Mathematical model of instrumental vibration error of angular velocity sensor

The problem of mathematical description of the influence of harmful deterministic and broadband random vibrations of a moving object on the measurement result of the sensor of the angular velocity of rotation of this object installed on it is considered. It is shown that under such conditions a systematic instrumental vibration error arises in the angular velocity sensor. The source of this error is the nonlinearity of the static conversion function of the angular velocity sensor and the asymmetry of its conversion coefficient. 
A mathematical model of this error has been obtained. Formulas for calculating the vibrational error of the angular velocity sensor are obtained depending on the apparent angular velocity of the flight of the aircraft, the vibration parameters of the base on which the sensor is installed and the parameters of the nonlinear sensor conversion function. 
This model makes it possible to calculate the value of the vibration error under specified vibration conditions for a specific angular velocity sensor (direct analysis problem), as well as to select an angular velocity sensor based on the values ​​of its conversion function coefficients, based on ensuring the required accuracy of measuring the angular velocity of a moving object using this angular velocity sensor (inverse synthesis problem).