Localization in High-Dimensional Monte Carlo Filtering

Abstract: The high dimensionality and computational constraints associated with filtering problems in large-scale geophysical applications are particularly challenging for the Particle Filter (PF). Approximate but efficient methods such as the Ensemble Kalman Filter (EnKF) are therefore usually preferred. A key element of these approximate methods is localization, which is in principle a general technique to avoid the curse of dimensionality and consists in limiting the influence of observations to neighboring sites. However, while it works effectively with the EnKF, localization introduces harmful discontinuities in the estimated physical fields when applied blindly to the PF. In the present paper, we explore two possible local algorithms based on the EnKPF, a hybrid method combining the EnKF and the PF. A simulation study in a conjugate normal setup allows to highlight the trade-offs involved when applying localization to PF type of algorithms in the high-dimensional setting. Experiments with the Lorenz96 model demonstrate the ability of the local EnKPF algorithms to perform well even with a small number of particles compared to the problem size.