CAR-EnKF: A Covariance-Adaptive and Recalibrated Ensemble Kalman Filter Framework

Abstract

The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conventional EnKF implementations can become overconfident in the presence of measurement nonlinearity. The commonly used covariance inflation technique only partially alleviates this issue. This paper proposes a covariance-adaptive and recalibrated ensemble Kalman filter (CAR-EnKF) framework for nonlinear state estimation. The framework introduces two improvements that are only active for nonlinear measurements and reduce to the conventional EnKF framework without covariance inflation in the linear case: (i) a recalibration mechanism that reassesses the effect of the chosen Kalman gain after updating the ensemble mean, and (ii) a positive semidefinite covariance compensation term that accounts for measurement nonlinearity. An adaptive update law based on the normalized innovation squared further tunes the compensation magnitude online. The framework is algorithmically general and is specialized here to the stochastic EnKF and the ensemble transform Kalman filter (ETKF). Experiments on feature-based SLAM and the Lorenz--96 system show that CAR-EnKF consistently reduces RMSE relative to conventional EnKF baselines, with especially large improvements at low measurement-noise levels. The related codes are available at \href{https://github.com/Shida-Jiang/CAR-EnKF-A-Covariance-Adaptive-and-Recalibrated-Ensemble-Kalman-Filter-Framework}