  We consider the problem of estimating the 3D orientation of a user, using the
downlink mmWave signals received from multiple base stations. We show that the
received signals from several base stations, having known positions, can be
used to estimate the unknown orientation of the user. We formulate the
estimation problem as a maximum likelihood estimation problem in the the
manifold of rotation matrices. In order to provide an initial estimate to solve
the non-linear non-convex optimization problem, we resort to a least squares
estimation problem that exploits the underlying geometry. Our numerical results
show that the problem of orientation estimation can be solved when the signals
from at least two base stations are received. We also provide the orientation
lower error bound, showing a narrow gap between the performance of the proposed
estimators and the bound.
