Modeling bias in ensemble-based state estimators for aerodynamic flows

Ensemble-based estimators have been shown to be an efficient way of estimating the state of the high-dimensional systems that arise from the discretization of fluid flows. Since the computational cost of these models has a significant impact in the runtime, dealing with modeling errors is a practical inevitability. When these errors have non-zero mean and are left unaccounted for, the introduced bias can severely impair the estimator performance. In this work, we propose a low-rank representation for the modeling error and use colored-noise processes to represent the dynamics of the slow-varying portion of bias. The Ensemble Kalman Filter is then employed to simultaneously correct both the state and bias parameters. The methodology is demonstrated using the twin-experiment strategy: the state of a fine-grid 2D low-Re flow simulation past an inclined flat plate is estimated using an ensemble of coarse-mesh simulations and pressure measurements taken on the surface of the plate. This scheme is shown to improve the estimator accuracy by 70% when compared to a bias-blind strategy.