  Accurate and ubiquitous localization is crucial for a variety of applications
such as logistics, navigation, intelligent transport, monitoring, control, and
also for the benefit of communications. Exploiting millimeter-wave (mmWave)
signals in 5G and Beyond 5G systems can provide accurate localization with
limited infrastructure. We consider the single base station (BS) localization
problem and extend it to 3D position and 3D orientation estimation of an
unsynchronized multi-antenna user equipment (UE), using downlink multiple-input
multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) signals.
Through a Fisher information analysis, we show that the problem is often
identifiable, provided that there is at least one multipath component in
addition to the line-of-sight (LoS), even if the position of corresponding
incidence point (IP) is a priori unknown. Subsequently, we pose a maximum
likelihood (ML) estimation problem, to jointly estimate the 3D position and 3D
orientation of the UE as well as several nuisance parameters (the UE clock
offset and the positions of IPs corresponding to the multipath). The ML problem
is a high-dimensional non-convex optimization problem over a product of
Euclidean and non-Euclidean manifolds. To avoid complex exhaustive search
procedures, we propose a geometric initial estimate of all parameters, which
reduces the problem to a 1-dimensional search over a finite interval. Numerical
results show the efficiency of the proposed ad-hoc estimation, whose gap to the
Cram\'er-Rao bound (CRB) is tightened using the ML estimation.
