  Accurate measurement of inertial quantities is essential in geophysics,
geodesy, fundamental physics and navigation. For instance, inertial navigation
systems require stable inertial sensors to compute the position and attitude of
the carrier. Here, we present the first hybridized cold-atom inertial sensor
based on matter wave interferometry where the atomic measurements are used to
correct the drift and bias of both an accelerometer and a gyroscope at the same
time. We achieve respective bias stabilities of $7 \times 10^{-7}$ m/s$^2$ and
$4 \times 10^{-7}$ rad/s after two days of integration, corresponding to a
100-fold and 3-fold increase on the stability of the hybridized sensor compared
to the force-balanced accelerometer and Coriolis vibrating gyroscope operated
alone. The instrument has been operated under up to 100-times the Earth
rotation rate. Compared to state-of-the-art atomic gyroscope, the simplicity
and scalability of our architecture make it easily extendable to a compact full
six-axis inertial measurement unit, providing a pathway towards autonomous
positioning and orientation using cold-atom sensors.
