Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data

Many real-world problems require to estimate parameters of interest in a Bayesian framework from data that are collected sequentially in time. Conventional methods to sample the posterior distributions, such as Markov Chain Monte Carlo methods can not efficiently deal with such problems as they do not take advantage of the sequential structure. To this end, the Ensemble Kalman inversion (EnKI), which updates the particles whenever a new collection of data arrive, becomes a popular tool to solve this type of problems. In this work we present a method to improve the performance of EnKI, which removes some particles that significantly deviate from the posterior distribution via a resampling procedure. Specifically we adopt an idea developed in the sequential Monte Carlo sampler, and simplify it to compute an approximate weight function. Finally we use the computed weights to identify and remove those particles seriously deviating from the target distribution. With numerical examples, we demonstrate that, without requiring any additional evaluations of the forward model, the proposed method can improve the performance of standard EnKI in certain class of problems.