Performance of speech recognition systems strongly degrades in the presence of background noise, like the driving noise inside a car. In contrast to existing works, we aim to improve noise robustness focusing on all major levels of speech recognition: feature extraction, feature enhancement, speech modelling, and training. Thereby, we give an overview of promising auditory modelling concepts, speech enhancement techniques, training strategies, and model architecture, which are implemented in an in-car digit and spelling recognition task considering noises produced by various car types and driving conditions. We prove that joint speech and noise modelling with a Switching Linear Dynamic Model (SLDM) outperforms speech enhancement techniques like Histogram Equalisation (HEQ) with a mean relative error reduction of 52.7% over various noise types and levels. Embedding a Switching Linear Dynamical System (SLDS) into a Switching Autoregressive Hidden Markov Model (SAR-HMM) prevails for speech disturbed by additive white Gaussian noise.