  The lateral position of vehicles within their lane is a decisive factor for
the range of vision of vehicle sensors. This, in turn, is crucial for a
vehicle's ability to perceive its environment and gain a high situational
awareness by processing the collected information. When aiming for increasing
levels of vehicle autonomy, this situational awareness becomes more and more
important. Thus, when validating an autonomous driving function the
representativeness of the submicroscopic behavior such as the lateral offset
has to be ensured. With simulations being an essential part of the validation
of autonomous driving functions, models describing these phenomena are
required. Possible applications are the enhancement of microscopic traffic
simulations and the maneuver-based approach for scenario-based testing. This
paper presents a two-level stochastic approach to model the lateral movement of
vehicles within their lane during road-following maneuvers under homogeneous
traffic conditions. A Markov model generates the coarse lateral offset profile.
It is superposed with a noise model for the fine movements. Both models are set
up using real-world data. The evaluation of the model shows promising
qualitative and quantitative results, the potential for enhancements and
extreme low computation times (10000 times faster than real time).
