In the present paper, a theory-based advancement of the car following model of Wiedemann is introduced. It is suitable for a more realistic simulation of human longitudinal guidance behaviour in the lower velocity range, like in urban traffic. The algorithm was identified and developed by means of a driving simulator study, which is introduced as well. While the decision making process in recent car following models based on Wiedemann is solely determined by the time headway to the leading vehicle, the results of the study show that information about time to collision is also used in the lower velocity range. This approach delivers a more realistic simulation of human car following behaviour, which can be integrated into driver models for microscopic traffic simulations and for the control of surrounding traffic in driving simulators.