  We report the operation of a cold-atom inertial sensor in a joint
interrogation scheme, where we simultaneously prepare a cold-atom source and
operate an atom interferometer in order to eliminate dead times. Noise aliasing
and dead times are consequences of the sequential operation which is intrinsic
to cold-atom atom interferometers. Both phenomena have deleterious effects on
the performance of these sensors. We show that our continuous operation
improves the short-term sensitivity of atom interferometers, by demonstrating a
record rotation sensitivity of $100$ nrad.s$^{-1}/\sqrt{\rm Hz}$ in a cold-atom
gyroscope of $11$ cm$^2$ Sagnac area. We also demonstrate a rotation stability
of $1$ nrad.s$^{-1}$ after $10^4$ s of integration, improving previous results
by an order of magnitude. We expect that the continuous operation will allow
cold-atom inertial sensors with long interrogation time to reach their full
sensitivity, determined by the quantum noise limit.
