The knowledge about skeletal kinematics is essential in many biomechanical and medical applications. However, an accurate, non-invasive and radiation-free method for bone motion tracking is still an open issue. This thesis addresses the development of a novel method for bone pose estimation that is both, non-invasive and accurate. The main principal is to palpate three prominent bone protuberances using pressure sensor planes attached to the skin. Bone protuberances are approximated by three ellipsoids that are rigidly attached together.

At first, the geometrical problem of the planar case is analyzed, where ellipsoids become ellipses and sensor planes become lines. After deriving the constraint equations describing the mathematical model of the system, Gröbner bases are used to find the number of possible solutions for two different numerically defined configurations of the lines and the ellipses.
As a result, a maximum number of 32 different real solutions for the symmetrical and a maximum number of 64 different complex and real solutions for the general case are obtained. However, using the example of the symmetric case, it can be shown that the solution variety can be significantly reduced. From the 32 real solutions only three solutions are physically plausible, taking into account that pressure points are generated by an ellipse arc facing the lines.

This work also presents the general formulation of the constraint equations for the three dimensional case. As a solution approach, an optimization cost function is proposed including the squared minimal distances between sensors and ellipsoids allowing bone pose tracking that is insensitive toward input errors. Furthermore, a dual fluoroscopy validation of the method for three basic movements of the shank: flexion/extension, abduction/adduction and internal rotation is presented.
It is shown that by pressure sensor palpation, bone tracking precisions of 0.5 mm to 1.0 mm and 0.3° to 0.6° can be attained with respect to dual fluoroscopy manual registration, thus, reaching the same order of magnitude as state of the art model based tracking techniques.

Finally, this thesis regards the limiting case where ellipsoids become points allowing the introduction of an automatable procedure approximating the rigid body bone geometry based on data from a previously performed bone pose measurement.
Thereby, it is possible to fully circumvent radiation exposure that might be necessary to extract ellipsoid parameters from e. g. a computed tomography scan. Results indicate that deviations to the ellipsoid-approximated bone model are in the submillimeter range and may thus be negligible for many applications.