State estimation approach to nonstationary inverse problems: discretization error and filtering problem

We examine a certain class of nonstationary inverse problems. We view them as a state estimation problem. The time evolution of the state of the system is modeled by a stochastic differential equation. The observation equation is linear with additive measurement noise. We introduce the time discrete infinite dimensional state estimation system concerning the problem. For computational reasons the space discretization is performed. The discretization errors in the discretized state evolution and observation equations are analysed stochastically. The solution to the corresponding finite dimensional filtering problem is presented.