Abstract

The implicit particle filter is one of a number of recently-proposed particle filtering schemes in which the trajectory of each particle is informed by observations within each assimilation cycle. In the case of observations defined by a linear function of the state vector, taken every time step of the numerical model, the implicit particle filter is equivalent to the optimal importance filter, i.e., at each step, any given particle is drawn from the density of the system conditioned jointly upon the observation and the state of the particle at the previous time. The optimal importance filter was implemented for a shallow water model with O(10^4) state variables, and performed well with nominal demands on computing resources, but it exhibited some characteristics of the degeneracy some authors have predicted. We note the similarity of our scheme to other recently-devised schemes, and propose a potential solution in the form of a fixed-lag smoother.