A seamless multilevel ensemble transform particle filter - Gregory,ACA; Cotter,CJ (SIAM Journal on Scientific Computing, 2017)
This paper presents a seamless algorithm for the application of the multilevel MonteCarlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combi-nation of optimal coupling transformations between coarse and fine ensembles in difference estimatorswithin a multilevel framework, to minimise estimator variance. It differs from that of Gregory et al.(2016) in that strong coupling between the coarse and fine ensembles is seamlessly maintained duringall stages of the assimilation algorithm, instead of using independent transformations to equal weightsfollowed by recoupling with an assignment problem. This modification is found to lead to an increasedrate in variance decay between coarse and fine ensembles with level in the hierarchy, a key componentof MLMC. This offers the potential for greater computational cost reductions. This is shown, alongsideevidence of asymptotic consistency, in numerical examples.