  Real-time motion tracking of kinematic chains is a key prerequisite in the
control of, e.g., robotic actuators and autonomous vehicles and also has
numerous biomechanical applications. In recent years, it has been shown that,
by placing inertial sensors on segments that are connected by rotational
joints, the motion of that kinematic chain can be tracked accurately. These
methods specifically avoid using magnetometer measurements, which are known to
be unreliable since the magnetic field at the different sensor locations is
typically different. They rely on the assumption that the motion of the
kinematic chain is sufficiently rich to assure observability of the relative
pose. However, a formal investigation of this crucial requirement has not yet
been presented, and no specific conditions for observability have so far been
given. In this work, we present an observability analysis and show that the
relative pose of the body segments is indeed observable under a very mild
condition on the motion. We support our results by simulation studies, in which
we employ a state estimator that neither uses magnetometer measurements nor
additional sensors and does not impose assumptions on the accelerometer to
measure only the direction of gravity, nor on the range of motion or degrees of
freedom of the joints. We investigate the effect of the amount of excitation
and of stationary periods in the data on the accuracy of the estimates. We then
use experimental data from two mechanical joints as well as from a human gait
experiment to validate the observability criterion in practice and to show that
small excitation levels are sufficient for obtaining accurate estimates even in
the presence of time periods during which the motion is not observable.
