We consider the problem of robust automatic speech recognition (ASR) in noisy conditions. The performance improvement brought by speech enhancement is often limited by residual distortions of the enhanced features, which can be seen as a form of statistical uncertainty. Uncertainty estimation and propagation methods have recently been proposed to improve the ASR performance with deep neural network (DNN) acoustic models. However, the performance is still limited due to the use of uncertainty only during decoding. In this paper, we propose a consistent approach to account for uncertainty in the enhanced features during both training and decoding. We estimate the variance of the distortions using a DNN uncertainty estimator that operates directly in the feature maximum likelihood linear regression (fMLLR) domain and we then sample the uncertain features using the unscented transform (UT). We report the resulting ASR performance on the CHiME-2 and CHiME-3 datasets for different uncertainty estimation/propagation techniques. The proposed DNN uncertainty training method brings 4% and 8% relative improvement on these two datasets, respectively, compared to a competitive fMLLR-domain DNN acoustic modeling baseline.