This work proposes a robust and non-gaussian version of the
shrinkage-based EnKF implementation, the EnKF-KA. The proposed method is
based in the robust H filter and in 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 method is tested using the Lorenz-96 model to
evaluate the robustness and performance under different scenarios as
ensemble size, observation error, errors in the model specifications,
and ensemble gaussianity. The results suggest good robustness of the
proposed method in all the evaluated cases compared with the standard
EnKF, the shrinkage-based EnKF-KA, and the robust EnTLHF.