Efficient Kernel-Based Ensemble Gaussian Mixture Filtering

AbstractThe Bayesian filtering problem for data assimilation is considered following the kernel-based ensemble Gaussian mixture filtering (EnGMF) approach introduced by Anderson and Anderson. In this approach, the posterior distribution of the system state is propagated with the model using the ensemble Monte Carlo method, providing a forecast ensemble that is then used to construct a prior Gaussian mixture (GM) based on the kernel density estimator. This results in two update steps: a Kalman filter (KF)-like update of the ensemble members and a particle filter (PF)-like update of the weights, followed by a resampling step to start a new forecast cycle. After formulating EnGMF for any observational operator, the influence of the bandwidth parameter of the kernel function on the covariance of the posterior distribution is analyzed. Then the focus is on two aspects: (i) the efficient implementation of EnGMF with (relatively) small ensembles, where a new deterministic resampling strategy is proposed preservi...

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