Constrained ensemble Kalman filter based on Kullback–Leibler divergence

Abstract

Conventional recursive state estimation procedures cannot handle inequality constraints; therefore, they might result in physically meaningless state estimates. In this work, we develop a novel state estimation technique to incorporate inequality constraints in ensemble Kalman filters (EnKF). For this purpose, we first solve for the unconstrained EnKF state estimation, and then construct a constrained distribution based on the unconstrained one by formulating an optimization problem using the Kullback–Leibler (KL) divergence. The proposed constraint implementation technique is cast as a convex optimization problem involving second order cone constraints which can be solved to global optimality. This constraint implementation step can be integrated into any Gaussian filter. Demonstrative case studies of chemical reaction systems are presented to compare and illustrate the efficacy of the proposed state estimation methodology.