In earlier work we studied the effect of statistical normalisation for phase-based features and observed it leads to a significant robustness improvement. This paper explores the extension of the generalised Vector Taylor Series (gVTS) noise compensation approach to the group delay (GD) domain. We discuss the problems it presents, propose some solutions and derive the corresponding formulae. Furthermore, the effects of additive and channel noise in the GD domain were studied. It was observed that the GD of the noisy observation is a convex combination of the GDs of the clean signal and the additive noise and also in the expected sense, channel GD tends to zero. Experiments on Aurora-4 showed that, despite training only on the clean speech, the proposed features provide average WER reductions of 0.8% absolute and 4.1% relative compared to an MFCC-based system trained on the multi-style data. Combining the gVTS with a bottleneck DNN-based system led to average absolute (relative) WER improvements of 6.0% (23.5%) when training on clean data and 2.5% (13.8%) when using multi-style training with additive noise.