Particle filter data assimilation for ubiquitous unstable trajectories of two-dimensional three-state cellular automata

Estimating the states of error-growing (sensitive to initial state) cellular automata (CA) based on noisy imperfect data is challenging due to the discreteness of the dynamical system. This paper proposes particle filter (PF)–based data assimilation (DA) for three-state error-growing CA and demonstrates that the PF-based DA can predict the present and future state even with noisy and sparse observations. The error-growing CA used in the present study comprised a competitive system of land, grass, and sheep. To the best of the authors’ knowledge, this is the first application of DA to such CA. The performance of DA for different observation sets was evaluated in terms of observational error, density, and frequency, and a series of sensitivity tests of the internal parameters in the DA was conducted. The inflation and localization parameters were tuned according to the sensitivity tests.