  Mild Traumatic Brain Injuries (mTBI) are caused by violent head motions or
impacts. Most mTBI prevention strategies explicitly or implicitly rely on a
"brain injury criterion". A brain injury criterion takes some descriptor of the
head's motion as input and yields a prediction for that motion's potential for
causing mTBI as the output. The inputs are descriptors of the head's motion
that are usually synthesized from accelerometer and gyroscope data. In the
context of brain injury criterion the head is modeled as a rigid body. We
present an algorithm for determining the complete motion of the head using data
from only four head mounted tri-axial accelerometers. In contrast to inertial
measurement unit based algorithms for determining rigid body motion the
presented algorithm does not depend on data from gyroscopes; which consume much
more power than accelerometers. Several algorithms that also make use of data
from only accelerometers already exist. However, those algorithms, except for
the recently presented AO-algorithm [Rahaman MM, Fang W, Fawzi AL, Wan Y,
Kesari H (2020): J Mech Phys Solids 104014], give the rigid body's acceleration
field in terms of the body frame, which in general is unknown. Compared to the
AO-algorithm the presented algorithm is much more insensitive to bias type
errors, such as those that arise from inaccurate measurement of sensor
positions and orientations.
