The Extension of the Gauss Approach for the Solution of an Overdetermined Set of Algebraic Non Linear Equations
The Extension of the Gauss Approach for the Solution of an Overdetermined Set of Algebraic Non Linear Equations
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DOI：
10.1109/tcsii.2018.2796938
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发表时间：
2018-01
期刊：
影响因子：
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通讯作者：
N. Bretas;A. Bretas
中科院分区：
文献类型：
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作者：
N. Bretas;A. Bretas
本文介绍了高斯方法的扩展，用于求解超定代数非线性方程组。此外，还表明，高斯方法中的测量误差位于测量方向，并且该误差具有独特的分解：1）第一个分量，与雅可比范围空间正交，残差；2）另一个分量在雅可比范围空间上。当最小化残差时，后者隐藏在雅可比空间中。高斯方法的扩展在某种意义上就是最小化误差范数。在工程中，测量可能存在较大误差，因此需要检测、识别和纠正这些误差。为此目的将开发最大归一化误差测试。考虑到网络攻击的可能性（建模为恶意数据攻击），纠错步骤至关重要。电力网络上的应用将用于显示使用高斯最小化时隐藏的误差分量，并说明所提出过程的所有步骤以及与当前高斯方法的比较。
In this brief is presented an extension of the Gauss approach for the solution of an overdetermined set of algebraic non linear equations. Further, it is shown that the measurement error, in the Gauss approach, is in the measurement direction and that error has a unique decomposition: 1) the first component, which is orthogonal to the Jacobian range space, the residual and 2) the other which is on the Jacobian range space. The latter is hidden in the Jacobian space when one minimizes the residual. The extension of the Gauss approach is then in the sense to minimize the norm of the error. In engineering, the measurements may have gross errors, and then detection, identification, and correction of those errors are necessary. The Largest Normalized Error Test will be developed for that purpose. Considering the cyber-attack possibility, modeled as a malicious data attack, the error correction step is paramount. Applications on power networks will be used to show the hidden error component when using the Gauss minimization, and also to illustrate all the steps of the presented procedure as well as comparison to the current Gauss approach.