To study human movement generation, as well as to develop efficient control algorithms for humanoid or dexterous manipulation robots, overcoming the limits and drawbacks of inverse kinematics based methods is needed. Adequate methods must deal with high dimensionality, uncertainty , and must perform in real-time (constraints shared by robots and humans). This paper introduces a Bayesian filtering method, hierarchically applied in the operational and joint spaces to break down the complexity of the problem. The method is validated in simulation on a robotic arm in a cluttered environment, with up to 51 degrees of freedom.