Efficient Implementation of Marginal Particle Filter by Functional Density Decomposition

The paper considers the solution to the state estimation problem of nonlinear dynamic stochastic systems by the particle filters. It focuses on the marginal particle filter algorithms which generate samples directly in the marginal space for the recent state. Their standard implementation calculates the sample weights by combining the samples from two consecutive time instants in the transition and proposal density function evaluations. This results in computational complexity quadratic in sample size. The paper proposes an efficient implementation of the marginal particle filter for which a functional tensor decomposition of the transition and proposal densities is calculated. The computational complexity of the proposed implementation is linear in sample size and the decomposition rank can be used to achieve a trade-off between accuracy and computational costs. The balance between the complexity and the estimate quality can be tuned by selecting the rank of the decomposition. The proposed implementation is demonstrated using two numerical examples with a univariate non-stationary growth model and terrain-aided navigation scenario.