Quadrature-Induced Noise in Coriolis Vibratory Gyroscopes

In this paper, we present a model for noise performance estimation of Coriolis Vibratory Gyroscopes (CVG) in the presence of quadrature coupling. Analytical equations based on a low-order averaged model of a CVG were derived and used for numerical simulation of the Zero-Rate Output (ZRO) in the open-loop angular rate mode of operation. We demonstrated that as a result of the quadrature coupling and noise in the drive oscillation frequency, Quadrature Noise (QN) is introduced to the gyroscope output. For example, in the case of a Dual Foucault Pendulum (DFP) gyroscope with a frequency split on the order of 0.48 Hz, the QN was shown to have an experimentally measured Angle Random Walk (ARW) on the order of 0.39 $\left( {deg/\sqrt {hr} } \right)$, which was orders of magnitude higher than a theoretical ARW of 0.0024 $\left( {deg/\sqrt {hr} } \right)$ predicted by the Mechanical-Thermal Noise (MTN) model. This observed discrepancy was a motivation for the development of the model. A good agreement between the noise characteristics of the experimentally measured ZRO and a numerically simulated ZRO was observed, when accounting for the quadrature coupling. We concluded that the quadrature- induced noise is a major factor limiting the performance of high quality factor gyroscopes in nearly mode-matched conditions. This paper presents an analytical model for the noise estimation, which was supported experimentally.