  The exquisite precision of atom interferometers has sparked the interest of a
large community for use cases ranging from fundamental physics to geodesy and
inertial navigation. However, their practical use for onboard applications is
still limited, not least because rotation and acceleration are intertwined in a
single phase shift in free-fall atom interferometers, which makes the
extraction of a useful signal more challenging. Moreover, the spatial
separation of the wave packets due to rotations leads to a loss of signal. Here
we present an atom interferometer operating over a large range of random
angles, rotation rates and accelerations. An accurate model of the expected
phase shift allows us to untangle the rotation and acceleration signals. We
also implement a real-time compensation system using two fibre-optic gyroscopes
and a tip-tilt platform to rotate the reference mirror and maintain the full
contrast of the atom interferometer. Using these theoretical and practical
tools, we reconstruct the fringes and demonstrate a single-shot sensitivity to
acceleration of 24 $\mu$g, for a total interrogation time of 2T = 20 ms, for
angles and rotation rates reaching 30$^\circ$ and 14 $^\circ$/s respectively.
Our hybrid rotating atom interferometer unlocks the full potential of quantum
inertial sensors for onboard applications, such as autonomous navigation or
gravity mapping.
