Observation quality control using a robust ensemble time-localized H-infinity filter with measurements corrupted by strong outliers

Abstract Accurate state estimation in complex dynamical systems is crucial for understanding and predicting nonlinear physical processes. However, conventional ensemble-based Kalman filtering methods, which rely on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="script">L</mml:mi> </mml:math> 2-norm updates, are highly sensitive to outliers and gross observational errors, resulting in degraded performance in chaotic regimes. To address this challenge, we develop the EnTLHF-R, an enhanced Ensemble Time-localized H-infinity Filter that integrates observation error estimation, dynamic quality control, and the Huber loss function. By combining the efficiency of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="script">L</mml:mi> </mml:math> 2 updates with the robustness of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="script">L</mml:mi> </mml:math> 1, the proposed framework effectively suppresses the impact of additive and innovation outliers while preserving sensitivity to reliable observations. Simulation experiments using the Lorenz-96 model demonstrate that EnTLHF-R achieves markedly improved stability and accuracy in high-dimensional chaotic systems. These results highlight the method’s potential for advancing robust data assimilation in nonlinear physical systems and improving predictability under adverse observational conditions.