Nonlinear Processes in Geophysics On the Kalman Filter error covariance collapse into the unstable subspace
Nonlinear Processes in Geophysics On the Kalman Filter error covariance collapse into the unstable subspace
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地球物理学中的非线性过程关于卡尔曼滤波器误差协方差崩溃到不稳定子空间
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
L. Palatella
中科院分区：
文献类型：
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作者：
A. Trevisan;L. Palatella
将扩展卡尔曼滤波器应用于混沌系统时，误差协方差矩阵的秩经过足够多的迭代后降为N +N0，其中en和N0分别为正Lyapunov指数和空Lyapunov指数的个数。这是由于全扩展卡尔曼滤波器解的不稳定中立切子空间的坍缩。因此，解与将同化限制在具有非负李雅普诺夫指数的李雅普诺夫向量所张成的空间中得到的解是相同的。通过理论论证和数值验证，证明了在不稳定和中性子空间（EKF- aus）中同化的完整EKF及其简化形式的渐近状态估计和协方差估计是相同的。讨论了这些发现对卡尔曼滤波器在混沌模型中的应用的影响。
When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N +N0 whereN andN0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with nonnegative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS) are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.