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The Ensemble Kalman Filter in the Near-Gaussian Setting

J. A. CarrilloF. HoffmannA. M. StuartU. Vaes
Dec 2022
摘要
The ensemble Kalman filter is widely used in applications because, for highdimensional filtering problems, it has a robustness that is not shared forexample by the particle filter; in particular it does not suffer from weightcollapse. However, there is no theory which quantifies its accuracy as anapproximation of the true filtering distribution, except in the Gaussiansetting. To address this issue we provide the first analysis of the accuracy ofthe ensemble Kalman filter beyond the Gaussian setting. Our analysis isdeveloped for the mean field ensemble Kalman filter. We rewrite this filter interms of maps on probability measures, and then we prove that these maps arelocally Lipschitz in an appropriate weighted total variation metric. Usingthese stability estimates we demonstrate that, if the true filteringdistribution is close to Gaussian after appropriate lifting to the joint spaceof state and data, then it is well approximated by the ensemble Kalman filter.Finally, we provide a generalization of these results to the Gaussian projectedfilter, which can be viewed as a mean field description of the unscented Kalmanfilter.
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