2015/07/30 by Patrick Rebeschini, Ramon van Handel · 3 citations
Earth and Planetary Sciences · Environmental Science · #Climate variability and models #Flood Risk Assessment and Management #Meteorological Phenomena and Simulations
paper · doi:10.1214/14-aap1061
openalex publication_date 2015/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The discovery of particle filtering methods has enabled the use of nonlinear filtering in a wide array of applications. Unfortunately, the approximation error of particle filters typically grows exponentially in the dimension of the underlying model. This phenomenon has rendered particle filters of limited use in complex data assimilation problems. In this paper, we argue that it is often possible, at least in principle, to develop local particle filtering algorithms whose approximation error is dimension-free. The key to such developments is the decay of correlations property, which is a spatial counterpart of the much better understood stability property of nonlinear filters. For the simplest possible algorithm of this type, our results provide under suitable assumptions an approximation error bound that is uniform both in time and in the model dimension. More broadly, our results provide a framework for the investigation of filtering problems and algorithms in high dimension.