  In recent years, it has been shown that the motion of kinematic chains can be
estimated using measurements from inertial sensors placed on segments connected
by rotational joints. These methods specifically avoid using magnetometer
measurements, which are known to cause issues 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 / yield
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 these results
by a simulation study, in which we also show the effect of stationary periods
in the data and of the amount of excitation on the accuracy of the estimates.
We use experimental data from a human gait experiment to show that the
excitation level is sufficient for obtaining accurate estimates even when the
subject remains stationary for a period of 47 seconds halfway during the
experiment.
