  In this work, we consider a differential description of the evolution of the
state of a reaction-diffusion system under environmental fluctuations. We are
interested in estimating the state of the system when only partial observations
are available. To describe how observations and states are related, we combine
multiplicative noise-driven dynamics with an observation model. More
specifically, we ensure that the observations are subjected to error in the
form of additive noise. We focus on the state estimation of a
Belousov-Zhabotinskii chemical reaction. We simulate a reaction conducted in a
quasi-two-dimensional physical domain, such as on the surface of a Petri dish.
We aim at reconstructing the emerging chemical patterns based on noisy spectral
observations. For this task, we consider a finite difference representation on
the spatial domain, where nodes are chosen according to observation sites. We
approximate the solution to this state estimation problem with the Block
particle filter, a sequential Monte Carlo method capable of addressing the
associated high-dimensionality of this state-space representation.
