Weigh-in-motion (WIM) systems aim at dynamic weighing of the railway vehicles through a reasonable number of measurement stations placed along the track. Such systems may overcome disadvantages in terms of costs and traffic management typical of conventional static weighing systems. In the present work the authors present an innovative algorithm for high speed dynamical WIM applications aimed at the estimation of axle or wheel loads of a generic train composition by means of indirect track measurements. The formulation of the proposed algorithm is quite general and it can be customized for several track measurements (rail shear, rail bending, vertical forces on the sleepers etc.) as well as a combination of them; consequently it can be employed in different kinds of measurement stations. The vertical loads and the possible imbalances are estimated by supposing the system approximately linear with respect to the loads and by means of least square minimization techniques. A wide simulation campaign has been carried out to test the algorithm accuracy and robustness under any operating conditions, obtaining good results (estimation errors always below the 2 %). Future developments of the present work will include the algorithm validation by means of some dedicated experimental campaigns performed by Ansaldo STS and ECM SpA, the industrial partners of this research project.