A scalable optimal-transport based local particle filter

Abstract: Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large ensemble sizes for accurate estimates in complex spatial models. Localisation approaches, which perform local state updates by exploiting low dependence between variables at distant points, have been suggested as a potential resolution to this issue. Naively applying the resampling step of the particle filter locally however produces implausible spatially discontinuous states. The ensemble transform particle filter replaces resampling with an optimal-transport map and can be localised by computing maps for every spatial mesh node. The resulting local ensemble transport particle filter is however computationally intensive for dense meshes. We propose a new optimal-transport based local particle filter which computes a fixed number of maps independent of the mesh resolution and interpolates these maps across space, reducing the computation required and allowing it to be ensured particles remain spatially smooth. We numerically illustrate that, at a reduced computational cost, we are able to achieve the same accuracy as the local ensemble transport particle filter, and retain its improved robustness to non-Gaussianity and ability to quantify uncertainty when compared to local ensemble Kalman filters.