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Particle filtering (PF) is an often used method to estimate the states of dynamical systems. A major limitation of the standard PF method is that the dimensionality of the state space increases as the time proceeds and eventually may cause degeneracy of the algorithm. A possible approach to alleviate the degeneracy issue is to compute the marginal posterior distribution at each time step, which leads to the so-called marginal PF method. A key issue in the marginal PF method is to construct a good sampling distribution in the marginal space. When the posterior distribution is close to Gaussian, the Ensemble Kalman filter (EnKF) method can usually provide a good sampling distribution; however the EnKF approximation may fail completely when the posterior is strongly non-Gaussian. In this work we propose a defensive marginal PF (DMPF) algorithm which constructs a sampling distribution in the marginal space by combining the standard PF and the EnKF approximation using a multiple importance sampling (MIS) scheme. An important feature of the proposed algorithm is that it can automatically adjust the relative weight of the PF and the EnKF components in the MIS scheme in each step, according to how non-Gaussian the posterior is. With numerical examples we demonstrate that the proposed method can perform well regardless of whether the posteriors can be well approximated by Gaussian.

A Defensive Marginal Particle Filtering Method for Data Assimilation