  The combination of ultrawideband (UWB) radios and inertial measurement units
(IMU) can provide accurate positioning in environments where the Global
Positioning System (GPS) service is either unavailable or has unsatisfactory
performance. The two sensors, IMU and UWB radio, are often not co-located on a
moving system. The UWB radio is typically located at the extremities of the
system to ensure reliable communication, whereas the IMUs are located closer to
its center of gravity. Furthermore, without hardware or software
synchronization, data from heterogeneous sensors can arrive at different time
instants resulting in temporal offsets. If uncalibrated, these spatial and
temporal offsets can degrade the positioning performance. In this paper, using
observability and identifiability criteria, we derive the conditions required
for successfully calibrating the spatial and the temporal offset parameters of
a tightly-coupled UWB-IMU system. We also present an online method for jointly
calibrating these offsets. The results show that our calibration approach
results in improved positioning accuracy while simultaneously estimating (i)
the spatial offset parameters to millimeter precision and (ii) the temporal
offset parameter to millisecond precision.
