State Estimation for Non-linear Fully-implicit, Index-1 Differential Algebraic Equation Systems

TLDR: A linear transformation of the mass matrix is proposed which enables us to find candidate algebraic states for the fully–implicit index-1 DAE system and is relatively simpler than constructing the transformation matrices in the Weierstrass–Kronecker canonical form.

Abstract: The Kalman filter and its variants have been developed for state estimation in semi-explicit, index-1 DAE systems in current literature. In this work, we develop a method for state estimation in non-linear fully-implicit, index-1 differential algebraic equation (DAEs) systems. In order to extend the Kalman filtering techniques for fully-implicit index-1 DAE systems, in the correction step we convert the fully-implicit DAE into a system of ordinary differential equations (ODEs). This is achieved by the index reduction of DAE using the method of successive differentiation of algebraic equations. This is a challenging problem as the fully-implicit DAE system does not contain explicit algebraic states unlike in the semi-explicit case. In this work, we propose a linear transformation of the mass matrix which enables us to find candidate algebraic states for the system. This transformation on the mass matrix is relatively simpler than constructing the transformation matrices in the Weierstrass-Kronecker canonical form. We illustrate our proposed method with two examples, a linear and a non-linear fully-implicit index-1 DAE system.