  Sensor-to-segment calibration is a crucial step in inertial motion tracking.
When two segments are connected by a hinge joint, for example in human knee and
finger joints as well as in many robotic limbs, then the joint axis vector must
be identified in the intrinsic sensor coordinate systems. There exist methods
that identify these coordinates by solving an optimization problem that is
based on kinematic joint constraints, which involve either the measured
accelerations or the measured angular rates. In the current paper we
demonstrate that using only one of these constraints leads to inaccurate
estimates at either fast or slow motions. We propose a novel method based on a
cost function that combines both constraints. The restrictive assumption of a
homogeneous magnetic field is avoided by using only accelerometer and gyroscope
readings. To combine the advantages of both sensor types, the residual weights
are adjusted automatically based on the estimated signal variances and a
nonlinear weighting of the acceleration norm difference. The method is
evaluated using real data from nine different motions of an upper limb
exoskeleton. Results show that, unlike previous approaches, the proposed method
yields accurate joint axis estimation after only five seconds for all fast and
slow motions.
