  Inertial measurement units are commonly used in a growing number of
application fields to track or capture motions of kinematic chains, such as
human limbs, exoskeletons or robotic actuators. A major challenge is the
presence of magnetic disturbances that result in unreliable magnetometer
readings. Recent research revealed that this problem can be overcome by
exploitation of kinematic constraints. While typically each segment of the
kinematic chain is equipped with an IMU, a novel approach called sparse
inertial motion tracking aims at infering the complete motion states from
measurements of a reduced set of sensors. In the present contribution, we
combine the magnetometer-free and the sparse approach for real-time motion
tracking of double-hinge joint systems with non-parallel joint axes. Analyzing
the observability of the system, we find a condition which assures that the
relative orientations between all segments are uniquely determined by a
kinematic constraint, which contains only the gyroscope readings. Furthermore,
we propose a moving-horizon estimator and validate it in a simulation study of
three movements with different degrees of excitation. The results of this study
confirm all theoretical conjectures and demonstrate that magnetometer-free
sparse inertial real-time motion tracking is feasible under precise and simple
excitation conditions.
