This presentation considers the aim of increasing the efficiency of a particular particle filtering algorithm, by extending the multilevel Monte Carlo variance reduction technique to it. In particular, the presentation will show how multilevel Monte Carlo can be applied to the ensemble transform particle filter (EPTF). A key aspect of this adaptation is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles within filters for low and high dimensional systems. Finally, the modifications to the proposed algorithm needed to allow for a higher rate of variance decay between finer adjacent ensembles will be discussed.