A Newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements
A Newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements
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DOI：
10.1007/s11200-013-0254-7
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发表时间：
2014-04
影响因子：
0.9
通讯作者：
Yongjun Zhou;X. Kou;Jianjun Zhu;Jonathan Li
中科院分区：
文献类型：
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作者：
Yongjun Zhou;X. Kou;Jianjun Zhu;Jonathan Li
对于EIV模型的加权总体最小二乘（WTLS）解法，有三个关键问题：（1）如何获得设计矩阵的方差协方差矩阵的完美描述：（2）如何找到一种有效的算法来处理各种情况，特别是当设计矩阵与右侧向量互相关时;（3）如何评价所提出方法的精度。本文提出了一种特殊的EIV模型，其中设计矩阵的每个随机元素是输入向量的函数。在这种模型中，误差污染的输入和输出向量被等效地视为测量。提出了一种基于误差传播规律的增广设计矩阵方差协方差矩阵的计算方法。它适用于更一般的情况，即使在色散矩阵的互协方差非零的情况下，也能得到色散矩阵。这也证明了它与后面介绍的规则是一致的。一种WTLS的方法，称为牛顿迭代WTLS算法，其次是一个近似的精度评估方法。实例分析表明，该算法可以达到与现有的WTLS或结构化TLS方法相同的精度。提出的牛顿WTLS算法的目的是提供一个完整的WTLS调整方法与一般的权重矩阵的特定EIV模型。
For a weighted total least-squares (WTLS) solution to errors-in-variables (EIV) model, three issues are essential: (1) how to acquire a perfect description of the variancecovariance matrix of the design matrix; (2) how to find an effective algorithm to deal with all the situations, particularly, when the design matrix and right hand side vector are cross-correlated; (3) how to evaluate the accuracy of the proposed methods. This paper presents a specific EIV model in which each random element of the design matrix is a function of the input vector. In such a model, the error corrupted input and output vectors are treated as the measurements equivalently. A scheme of calculating the variance-covariance matrix of the augmented design matrix based on error propagation laws is presented. It is suitable for achieving the dispersion matrices in more general cases even in the presence of the nonzero cross-covariance of dispersion matrix. It is also proved to be consistent with the rules introduced rearlier. A WTLS approach, called Newton iterative WTLS algorithm followed by an approximated accuracy assessment method is developed. Case studies demonstrate that the proposed algorithm can achieve the same accuracy as the existing WTLS or structured TLS methods. The proposed Newton WTLS algorithm aims to provide a complete WTLS adjustment method with a general weight matrix for the specific EIV model.