  Many recent advances in sequential assimilation of data into nonlinear
high-dimensional models are modifications to particle filters which employ
efficient searches of a high-dimensional state space. In this work, we present
a complementary strategy that combines statistical emulators and particle
filters. The emulators are used to learn and offer a computationally cheap
approximation to the forward dynamic mapping. This emulator-particle filter
(Emu-PF) approach requires a modest number of forward-model runs, but yields
well-resolved posterior distributions even in non-Gaussian cases. We explore
several modifications to the Emu-PF that utilize mechanisms for dimension
reduction to efficiently fit the statistical emulator, and present a series of
simulation experiments on an atypical Lorenz-96 system to demonstrate their
performance. We conclude with a discussion on how the Emu-PF can be paired with
modern particle filtering algorithms.
