Although the simple diffusion model can effectively describe the movement of eukaryotic cells on a culture surface observed at relatively low sampling frequency, at higher sampling rates more complex models are often necessary to better fit the experimental data. Currently available models can describe motion paths by involving additional parameters, such as linearity or directional persistence in time. However sometimes difficulties arise as it is not easy to effectively evaluate persistence in presence of a directional bias. Here we present a procedure which helps solve this problem, based on a model which describes displacement as the vectorial sum of three components: diffusion, persistence and directional bias. The described model has been tested by analysing the migratory behaviour of simulated cell populations and used to analyse a collection of experimental datasets, obtained by observing cell cultures in time lapse microscopy. Overall, the method produces a good description of migration behaviour as it appears to capture the expected increase in the directional bias in presence of wound without a large concomitant increase in the persistence module, allowing it to remain as a physically meaningful quantity in the presence of a directional stimulus.