Considering MEMS used for inertial navigation, we distinguish vibrating beam accelerometers (VBA) and Coriolis effect based gyroscopes (Coriolis Vibrating Gyroscopes, CVG). ONERA has developed a piezoelectric micro-gyroscope : the VIG (Vibrating Integrated Gyro). Multiple and coupled physics interact inside this device which require to point at the various phenomena limiting the overall system performances. This PhD thesis introduces a system model, based on experimental measurements (mechanical structure and electronics architectures), focusing on performances improvements such as resolution, scale factor and especially bias stability. The first step consists of building a VIG vibrating structure detailed model, where finer aspects were progressively integrated. These aspects include piezoelectricity and structure couplings (capacitive and mechanical). Secondly, the sensor electronics model insists on charge amplifiers and quadrature error on the gyro output. Eventually, we realised a performances analysis, model-based, revealing the thermal bias stability problem, and giving a technical improvement by a factor of five on the bias stability (active compensation).