第一节 测量误差概述
　　 一、测量误差的概念
　　 自然界任何客观事物或现象都具有不确定性，加之受科学技术发展水平的限制，导致人们认识能力的局限性，使得人们只能不断地接近客观事物或现象的本质，而不能穷尽它，即人们对客观事物或现象的认识总会存在不同程度的误差，这种误差在对某量进行观测和量测的过程中反映出来，即测量值与真值的差异，称为测量误差或观测误差。
　　 二、观测与观测值
　　 测量是人们认识阐然、认识客观事物的必要手段和途径。通过一定的仪器、工具和方法对某量进行量测，称为测量或观测，获得的数据称为测量值或观测值。
　　 三、观测值的分类
　　 1．同精度观测和不同精度观测
　　 按测量时所处的观测条件可分为同精度观测和不同精度观测，相应的观测值称为同精度观测值和不同精度观测值。
　　 构成测量工作的要素包括观测者、测量仪器和外界环境条件，通常将这些测量工作的要素统称为观测条件。观测成果的质量与观测条件的好坏有着密切的联系。当观测条件好时，观测中所产生的误差平均就可能相应地小一些，因而观测成果的质量就要高一些；反之，观测条件差时，观测成果的质量就要低一些。所以我们可以说，观测成果的质量高低也就客观地反映了观测条件的优劣。用同一精度等级的仪器、设备，用相同的方法和在相同的外界条件下，山具有大致相同技术水平的人在相同观测条件下所进行的观测称为同精度观测，反之，则称为不同精度观测。同精度观测得到的观测值称为同精度观测值或等精度观测值；反之，称为不同(不等)精度观测值。例如，同一观测者分别用DJ6型经纬仪和DJ2型经纬仪测得的—测回水平角度属于不同精度观测值；同样使用DJ6型经纬仪第一次测二测回，第二次测四测回，分别所得到的均值则也属寸：不同精度观测值。
　　 2．直接观测和间接观测
　　 按观测量与未知量之间的关系可分为直接观测和间接观测，相应的观测值称为直接观测值和间接观测值。
　　 为确定某未知量而直接进行的观测，即被观测量就是所求未知量本身，称为直接观测，观测值称为直接观测值。通过被观测量与未知量的函数关系来确定未知量的观测称为间接观测，观测值称为间接观测值。例如，为确定两点间的距离，用钢尺直接丈量属于直接观测；而视距测量则属于间接观测。
　　 3．独立观测和非独立观测
　　 按观测值之间相互独立或依存关系可分为独立观测和非独立观测。
　　 各观测量之间无任何依存关系，是相互独立的观测，称为独立观测，观测值称为独立观测值。若各观测量之间存在一定的几何或物理条件的约束，则称为非独立观测，观测值称为非独立观测值。如对某一单个未知量进行重复观测，各次观测是独立的，各虬岘测值属于独立观测值。观测某平面三角形的三个内角，因三角形内角之和应满足180°个几何条件，则属于非独立观测，三个内角的观测值属于非独立观测值。
　　 四、测量误差的来源
　　 1．真误差的定义
　　 测量中的被观测量，客观上都存在着一个真实值，简称真值。对被观测量进行观测得到观测值。一般情况观测值与真值都不相等，即观测值与真值之间有差异，这个差异称为真误差，即：
　　 真误差=观测值-真值　　　　

          2．测量误差的反映
　　 测量十不可避免地存在着测量误差。例如，为求某段距离，往返丈量若干次；为求某角度，重复观测几测回，这些重复观测的观测值之间总是存在着差异。又如，为求某平面三角形的三个内角，只要对其中两个内角进行观测就可得山第三个内角值。但为检验测量结果，对三个内角均进行观测，这样三个内角之和往往与真值180°产生差异。第三个内角的观测是“多余观测”。这些“多余观测”导致的差异事实上就是测量误差。换句话说，测量误差正是通过“多余观测”产生的差异反映出来的。
　　 3．测量误差产生的原因
　　 测量误差产生的原因很多，按其来源概括起来有以下三方面。
　　 1)测量仪器
　　 观测通常是利用专用的仪器、工具进行的。由于仪器制造和校正不完善，使仪器只具有一定限度的准确度，由此观测所得的数据必然带有误差，从而导致观测值的精度受到一定的影响。例如，用只刻有厘米分划的普通水准尺进行水准测量时，就难以保证估读的毫米值完全准确。
　　 2)观测者
　　 由于观测者的视觉、听觉等感官的鉴别能力有一定的局限性，在观测过程中，无论观测者多么认真仔细，但在仪器安置、使用中都会不可避免地产生误差，如整平误差、照准误差、读数误差等。同时，观测者的工作态度、技术水平等也是对观测结果的误差有直接影响。
 

Measurement error outlined in Section
First, the concept of measurement error
Any objective things or phenomena in nature have uncertainty, exacerbated by restrictions on the level of scientific and technological development, leading to people's cognitive limitations, makes it but to keep close to the objective nature of things or phenomena, but not exhausted it, that people objective understanding of things or phenomena there will always be varying degrees of error, this error is a certain amount to the process of observation and measurements reflected in the measured value and true value of the difference, known as measurement error or observation error.
Second, observation and observation
Measurement is illustrates natural awareness, understanding of objective things, the necessary means and ways. By means of some instruments, tools and methods for the measurement of a quantity known as measurements or observations, the data obtained as measured values or observations.
Third, the classification of observations
1. With the precision of observation and accuracy of observation of different
By observing the conditions in which measurements can be divided into different with the precision of observation and accuracy of observation, the corresponding observed value is called with the precision of the observed values and different precision observations.
Constitutes a survey of the elements of observers, measuring instruments and external environmental conditions, these measurements are usually referred to as elements of the work of observation conditions. Observing the outcome of the quality and observation condition is closely linked to good or bad. When the observing conditions are good, the observational errors arising from the average may be correspondingly smaller, thus observing the quality of the results should be higher; the other hand, poor observation, the observed quality of the results should be lower. So we can say that the quality of the level of observation results also reflect the objective conditions for observing the pros and cons. With the same accuracy class instruments, equipment, using the same methods and at the same external conditions, the mountains have about the same level of technology observed in the same person who carried out under the conditions of observation is called with the precision of observation, the other hand, is called a different accuracy of observation. Observations obtained with the precision of observed values is called with the precision of observed values or values such as accuracy of observation; On the contrary, as different (range) accuracy of observations. For example, the same observers were used to DJ6 type DJ2-based theodolite theodolite and measured - and measured the angle back to the level of accuracy of observations belonging to different values; the same type used DJ6 theodolite test 2 test back to the first and the second test four test back, respectively, by get the mean while is also an inch: different precision observations.
2. Direct observation and indirect observation
According to the measurements and the relationship between the unknown quantity can be divided into direct observation and indirect observation, the corresponding observed value is called the direct observation and indirect observations.
To determine an unknown volume of direct observation, he incurs the measurements is the unknown quantity of the demand itself, known as direct observation, observation known as the directly observed values. Through the concept of measurement and the unknown quantity is a function of the observation to determine the unknown quantity is called an indirect observations, the observed values is called an indirect observations. For example, in order to determine the distance between two points with a ruler belonging to the direct measurement of the direct observation; while the line of sight measurement is part of an indirect observation.
3. Independent observers and non-independent observations
Between the observed values by an independent or dependent relationship could be divided into two independent observers and non-independent observations.
Between the various observables without any dependencies, are independent observations and independent observations, observations and independent observations. If the concept of measurement exists between the geometric or physical conditions, constraints, claimed that a non-independent observations, the observations referred to as non-independent observations. If an unknown quantity of a single repeated observations, the various observations are independent, the measured value Qiu Da Nang is an independent observation. Observation of the three angles of a triangle plane, because the triangle angles, and should meet the 180 ° of a geometric conditions are non-independent observations, the three angles of the observations are non-independent observations.
Fourth, the source of measurement error
1. The definition of true error
The concept of measurement has been measured both objectively there is a real value, referred to as true value. Right view of measurements have been observed to be the observed values. In general observations with the true value is not equal to that observed value and the difference between the true value, the difference known as the true error, namely:
　　 　　　　

           2. Reflect the measurement error
Measurement 10 measurement errors inevitably exist. For example, for the sake of a certain distance from a number of measurement; for the sake of a certain angle, repeated observations of several measurements back to repeat observations of these observations there is always a difference between the values. In another example, for the sake of the three angles of a plane triangle, as long as these two angles can be observed values of Te-shan of the third interior angle. However, to test measurement results, the three angles were observed, so that the sum of three angles 180 ° true value often differ. Third angles of the observations are "redundant observation." These "redundant observation," in fact caused by differences in measurement error. In other words, measurement error is through, "superfluous observe the" differences resulting from the reflected.
3. Causes of measurement error
Measurement error resulting from many causes, according to their sources summed up in the following three aspects.
1) Measuring Instruments
Observation is usually the use of special instruments, tools, carried out. Owing to equipment manufacture and calibration imperfect, so that equipment can only have certain limits of accuracy, thus the data derived from observations with the inevitable errors, resulting in the precision of the observed values by a certain extent. For example, using only the partition inscribed cm ruler to the standard of the ordinary standard of measurement, it is difficult to guarantee the value of assessing reading millimeters entirely accurate.
2) The observer
As the observer's visual, auditory and other sensory ability to identify certain limitations, in the observation process, no matter how seriously careful observers, but the instrument placement, use will inevitably lead to errors, such as the leveling error, according to quasi-error, reading errors. Meanwhile, the observer of the work attitude and technical level is also the result of the error of observation have a direct impact.