Unscented Kalman Filter for Higher Index Nonlinear Differential-Algebraic Equations

This contribution concerns the unscented Kalman filter (UKF) for higher index nonlinear differential-algebraic equation (DAE) systems. First, a short introduction to DAE systems is given. A solution concept for nonlinear DAE systems is discussed focusing on properties which are essential for the application of the UKF algorithm. The introduction of a stochastic noise in DAE systems and the contrast to stochastic ordinary differential equations (ODE) are described subsequently. Further, the unscented Kalman filter algorithm is reviewed and former filtering approaches considering DAE systems are summarized. Finally, a direct generalized state estimation approach for higher index nonlinear DAE systems utilizing the UKF is proposed. Particularly, the estimation of the DAE inconsistent generalized state is permitted and several concepts for the consistent DAE initialization in the prediction step of the filtering algorithm are proposed. A simple example demonstrates the advantages of the proposed approach.