【摘要】 全面最小二乘法(TLS)是近年发展起来的一种数据处理方法,已经广泛应用于自动控制、系统识别、信号处理、物理学等各个学科当中,但是研究全面最小二乘在平差中应用的文章还很少。全面最小二乘法可以把系数矩阵和观测值两者的误差全都考虑进去,从而使平差更精确,数据可靠性更高。本文首先分别介绍了全面最小二乘法的基本原理和相关算法,然后设计两种方案即系数矩阵误差很小和较大的情况下,再分别用最小二乘和全面最小二乘对两种方案进行处理,最后得出结论:在系数矩阵误差很小的情况下,两种处理方法都能达到精度要求,在系数矩阵误差较大的情况下,全面最小二乘可以达到精度要求,最小二乘达不到精度要求。总之,全面最小二乘方法优于最小二乘方法。更多还原

【Abstract】 The total least squares(TLS) ,which is a kind of data processing method developed in recent years, has already caused of the attention of various fields specialist, but the article about the application of total least squares method in adjustment has been seldom seen. The total least squares method can take both the errors of coefficient matrix and the errors of measurements into consideration, so it can make adjustment more accurate, reliability higher. This text has introduced the basic principles of least squares and total least squares separately at first, then designed two kinds of schemes namely under the situation that the error of the coefficient matrix is very little and greater, then dealt with two kinds of schemes with least squares and total least squares separately. At last the conclusion is: in the situation that the coefficient matrix error is very little, two kinds of methods both can reach the precision to require, and in the situation that the coefficient matrix error is bigger, total least squares can reach the precision to require, least squares can not reach the requirement of precision.In a word, total least squares is better than least squares.更多还原