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.