This paper describes how a constrained nonlinear least-squares optimization approach can be used to recover the configuration of the segments in an arbitrary mechanical system from motion capture data. By appending the difference between markers in the model and the measured marker trajectories to the set of kinematic constraint equations, a set of over-determinate nonlinear equations will be obtained. This set of equations is solved by means of optimization. We also propose an Unscented Kalman Filter approach to the problem of configuration recovery and show how the velocity equations for a mechanical system subject to holonomic constraints can be re-written to a nonlinear state-space model. The formalism allows us to encode knowledge about f.x. smoothness, or any other knowledge the user might have about the system, into the filter.
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