A Guided Sequential Monte Carlo Method for the Assimilation of Data into Stochastic Dynamical Systems

Abstract

Assimilation of measurements into stochastic dynamical systems is challenging due to the generally non-Gaussian behavior of the underlying probability density functions. While sequential Monte Carlo methods have emerged as a methodology for tackling assimilation problems under rather general circumstances, those methods suffer from the curse of dimensionality. At the same time ensemble transform filters, such as the ensemble Kalman filter, have emerged as attractive alternatives to sequential Monte Carlo methods since they also work for high dimensional problems. Typical ensemble transform filters are however based on rather crude approximations to the involved probability density functions and are therefore of limited accuracy. For that reason there have been a number of recent attempts to combine sequential Monte Carlo methods with ensemble transform techniques, so-called guided sequential Monte Carlo (GSMC) methods. In this paper, we first put ensemble transform filters in the context of coupling and optimal transportation and secondly propose a new GSMC method based on combining approximate couplings with importance sampling. The effect of various filtering strategies is demonstrated for a simple Brownian dynamics model.