Constrained maximum likelihood positioning for UWB based human motion tracking

In this paper, the problem of human motion tracking with ultra-wideband radio nodes is addressed. We provide a general maximum likelihood formulation of the positioning problem based on range measurements which can handle synchronous and asynchronous agents. Geometrical constraints on the node topology, which are imposed by the human body, are also taken into account. For a Gaussian ranging error model and the specific problem of arm motion tracking, we derive the maximum likelihood estimation rule and calculate an analytical expression for the unconstrained and constrained Cramér-Rao Lower Bound. With these results, we study analytically and via computer simulations under what circumstances the geometrical constraints lead to performance gains. It is found that the largest benefits are obtained in case of asynchronous agents and for certain arm positions. Intuitive reasons for this phenomenon are given. Finally, we verify these findings and evaluate the position location performance experimentally with range estimates obtained from measured ultra-wideband channel impulse responses including the impact of the human body.