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首页> 外文期刊>Journal of surveying engineering >Comparison of Structured and Weighted Total Least-Squares Adjustment Methods for Linearly Structured Errors-in-Variables Models
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Comparison of Structured and Weighted Total Least-Squares Adjustment Methods for Linearly Structured Errors-in-Variables Models

机译：线性结构变量误差模型的结构化和加权总最小二乘平差方法的比较

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摘要

The paper focuses on a specific errors-in-variables (EIV) model named the linearly structured EIV (LSEIV) model in which all the random elements of design matrix are in a linear combination of an input vector with random errors. Two existing structured total least-squares (STLS) algorithms named constrained TLS (CTLS) and structured TLS normalization (STLN) are introduced to solve the LSEIV model by treating the input and output vectors as the noisy structure vectors. For comparison purposes, the weighted TLS (WTLS) method is also performed based on the partial EIV model. Approximated accuracy assessment methods are also presented. The plane fitting and Bursa transformation examples are illustrated to demonstrate the accuracy and computational efficiency performance of the proposed algorithms. It shows that the proposed STLS and WTLS algorithms can achieve the same accuracy if the dispersion matrix of the WTLS method is constructed based on the partial EIV model.
机译：本文着重于一个名为线性结构化EIV（LSEIV）模型的特定的变量误差（EIV）模型，其中设计矩阵的所有随机元素都在具有随机误差的输入矢量的线性组合中。引入了两种现有的结构化总最小二乘（STLS）算法，分别称为约束TLS（CTLS）和结构化TLS规范化（STLN），以通过将输入和输出矢量视为噪声结构矢量来求解LSEIV模型。为了进行比较，还基于部分EIV模型执行了加权TLS（WTLS）方法。还介绍了近似的准确性评估方法。举例说明了平面拟合和Bursa变换示例，以证明所提出算法的准确性和计算效率。结果表明，如果基于部分EIV模型构造WTLS方法的色散矩阵，则所提出的STLS和WTLS算法可以达到相同的精度。

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