Nonlinear state estimation of differential algebraic systems

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. Moving Horizon Estimation (MHE) has been a popular approach in chemical engineering community for the estimation of both ODE and differential algebraic equation (DAE) systems but is computationally demanding. There has been some work on applying Extended Kalman filter for state estimation of DAE systems with measurements as functions of only the differential states. This work describes the estimation of nonlinear DAE systems with measurements being a function of both the differential and algebraic states. An Unscented Kalman filter (UKF) formulation is also derived for semi-explicit index 1 DAE systems. The utility of these formulations are demonstrated through a case study.