The Sagnac effect is at the heart of the modern precision inertial sensors. An interferometer with a physical area, when spun, exhibits a phase shift at its output. Measuring this phase-shift leads to a direct measurement of the rotation rate. The SYRTE dual-axis cold-atom gyroscope represents the state-of-art of atomic gyroscopes. With its large physical area (11cm2) and a long interrogation time of 800 ms, it offers both the sensitivity and stability 3 × 10^10 rad.s−1 to push the Sagnac measurement to an unprecedented accuracy level. Demonstrating such performance required the control and characterization of the experimental parameters and systematic effects and the precise knowledge of the scale factor. The cold-atom gyroscope experiment is based on atomic interferometry, where cooled Cesium-atoms (2μK) are launched vertically (∼ 5m/s) to be interrogated with a sequence of four Raman pulses (allowing an internal and external control over atomic states). The pulses play the role of atomic optics by splitting and guiding the matter-waves along the arms of the interferometer. By the end, transition probability measurement gives access to the phase-shift induced by rotation. I will present our recent work done to develop new methods that will improve the gyroscope sensitivity. The Double diffraction, atom diffraction in both ±¯h⃗keff directions, should enables a measurement setup with no dead time based on the use of two correlated interleaved interferometers. Thus, the vibration and rotation noises that limits the sensitivity should average to achieve the detection noise, targeting the standard quantum projection noise.