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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第一章 误差理论与最小二乘原理,Error Theory and The Least Squares Principle,第一章 误差理论与最小二乘原理Error Theory an,1,第一讲 绪 论（,Introduction）,(,复习,),思考题,1、什么是多余观测，它的作用是什么？,2、,什么是测量条件，它与误差有什么关系？,3、什么是平差？平差能否消除误差？,4、最小二乘原理的数学表达式是什么?有几种特例？,第一讲 绪 论（Introduction）(复习)思,2,No.2 Classes of Errors and Characteristics,2,、,All observations contain errors,上节课内容回顾：,3,、,Necessary and redundant observation,4,、,The role of redundant observation,1、,Observations generally require some form,instrumentation,that is used by an,observer,in certain,environment,No.2 Classes of Errors and Ch,3,No.2 Classes of Errors and Characteristics,上节课内容回顾：,5,、,Adjustment aims to eliminate inconsistencies among the observations,6,、,Adjustment follows the Least Squares,No.2 Classes of Errors and Ch,4,第二讲 误差分类及其特性,Classes of Errors and Characteristics,1、True Value and True Error,2、The Classes of Errors,3、The probability Characteristics of,Random Error,4、The Statistics Meaning of True Value,第二讲 误差分类及其特性1、True Value,5,No.2 Classes of Errors and Characteristics,1 The Condition,s,of Surveying,1、,True Value and True Error,Observer,Instrument,Environment,Objective,No.2 Classes of Errors and Ch,6,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,2 Equal Precision Surveying,Observing in the same condition,Question:,what is the same condition?,No.2 Classes of Errors and Ch,7,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,3 True Value and Estimate Value,True Value,（真值）,:,反映一个量真正大小、绝对准确的数值,以一定准确程度反演一个量大小的数值,Estimate Value,（估值）,:,No.2 Classes of Errors and Ch,8,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,3 True Value and Estimate Value,Note,：,1,、真值一般无法求得,2,、一个量观测值和平差值是真值还是估值？,No.2 Classes of Errors and Ch,9,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,4 True Error,（真误差）,True Error is the difference between an,observation of a quantity and true value,OR,True Error is the difference between the estimate value of a quantity and true value,No.2 Classes of Errors and Ch,10,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,4 True Error,（真误差）,For:,True value,：,X,；,Estimate value:L,；,True error:,then,No.2 Classes of Errors and Ch,11,No.2 Classes of Errors and Characteristics,1、,True Value and True Error,4 True Error,Note:,一般情况下，在测量中虽然真值是客观存在的，但观测值的真值及真误差都是不可能知道的，而观测值的某些函数值的真值却是可以知道。根据观测值的函数值与其真值的差异，可以判断观测值中是否存在粗差。,(,Since X can never be known,will never be known as well,),No.2 Classes of Errors and Ch,12,No.2 Classes of Errors and Characteristics,4)、,True Error,Example1:,设，平面三角形内角观测值为,L,1,，L,2,，L,3,三角形,内角和,的真误差闭合差（,Close Error）,W=(L1+L2+L3),估,-180,0,闭合差,的真误差,W,真,=(,L1+L2+L3),真,-180,0,0闭合差的真值,W,=,WW,真,W,闭合差的真误差,No.2 Classes of Errors and Ch,13,No.2 Classes of Errors and Characteristics,4)、,True Error,Example2:,设，某量真值为,X，,两观测值为,L,1,，L,2,双次观测之差定义为：,d=L,1,-L,2,双次观测之差的真值为：,d,真,=,L,1,真,L,2,真,XX0,双次观测之差的真误差,dd d,真,d,较差,No.2 Classes of Errors and Ch,14,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,（粗差）,2、,The Classes of Errors,2)、,Systematic Errors,（系统误差）,3)、,Random Errors,（偶然误差）,No.2 Classes of Errors and Ch,15,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,2、,The Classes of Errors,Blunders are mistakes or gross errors.It may be,caused by the wrong reading of instruments,transposing numbers or equipment failures.Blunder,are usually large and easily detected,.,No.2 Classes of Errors and Ch,16,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,2、,The Classes of Errors,Characteristics:,magnitude is significantly,large/small/different in comparison,to the measured values(abnormal,observation),No.2 Classes of Errors and Ch,17,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,2、,The Classes of Errors,Source:,Carelessness of the observer;,Failure of instrument;,Abnormity of environment.,观测时大数读错；,计算机输入数据错误；,航测相片判读错误；,控制网起始数据错误。,No.2 Classes of Errors and Ch,18,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,2、,The Classes of Errors,Effect:,Inhomogeneous observable;,Treatment:,Carefulness;,Checking through close error,；,Detecting,No.2 Classes of Errors and Ch,19,No.2 Classes of Errors and Characteristics,1)、,Blunders or Gross Errors,2、,The Classes of Errors,Example:,Measuring a distance,31.3m,31.1m,31.2m,13.1m,31.1m,注意：经典平差中，要求粗差消灭在平差前，,今后我们一般认为，待平差的观测值无粗差！,No.2 Classes of Errors and Ch,20,No.2 Classes of Errors and Characteristics,2)、,Systematic Errors,2、,The Classes of Errors,Systematic error affect the observations in the,same way,hence they are hard to detect by,repeated observation.,.,钢尺量距中的尺长误差,.,测距仪的加常数和乘常数,.,形变测量中的周期误差,.,天文测量中的人差,.,大气折光差,No.2 Classes of Errors and Ch,21,No.2 Classes of Errors and Characteristics,2)、,Systematic Errors,2、,The Classes of Errors,Characteristics:,.Same sign and value;,.,Constant error or bias;,.Systematic varieties;,.Accumulative,No.2 Classes of Errors and Ch,22,No.2 Classes of Errors and C
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