Total Least Squares Approach to Modeling: A Matlab Toolbox
Total Least Squares Approach to Modeling: A Matlab Toolbox
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发表时间：
2010
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通讯作者：
D. Bednárová
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作者：
D. Bednárová
本文论述一种称为总体最小二乘法或正交回归或变量误差法的数学方法。该方法可用于静态和动态过程的建模。其他广泛的应用领域是信号和图像处理。我们还提出了一个Matlab工具箱，它可以解决建模中与总体最小二乘法相关的基本问题。几个说明性的例子，以及。本文提出了总体最小二乘法（TLS），也称为变量误差法或正交回归法。人们很难说出另一种方法，它和最小二乘法一样经常使用。与此同时，很难命名另一种方法，这种方法伴随着如此强烈和持久的争议，如最小二乘法。也很难找到另一种方法，它是如此容易，同时作为人工最小二乘法。最小二乘法诞生的故事在文献中有很好的介绍，可以总结如下[4，6，12，17]。优先出版权肯定属于A。M. Legendre（1805），他也给了这个方法一个著名的名字，但是C. F.高斯（1809年）声称，他知道并使用这种方法早得多，约10年前勒让德的出版物。高斯的论点，他的优先权是不完美的。他的日记与计算声称是由最小二乘法失去了。当H. C.舒马赫建议重复高斯的损失计算声称要做的最小二乘法，高斯完全拒绝了这个想法的话，这种尝试只会表明，他不能信任。
This paper deals with a mathematical method known as total least squares or orthogonal regression or error-in-variables method. The mentioned method can be used for modeling of static and also dynamic processes. A wide area of other applications is in signal and image processing. We also present a Matlab toolbox which can solve basic problems related to the total least squares method in the modeling. Several illustrative examples are presented as well. In this paper we present the total least squares method (TLS), which is also known as error-in-variables method or orthogonal regression method. One could hardly name another method which is used as frequently as the method which is known as the least squares method. At the same time, it is difficult to name another method which was accompanied by such strong and long lasting controversy as the least squares method. It is also difficult to find another method, which is so easy and at the same time as artificial as the least squares method. The story of the birth of the least squares method is well covered in the literature and can be summarized as follows [4, 6, 12, 17]. The priority in publication definitely belongs to A. M. Legendre (1805), who also gave the method its famous name, but C. F. Gauss (1809) claimed that he knew and used this method much earlier, about 10 years before the Legendre's publications. Gauss's arguments for his priority were not perfect at all. His diaries with computations claimed to be made by the least squares method were lost. It is also known that when H. C. Schumacher suggested repeating Gauss's lost computations claimed to be done by the least squares method, Gauss totally rejected this idea with the words that such attempts would only suggest that he could not be trusted.