A Seamless Multilevel Ensemble Transform Particle Filter
For researchers in data assimilation and particle filtering, this offers an incremental improvement to multilevel Monte Carlo methods by enhancing variance decay.
This paper introduces a seamless multilevel ensemble transform particle filter that maintains strong coupling between coarse and fine ensembles throughout assimilation, leading to increased variance decay and potential computational cost reductions compared to prior methods.
This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combination of optimal coupling transformations between coarse and fine ensembles in difference estimators within 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 during all stages of the assimilation algorithm, instead of using independent transformations to equal weights followed by recoupling with an assignment problem. This modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside evidence of asymptotic consistency, in numerical examples.