Dimensional reduction for a Bayesian filter

An adaptive strategy is proposed for reducing the number of unknowns in the calculation of a proposal distribution in a sequential Monte Carlo implementation of a Bayesian filter for nonlinear dynamics. The idea is to solve only in directions in which the dynamics is expanding, found adaptively; this strategy is suggested by earlier work on optimal prediction. The construction should be of value in data assimilation, for example, in geophysical fluid dynamics.