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Title: The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems
Award ID(s):
1924723 1704256
NSF-PAR ID:
10287482
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Automatica
Volume:
131
Issue:
C
ISSN:
0005-1098
Page Range / eLocation ID:
109752
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. 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. 
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