The Gaussian Mixture Optimal Transport Ensemble Kalman Filter and its application to predict the capacity fade of lithium-ion batteries

In this paper, we propose a novel algorithm, the Gaussian Mixture Optimal Transport Ensemble Kalman Filter (GM-OT-EnKF), which combines the Gaussian mixture (GM) with the optimal transport Ensemble Kalman filter (OT-EnKF). We utilize an ensemble of state realizations to demonstrate state propagation, followed by clustering the ensemble to recover the GM of the propagated uncertainty. The posterior density is updated using the OT-EnKF, recognized for its optimality among quadratic functions minimizing the Monge-Kantorovich dual problem in optimal transport. The accuracy of the GMOT-EnKF is validated through its application in estimating and predicting capacity fade in lithium-ion batteries. It outperforms the EnKF, OT-EnKF, and the particle Gaussian mixture filter.