A Knowledge-Aided Robust Ensemble Kalman Filter Algorithm for Non-Linear and Non-Gaussian Large Systems

This work proposes a robust and non-Gaussian version of the shrinkage-based knowledge-aided EnKF implementation called Ensemble Time Local H_∞ Filter Knowledge-Aided (EnTLHF-KA). The EnTLHF-KA requires a target covariance matrix to integrate previously obtained information and knowledge directly into the data assimilation (DA). The proposed method is based on the robust H_∞ filter and on its ensemble time-local version the EnTLHF, using an adaptive inflation factor depending on the shrinkage covariance estimated matrix. This implies a theoretical and solid background to construct robust filters from the well-known covariance inflation technique. The proposed technique is implemented in a synthetic assimilation experiment, and in an air quality application using the LOTOS-EUROS model over the Aburrá Valley to evaluate its potential for non-linear and non-Gaussian large systems. In the spatial distribution of the PM_2.5 concentrations along the valley, the method outperforms the well-known Local Ensemble Transform Kalman Filter (LETKF), and the non-robust knowledge-aided Ensemble Kalman filter (EnKF-KA). In contrast to the other simulations, the ability to issue warnings for high concentration events is also increased. Finally, the simulation using EnTLHF-KA has lower error values than using EnKF-KA, indicating the advantages of robust approaches in high uncertainty systems.