A potential implicit particle method for high-dimensional systems

Abstract

This paper presents a particle method designed for high-dimensional state estimation. Instead of weighing random forecasts by their distance to given observations, the method samples an ensemble of particles around an optimal solution based on the observations (i.e., it is implicit). It differs from other implicit methods because it includes the state at the previous assimilation time as part of the optimal solution (i.e., it is a lag-1 smoother). This is accomplished through the use of a mixture model for the background distribution of the previous state. In a high-dimensional, linear, Gaussian example, the mixture-based implicit particle smoother does not collapse. Furthermore, using only a small number of particles, the implicit approach is able to detect transitions in two nonlinear, multi-dimensional generalizations of a double-well. Adding a step that trains the sampled distribution to the target distribution prevents collapse during the transitions, which are strongly nonlinear events. To produce similar estimates, other approaches require many more particles.