Simultaneous Angular Rate Estimates Extracted From a Single Axisymmetric Resonator

An axisymmetric planar microelectromechanical (MEM) resonator resonator is configured, such that the
$n = 2$
elliptical pair of modes near 13.5kHz, and the
$n = 3$
pair of modes near 23.8kHz, are both degenerate, i.e., the frequency difference within a given pair of modes is close to the resonance bandwidth. This configuration enables not only the exploitation of the standard elliptical pair of modes for angular rate sensing but also permits the operation of the
$n = 3$
pair of modes as a high-sensitivity Coriolis vibratory gyro. The performance for each pair of modes separately acting as a vibratory gyro is quantified, however, the control architecture also facilitates the
simultaneous
operation of both pairs of modes. In this scenario, two measurements of angular rate are extracted from a single resonator and although the short-term rate noise associated with the
$n = 3$
pair is an order of magnitude larger than the rate extracted from the
$n = 2$
pair, the long-term drift in the rate offsets are correlated. Thus, a filter architecture for fusing the rate measurements is proposed and it is shown how the derived rate estimate possesses superior offset stability but also retains the low short-term noise associated with the rate measurement from the
$n = 2$
pair.