A Variational Pseudo-Observation Guided Nudged Particle Filter

Abstract: Nonlinear filtering with standard PF methods requires mitigative techniques to quell weight degeneracy, such as resampling. This is especially true in high-dimensional systems with sparse observations. Unfortunately, such techniques are also fragile when applied to systems with exceedingly rare events. Nonlinear systems with these properties can be assimilated effectively with a control-based PF method known as the nPF, but this method has a high computational cost burden. In this work, we aim to retain this strength of the nudged method while reducing the computational cost by introducing a variational method into the algorithm that acts as a continuous pseudo-observation path. By maintaining a PF representation, the resulting algorithm continues to capture an approximation of the filtering distribution, while reducing computational runtime and improving robustness to the "rare" event of switching phases. Preliminary testing of the new approach is demonstrated on a stochastic variant of the nonlinear and chaotic L63 model, which is used as a surrogate for mimicking "rare" events. The new approach helps to overcome difficulties in applying the nPF for realistic problems and performs favorably with respect to a standard PF with a higher number of particles.