翻译

Unit 11 Least-Squares Adjustment （最小二乘平差）

Whenever the surveyor conducts a field survey, no matter how simple or complex, he invariably makes more measurements than are absolutely necessary to locate the points in the survey.（无论何时测量人员进行【conduct操作、管理】外业测量，不管【no matter 不论】怎样简单或是复杂，他总是【invariably总是】进行多于绝对必要的观测来定位点在测量中）

A line taped in two directions introduces one measurement more than is necessary to establish the length of the line.（一条线由两个方向丈量，产生一个观测值，要多于确定【establish确定】直线长度所需的观测值）

Measuring all three angles of a triangle introduces one superfluous measurement.（测量一个三角形中所有三个内角产生一个多余【superfluous多余的】观测值）

These extra measurements are termed redundant measurements.（这些额外的【extra】观测值被称为多余【redundant多余的】观测值）

Least-squares adjustment is a mathematical and statistical technique for dealing with the optimal combination of redundant measurements together with the estimation of unknown parameters.（最小二乘平差是一个数学的和统计学的技术用以处理多余观测值的最优【optimal最佳的】联合，和【together with】未知参数的估计）

The least-squares adjustment is rigorously based on the theory of mathematical probability, whereas in general, the other methods do not have this rigorous base.（最小二乘平差严格地【rigorously严格地】基于数学概率理论，然而【whereas】通常【in general】，其它方法并没有这样严格的基础）

In a least-squares adjustment, the following condition of mathematical probability is enforced: the sum of the square of the errors times their respective weights are minimized.（在最小二乘平差中，下列数学概率的条件被要求【enforce强迫、坚持】：误差平方与其各自的权的乘积【time 乘v.】的和最小）

In surveying, errors in measurements conform to the laws of probability, and they follow the normal distribution theory.（测量中，测量误差遵照【conform to】概率的法则，它们遵循正态分布【normal distribution】的理论）

Thus they should be adjusted in a manner that follows these mathematical laws.（这样，它们将以这些数学法则的方式被平差）

A mathematical model for adjustment is composed of two parts: a functional model and a stochastic model.（一个平差的数学模型由两个部分组成【be composed of由...组成】：函数模型【functional model】和随机模型【stochastic model】）。

Mathematical Model （数学模型）

A functional model describes the geometric or physical characteristics of the survey problem.（一个函数模型描述了测量问题的几何或是物理特征）

In adjustment computations a functional model is an equation that represents or defines an adjustment condition.（在平差计算中一个函数模型是一个方程，表现或定义了一个平差条件【condition】）

It must either be known, or assumed.（它或者是已知或者是假定的）

If the functional model represents the physical situation adequately, the observation errors can be expected to conform to the normal distribution curves.（如果函数模型充分【adequately充分地】表现了物理情形【situation】，观测误差可以被认为【be expected】遵照【conform to】正态