Adaptive training is a widely used technique for building speech recognition systems on non-homogeneous training data. Recently there has been interest in applying these approaches for situations where there is significant levels of background noise. This work extends the most popular form of linear transform for adaptive training, constrained MLLR, to reflect additional uncertainty from noise corrupted observations. This new form of transform, Noisy CMLLR, uses a modified version of generative model between clean speech and noisy observation, similar to factor analysis. Adaptive training using NCMLLR with both maximum likelihood and discriminative criteria are described. Experiments are conducted on noise-corrupted Resource Management and in-car recorded data. In preliminary experiments this new form achieves improvements in recognition performance over the standard approach in low signal-to-noise ratio conditions.