Sequential Monte Carlo Filtering Using Nested Particles with Local Gaussian Assumptions

Abstract

Sequential Monte Carlo methods are used for numerically solving the optimal state estimation problem. The methodology is based on the evolution of random particles of the state probability density function according to dynamic models and noisy measurements. A key requirement in particle filters is to propose an importance density that approximates the optimal importance density as close as possible. Local linearization particle filters use banks of independent variants of Kalman filters to propose importance densities that are mindful of the latest measurement. The proposed nested particles filter with local Gaussian assumptions is a general framework that can incorporate many nonlinear filters to generate appropriate importance densities. In this approach, it is shown that local linearization can be avoided by performing local filtering with only a Gaussian prior assumption. Local filtering is naturally integrated into the nested particles filter by correcting the filters from the results of the particle filter. Two simulation examples are included to illustrate the validity of the nested particles filter in cases where very accurate measurements are given and where the filter is poorly initialized by the a priori information.