Modified Extended Kalman Filtering for Nonlinear Stochastic Differential Algebraic Systems

The extended Kalman filter (EKF) is one of the most widely used nonlinear filtering technique for a system of differential algebraic equations (DAEs). In this work we propose an alternate EKF approach for state estimation of nonlinear DAE systems that addresses shortcomings of the EKF approaches available in literature (Becerra et al., 2001; Mandela et al., 2010). The proposed approach is based on the idea that since the algebraic equations are assumed to be exact, the error covariance matrix of only the differential states needs to be directly propagated during the prediction step. The error covariance matrix for algebraic states and cross covariance matrix between the errors in differential and algebraic states, which are required to incorporate effect of prior algebraic state estimates on the update step, can be computed from the differential state error covariance matrix alone using the linearized algebraic equations. The update step of the proposed work also follows a similar philosophy and ensures that the covariance update is not approximate. The efficacy of the proposed EKF approach is evaluated using benchmark case studies of a Galvanostatic charge process and a drum boiler. Copyright (C) 2020 The Authors.