  Sequential Monte Carlo (SMC) methods comprise one of the most successful
approaches to approximate Bayesian filtering. However, SMC without good
proposal distributions struggle in high dimensions. We propose nested
sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework
by requiring only approximate, properly weighted, samples from the SMC proposal
distribution, while still resulting in a correct SMC algorithm. This way we can
exactly approximate the locally optimal proposal, and extend the class of
models for which we can perform efficient inference using SMC. We show improved
accuracy over other state-of-the-art methods on several spatio-temporal state
space models.
