Constrained Extended Kalman Filter based on Kullback-Leibler (KL) Divergence*

Extended Kalman Filter (EKF) is one of the most extensively used state estimator for nonlinear systems. As this technique cannot handle constraints, it might result in physically meaningless state estimates. Therefore, in this work, we focus on imposing inequality constraints in the state estimation problem to obtain physically meaningful state estimates as well as improve the estimation accuracy. For this purpose, we project the unconstrained EKF solution into the constrained region by minimizing the Kullback-Leibler (KL) divergence. The proposed constrained EKF framework updates the values of the states and error covariances by solving the convex optimization problem involving conic constraints. The efficacies of the proposed algorithm are demonstrated in a batch reaction system, and the performance of the proposed approach is found to outperform the recursive nonlinear dynamic data reconciliation solution.