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**MEMS Gyro bias Drift Mitigation by Simultaneous Operation of the n = 2 and n = 3 Modes**

*Howard Ge and Robert M'Closkey, University of California Los Angeles*

**Location:** Big Sur

Axisymmetric resonant structures have long been exploited as coriolis vibratory gyros (CVG), from Delco’s high performance Hemispherical Gyro to more recent 2D and 3D MEMS implementations. Axisymmetric structures can possess multiple pairs of nominally degenerate modes in which each pair exhibits some degree of coriolis coupling. In this paper we report a new technique by simultaneously operate the n = 2 and n = 3 pairs of modes in a disk resonator for two independent measurements of angular rate, and subsequently show that the bias errors associated with the two measurements are strongly correlated, thereby providing a very effective technique for in-situ bias drift cancellation.

The n = 2 and n = 3 pairs of mode are the first and second fundamental modes that are nominally isolated from central stem vibration, with Coriolis coupling factors of 0.4 and 0.3, respectively. The modal shape of the n = 2 mode is elliptical, while that of the n = 3 is trilobal.

The nominal frequency of the n = 2 mode pair occurs around 13.5 kHz, and for the n = 3 mode pair is around 27.5 kHz. The approximate 10 kHz separation in resonant frequencies between the n = 2 and n = 3 pairs of modes in this resonator design thus permitts us to separate the two modes from each other using frequency domain filtering, and then operate each mode pair as an independant CVG. Fig. 2 shows simultaneous rate measurements of a device operating in such configuration after

appropriate scale factors are applied. As the figure indicates, the two modes’ measurments are very consistent and repeatable, albeit with different noise characteristics.

The bias error drifts associated with the two measurements are strongly correlated to each other. A test was conducted in which a periodic thermal disturbance was introduced by a heater attached to the gyro. The thermal profile is given by the plot on the left side in Fig. 3. The induced bias drifts over the test period are plotted on the right. It is evident that there is very strong correlation between the n = 2 and n = 3 bias drifts. Using a least square fit, the correlation constant between the two measurments are found to be 0.0803. It is remarkable to notice that the combined rate measurement using the correlation achieves a bias temperature sensitivity reduction of over 500 times! The test is then repeated several times over a period of 6 months, and the correlation constant stay virtually unchanged.

To further demonstrate the effectiveness of this technique, the Allan deviation of the combined rate across 5 tests conducted on different days is shown in Fig. 4. All 5 tests were conducted under nominal laboratory condition with no temperature control. For comparison, the rate measurement using only the n = 2 mode pair is plotted in the same figure (dash blue line).

There is significant improvement in long-term bias stability with short-term noise essentially equal to that of n = 2 rate. In fact, the stability of bias has improved to the point where the ARW trend is readily identifiable in the Allan deviation, whereas it is obscured in the single-pair Allan deviation. The fused rate signal has an ARW figure of 0:027deg/rt-hr. The angle white noise (AWN) asymptote is also shown in Fig. 4.

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