Multi-dimensional feedback particle filter for coupled oscillators

This paper presents a methodology for state estimation of coupled oscillators from noisy observations. The methodology is comprised of two parts: modeling and estimation. The objective of the modeling is to express dynamics in terms of the so-called phase variables. For nonlinear estimation, a coupled-oscillator feedback particle filter is introduced. The filter is based on the construction of a large population of oscillators with mean-field coupling. The empirical distribution of the population encodes the posterior distribution of the phase variables. The methodology is illustrated with two numerical examples.