There has been much effort invested in increasing the robustness of human body tracking by incorporating motion models. Most approaches are probabilistic in nature and seek to avoid becoming trapped into local minima by considering multiple hypotheses, which typically requires exponentially large amounts of computation as the number of degrees of freedom increases. By contrast, in this paper, we use temporal motion models based on Principal Component Analysis to formulate the tracking problem as one of minimizing differentiable objective functions. The differential structure of these functions is rich enough to yield good convergence properties using a deterministic optimization scheme at a much reduced computational cost. Furthermore, by using a multi-activity database, we can partially overcome one of the major limitations of approaches that rely on motion models, namely the fact they are limited to one single type of motion. We will demonstrate the effectiveness of the proposed approach by using it to fit full-body models to stereo data of people walking and running and whose quality is too low to yield satisfactory results without motion models.