Counterexamples for degree of observability analysis method based on SVD theory
Counterexamples for degree of observability analysis method based on SVD theory
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发表时间：
2008
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通讯作者：
Hu Jun
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作者：
Hu Jun
常用的可观测度分析方法包括误差协方差矩阵的特征值和特征向量分析法以及可观测性矩阵的奇异值分解法。前者是在滤波后进行的，而后者可以用来分析滤波前整个系统的DOO。然而，奇异值分解方法不适合于分析系统状态的DOO。本文通过几个反例说明，由于SVD方法在坐标系拉伸时不具有不变性，因此在对系统状态进行无量纲化时，其结果可能与之相反。
The common methods to analyze the Degree of Observability(DOO) include the eigenvalues and eigenvectors analysis method of error covariance matrix and the Singular Value Decomposition(SVD) method of observability matrix. The former was carried out after filtering, while the latter can be used to analyze the DOO of the whole system before filtering. However, the SVD method is not suitable to analyze the DOO of the system states. This article gives several counterexamples to show that the conclusion could be contrary when we do transformation to make the state variables dimensionless for comparing the DOO of different system states,because the SVD method has no invariability character when the reference frame is stretched.