Development of iterative extended Kalman filter for DAE System

Abstract Extended Kalman filtering (EKF) is widely used for estimating states of systems modelled as ordinary differential equations (ODEs). The performance of this approach may deteriorate if the initial estimate is poor i.e. far from true state. Iterative version of EKF developed by Wishner et al. (1969) for systems modelled as ODEs can alleviate this difficulty with negligible additional computational efforts as it involves smoothing of the prior estimate. There are many systems that involve different time scales and are described by Differential-Algebraic equations (DAEs). Extension of Bayesian state estimation approach such as EKF for handling nonlinear DAEs is relatively recent development (Beccera et al. (2001) and Mandela et al. (2010)). In this work, taking motivation from Wishner et al. (1969), an iterative EKF (IEKF) scheme is proposed for systems modelled as DAEs. The efficacy of the proposed DAE-IEKF is evaluated using simulation studies of Nickel-Hydrogen electrode system and divided wall distillation column system. Analysis of the simulation results reveals that the proposed approach results in a reasonable improvement in the estimation performance when compared with performance of the conventional DAE-EKF.