Recursive constrained state estimation using modified extended Kalman filter

Abstract

The extended Kalman filter (EKF) remains the most preferred state estimator for solving both unconstrained and constrained state estimation problems in the field of Chemical Engineering. Given, the wide spread use of EKF, we have proposed a novel optimization free recursive formulation of the EKF, to handle elegantly bounds on the estimated state variables of a stochastic non-linear dynamic system. It is well known that in the EKF, the prior and posterior distributions are approximated to be a multivariate normal distribution. In the presence of bounds imposed on the state variables, the accuracy of the first two moments of the initial state distribution and prior distribution namely the means and covariance matrices, plays a significant role in the extended Kalman filter performance. Hence, in this paper, we propose two novel schemes to modify the prior and posterior distributions of the EKF in order to satisfy the bound constraints. In addition, the initial state distribution is also suitably modified in order to satisfy the bound constraints. The efficacy of the proposed state estimation schemes using the EKF is validated on two benchmark problems reported in the literature namely a simulated gas-phase reactor and an isothermal batch reactor involving constraints on estimated state variables. Extensive simulation studies show the effectiveness of the proposed optimization free recursive constrained state estimation schemes using extended Kalman filter.