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Spectral diagonal ensemble Kalman filters

机译：光谱对角线集成卡尔曼滤波器

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A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the approximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.
机译：开发了一种新型的集合卡尔曼滤波器，它基于在分析步骤中将样本协方差替换为频谱中的对角线。已经证明，当协方差本身在频谱基础上是对角线时，例如对于二阶平稳随机场和傅立叶基础，这种技术改善了协方差的近似。该方法通过小波扩展到状态变量是空间上不均匀的随机字段的情况。针对几种类型的观测，提供了快速傅里叶变换（FFT）和离散小波变换（DWT）的有效实现，其中包括在部分域中给出的高维数据，例如雷达和卫星图像。计算实验证明，该方法在Lorenz 96问题和具有非常小的集合且在多个分析周期内的浅水方程组中表现良好。

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