭圆第一节概述内容：概述。第二节点位误差内容：点位误差的概念。第三节误差曲线内容：误差曲线的概念。第四节误差椭圆内容：误差椭圆的应用。第五节相对误差椭圆内容：相对误差椭圆的应用。第六节点位落入误差椭圆内的概率重点讲授点位误差的概念、误差椭圆的求法及应用。三、教材与参考书教材：《误差理论与测量平差基础》,武汉大学出版社，武汉大学测绘学院测量平差学科组，2003。参考书：[1]《测量平差基础》，测绘出版社，武汉测绘科技大学大地测量系，1978。 [2] 《测量平差原理》，武汉测绘科技大学出版社，於宗俦等，1990。 [3] 《测量平差基础》，（第三版）测绘出版社，武汉测绘科技大学测量平差教研室等，1996。 [4]《误差理论与测量平差基础习题集》,武汉大学出版社，武汉大学测绘学院测量平差学科组，2005。四、作业和考核方式课外及课堂作业、课堂考试、期末考试。《Error Theory and Surveying Adjustment Foundation》 CURRICULUM INSTRUCTION Course Code: 024123 Course Director: QIU Weining Course Name in Chinese:误差理论与测量平差基础 Course Name in English: Theory of Errors and Foundation of Surveying Adjustment Course Type: Compulsory Course Credit:3 Course Duration:54 Specialty Level：Academic 2 year, Semester 4 Students Prerequisites:Generality of Topography, Figure Survey Principle, Advance Mathematics, Linearity Algebra, Probability andStatistic 1. Objectives 《Error Theory and Foundation of Surveying Adjustment》is a specialized fundamental course, teaching goal is that the student can grasp the survey data processing the basic principle and the method. 2. . Requirements The content of course is consisted of two parts: Error Theory and Foundation of Surveying Adjustment. The main content of Error theory is to expound the error properties of observations. The survey adjustment foundation mainly teaches the classics survey adjustment the basic principle, the method, the estimate theory and the precision evaluation. In the teaching process, these contents connect mutually, and are foundation mutually. Through studying the student know well theory of error and grasp the theory of error and the survey adjustment knowledge, the processing measuring error elementary theory, the data processing basic principle and the method. Key point is to grasp data processing basic principle and method. The solid foundation will be built for further studying the survey data processing theory and the following curriculum. 3. Lectures Contents and Duration Lectures Contents and Duration list Contents Duration Chapter 1,2,3 16 Chapter 4,5,6 14 Chapter 7 10 Chapter 8,9 6 Chapter 10 8 Chapter 1. Introduction §1.1 Observations Error §1.2 Research Object of Surveying Adjustment §1.3 Historical Review and Development of Surveying Adjustment §1.4 Task and Contents in This Course Key points：Conception ofObservation Errors , Task and Contents of Adjustment Chapter 2. Error Distributions §2.1 Normal Distribution §2.2 Properties of Random Errors §2.3 Index of Precision §2.4 Precision, Accuracy and Mean Square Error §2.5 Surveying of Uncertainty Key points：Distributions of Random Errors and digital Character Chapter 3. Laws of Propagation of Variances-Covariances and Weight §3.1 Propagation of Expected Value §3.2 Laws of Propagation of Variances and Covariances §3.3 Applications of Propagation of Errors §3.4 Define of Weight and General Method of Determining Weight §3.5 Cofactor L and Laws of Propagation of Cofactor §3.6 Applications of though real error to calculate MSE §3.7 Propagation of system errors Key points：Covariances and Cofactor, Weight and General Method of Determining Weight Chapter 4 Math model ofAdjustment andPrinciples of Least Squares §4.1 Introduction Adjustment §4.2 General Concepts of Function Model §4.3 Linearization ofFunction Model §4.4 Math Model ofAdjustment §4.5Estimation of Parameters and Principles of Least Squares Key points：Function Model ofAdjustment,Estimation of Parameters and Principles of Least Squares Chapter 5Conditional Adjustment §5.1Fundamentals ofConditional Adjustment §5.2 Conditional Equation §5.3 Precision Evaluation §5.4 Formulae collection ofConditional Adjustment and Demonstration of Level Network Adjustment Key points：Fundamentals ofConditional Adjustment, Conditional Equation. Chapter 6Conditional Adjustment Attach Parameter §6.1 Principle ofConditional Adjustment Attach Parameter §6.2 Precision Evaluation §6.3 Formulae collectionand Demonstration Key points：Principle ofConditional Adjustment Attach Parameter Chapter 7Indirect Adjustment §7.1 Principle ofIndirect Adjustment §7.2 Error Equation §7.3 Precision Assess §7.4 Formulae collection ofIndirect Adjustment and Demonstration of Level Network Adjustment §7.5 Especially Case ofIndirect Adjustment----- Direct Adjustment §7.6 Triangle network Coordinate Adjustment §7.7 Triangle network Coordinate Adjustment §7.7 Triangle network Coordinate Adjustment §7.9 GPS Network Coordinate Adjustment Key points：Principle ofIndirect Adjustment, Error Equation Chapter 8Indirect Adjustment Attach Restrict Condition §8.1 Principle ofIndirect Adjustment Attach Restrict Condition §8.2 Precision Evaluation §8.3 Formulae collectionand Demonstration In this chapter keystones are:Principle ofIndirect Adjustment Attach Restrict Condition Chapter 9 Function Model ofGeneralize Adjustment §9.1 Basic Method of Adjustment and Function Model ofGeneralize Adjustment §9.2 Principle of Adjustment §9.3 Precision Evaluation §9.4 Commonness and Characteristic of Several Adjustment Methods §9.5Statistical Properties of Adjustment Results Key points：Commonness and Characteristic of Several Adjustment Methods Chapter 10 Error Ellipse §10.1Introduction §10.2 Errors of Point Location §10.3 Errors Curve §10.4 Errors Ellipse §10.5 Relative Errors Ellipse §10.6Probability in Errors Ellipse Key points：Concept of Errors of Point Location,Algorithm and Application ofErrors Ellipse 4. Textbook and References Teaching material:《Error Theory and Foundation of Surveying Adjustment》 School of Geodesy and Geomatics Wuhan University. Publishing Company of Wuhan University.2003 Reference Books: [1] Foundation of Surveying Adjustment. MappingPublishing Company. Beijin 1978 [2] Principle of Surveying Adjustment. Yu zhongcou.Publishing Company of Wuhan University. 1990 [3] Foundation of Surveying Adjustment(3). MappingPublishing Company. Beijin 1996 [4] Exercises Volume ofError Theory and Foundation of Surveying Adjustment. School of Geodesy and Geomatics Wuhan University. Publishing Company of WuhanUniversity.2005 5.Assessment and Grade System Classroom Exercise 30% Final exam 70%

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