Continuous-discrete filtering techniques for estimating states of nonlinear differential-algebraic equations (DAEs) systems

This article presents a generalized state estimation framework for continuous-discrete nonlinear stochastic differential-algebraic equations systems. A key feature of this framework is that density of only differential states is independently propagated and updated during time propagation and measurement update steps. The density of algebraic states can be computed using their deterministic relationship with the differential states. For the case when densities can be assumed to be Gaussian, two filtering approaches, consistent with this framework, are proposed. The first one is a local linearization-based continuous-discrete extended Kalman filtering (CD-EKF) approach, while the second is deterministic sampling-based continuous-discrete cubature Kalman filtering approach derived using third-degree cubature rule. The proposed algorithms are continuous-discrete in nature, which involve time propagation in continuous time using numerical integration methods and the measurement update at discrete time instants. In these approaches, the effect of process noise is continuously incorporated during the time propagation step. The approaches are applied for estimating states of two benchmark case studies and results compared with other approaches. The results demonstrate that the proposed CD-EKF approach gives equivalent estimation performance as the sampling-based approaches while requiring lower computational time.