Implicit equal-weights particle filter

Abstract

Filter degeneracy is the main obstacle for the implementation of particle filters in nonlinear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced, in which samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1000 dimensional simple linear model and the 1000 dimensional nonlinear Lorenz96 model and compare the performance of the scheme with that of a local ensemble transformed Kalman filter (LETKF). The new scheme is never degenerate and shows good and consistent performance in all experiments. The LETKF has lower root-mean-square errors at observed grid points, but its ensemble spread is too low at unobserved grid points, where the IEWPF performs better. Furthermore, the IEWPF has a consistent spread in all experiments. This new filter opens up a new class of particle filters that, by construction, do not suffer from the curse of dimensionality.