The reconstruction of a vehicle collision consists of the processes of investigation, analysis and conclusions about the causes and the events during the traffic accident. In this perspective, a vehicle collision is considered in three distinct phases, the pre-collision, the collision and the post-collision phase. For the analysis of the collision phase two main approaches exist in the literature, the energy based and the momentum based one. The latter has been described in details by Brach et al. and can find a solution to a given set of parameters to reconstruct a collision. These parameters can be known or assumed using monitoring systems of the vehicle or physical evidence. In the present paper a computational model implementing the Planar Impact Mechanics (PIM) collision model has been set up in Matlab ® and its coupling with the least squares method has been investigated. As test cases, the RICSAC database, which consists of twelve staged collisions, has been used. Special attention has been given in the number of parameters which have been considered known (or assumed). The results indicate the importance of each parameter.