Estimation of straight line parameters with fully correlated coordinates
Estimation of straight line parameters with fully correlated coordinates
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DOI：
10.1016/j.measurement.2013.11.005
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发表时间：
2014-02
期刊：
影响因子：
5.6
通讯作者：
A. Amiri-Simkooei;F. Zangeneh-Nejad;J. Asgari;S. Jazaeri
中科院分区：
文献类型：
--
作者：
A. Amiri-Simkooei;F. Zangeneh-Nejad;J. Asgari;S. Jazaeri
线性回归问题是许多计量测量系统中广泛应用的一个问题。当两个变量受到不同的和可能相关的噪声时，本文提出了一个使用加权总最小二乘（WTLS）问题的简单可靠的线性回归拟合公式。该公式是对最近四篇研究论文的后续研究，其中该方法成功地应用于变量误差模型。它是对标准最小二乘法的一种简单修改，其主要结果是当变量x的所有元素之间的相关噪声的完整结构被使用时，所谓的垂直偏移量被最小化。该公式严谨，无需近似，可直接提供估计参数的不确定度。在特殊情况下，一般公式简化为文献中众所周知的标准线性回归模型。该算法在MATLAB中实现，并在附录A中提供，使用三个模拟和实验数据集验证了该算法的有效性。结果表明，使用所提出的公式可以在相对较短的时间内提供准确可靠的线路参数及其协方差矩阵估计。
Linear regression problem is a widely used problem in many metrological and measurement systems. This contribution presents a simple and reliable formulation for the linear regression fit using the weighted total least squares (WTLS) problem, when both variables are subjected to different and possibly correlated noise. The formulation is a follow up to four recent research papers in which the method was successfully applied to errors-in-variables models. It is a simple modification of the standard least squares method whose principal result is that the so-called perpendicular offsets are minimized when the full structure of correlated noise among all elements of variablex,yor both variables is supposed to be used. The formulation is rigorous, thus without approximation, and can directly provide the uncertainty of the estimated parameters. In a special case, the general formulation simplifies to the well-known standard linear regression model available in the literature. The effectiveness of the algorithm, which was implemented in MATLAB and is available in Appendix A, is demonstrated using three simulated and experimental data sets. The results indicate that accurate and reliable estimates of line parameters along with their covariance matrix can be provided using the proposed formulation in a relatively small amount of time.