Spectral Analysis of Vibratory Gyro Noise

This paper presents analysis of the noise spectra of closed-loop mode-matched vibratory gyros. Closed-form expressions for the noise-equivalent angular rate spectrum as well as the integrated angular rate (angle) variance are derived to explore the effects of modal frequency mismatch, closed-loop bandwidth, and the spectra of noise sources appearing at the sensor´s input and output. It is shown that noise sources located at the output of the sensor´s electromechanical transfer function create angle white noise in the closed-loop sensor. The angle white noise dominates the integrated rate behavior until it crosses the angle random walk asymptote at integration times exceeding the sensor´s open-loop time constant. Even though the closed-loop sensor asymptotically recovers the angle random walk figure associated with the mode-matched open-loop sensor, the results can be used to quantify the larger integrated rate variance that is produced as a consequence of extending the sensor´s bandwidth through feedback. A parameter, called the effective bandwidth, is introduced to capture the relative importance of the input noise versus output noise in determining the noise-equivalent rate spectrum. It is shown that the rate noise spectrum is robust to frequency mismatch as long as it does not exceed the effective bandwidth parameter. Empirical data obtained with a high performance MEMS vibratory gyro shows excellent agreement with the model predictions for a variety of sensor configurations including frequency-matched, frequency-mismatched, modified bandwidth, and manipulated input noise intensity cases.