The work we present is a part of a telemedicine project which aims to prevent the falls in the elderly at home. This can be realized by proposing a technology and a methodology in order to detect balance disorders. The main objective of this work is to develop a passive autonomous gait analysis system at home. We expose the previously used approaches for gait quality evaluation and then we propose a new solution. The suggested method is based on a 3D marker less human motion capture system. Thus, the gait parameters can be estimated using the 3D positions of some key points of the body. The motion capture system we developed uses an articulated body model and a new particle filtering algorithm. This new algorithm, which we call Interval Particle Filtering, reorganizes the articulated model's configurations search space in an optimal deterministic way and proved to be efficient in tracking natural human movement. In order to reduce the temporal complexity of the algorithm and to have a more precise tracking, a new factorized version of the algorithm is also introduced. This version called Factored Interval Particle Filtering uses the Dynamic Bayesian Networks formalism. We show 3D reconstructions of movement using this algorithm and we compare it to other approaches too.