Continuous Discrete Unscented Kalman Filtering for Nonlinear Differential Algebraic Equations Systems

Abstract

In this paper, we propose a filtering approach for state estimation of nonlinear continuous-discrete differential algebraic equations (DAE) systems. In such systems, while the process dynamics is a set of continuous time differential algebraic equations, the measurements are discrete time. We propose continuous-discrete unscented Kalman filter (UKF) for estimating states for such systems. The proposed approach is an extension of the work of Särkkä (2007) , which considered nonlinear continuous-discrete ordinary differential equations (ODE) systems. The key idea in approach is that the mean and covariance of the differential states are integrated directly using continuous time differential equations. This is in contrast to the prevalent discrete time approach in literature, which involves propagating individual sigma points through noise free model and then computing the mean and covariance of the states. In our proposed approach, the algebraic states are computed from differential states by solving the algebraic equations separately. This idea of handling algebraic states is borrowed from Mandela et al. (2010) . We demonstrate the applicability of the proposed continuous-discrete UKF approach by applying it for state estimation of a well known simulation case study.