SYMMETRIZED IMPLICIT SAMPLING FOR PARTLICE FILTER

Abstract

Particle filters are a data assimilation technique that estimate a posterior distribution given a set of observations. Particle filters often use samplers that produce independent, weighted samples. We analyze two implicit filters; the first is a linear map and second is a symmetrized linear map. Then we study three particle filters on a one dimensional example and a three dimensional system of ordinary di↵erential equations. The implicit sampler on a symmetrized linear map reduces the variance in weights compared to the implicit sampler on a linear map. By comparing these methods on specific examples, we do not find distinctive di↵erence between the three filters, though the bootstrap filter does show marginally better results than the others.