Discrete Kalman Filter Design for Kuramoto-Sivashinsky Equation

Kuramoto-Sivashinsky partial differential equation (KSE) has attracted a lot of attention from academia and industry due to its ability to describe various physical phenomena associated with both wave and propagation wave front dynamics. This work addresses infinite-dimensional discrete-time Kalman filter design for KSE by applying a state-of-the-art Crank-Nicolson discretization framework which does not account for spatial approximation or order reduction of the underlying model. A novel infinite-dimensional discrete-time Crank-Nicolson discretization is provided and utilized for KSE discretization in time, which is amenable to the ensuing discrete Kalman filter design. In addition, a two-step infinite-dimensional discrete-time Kalman filter is developed for the state estimation of KSE model augmented with the state and measurement noises. Finally, the effectiveness of the presented discrete-time Kalman filter is investigated and validated by simulations.