The primary metrics that prohibit the use of microelectromechanical systems (MEMS) gyroscopes for navigation-grade inertial navigation units (IMUs) are angle random walk (ARW), bias instability, and scale factor instability. The need for MEMS gyroscopes is due to their decreased cost, size, weight, and power (CSWaP) constraints compared to current navigation-grade solutions. Note that to avoid confusion, while in a statistical context a random walk describes a particular type of random process, ARW is used herein to quantify the effects of white, or Gaussian, noise processes on the rate estimate of a gyroscope.

The accepted theory about how to mitigate effects associated with thermomechanical noise, and thus lower ARW, quality factors on the order of a million are needed. While resonators with quality factors on the order of a million have been demonstrated in laboratory settings, navigation-grade ARW has only been demonstrated in high-vacuum systems (<10 μTorr) that would be challenging to implement in a portable system. Other means of reducing ARW, such as increasing the amplitude of the drive mode, can be problematic. For electrostatically transduced devices, which is one of the more common methods used with MEMS, large oscillations can introduce nonlinear behavior such as electrostatic softening or pull-in.

Relatively recent works have demonstrated that virtual carouseling and closed loop scale factor can be used to significantly reduce bias and scale factor instability, respectively. However, it is important to note that it is unknown if these methods will degrade the performance of a gyroscope with navigation-grade ARW.

The proposed time-domain switching micromachined gyroscope (TDSMG) seeks to address ARW, bias instability, and scale factor instability by using measurements from discrete trigger events that occur when the proof mass of the gyroscope passes known locations. It builds upon work done with the time-domain switching accelerometer that can estimate acceleration without the need for adjustable parameters. In addition, instead of the sensor's resolution being limited by noise from the amplifiers, it is controlled by the computational precision of the means used to estimate rotation rate and by the precision time is measured. There are no issues associated with noise from feedback electronics as feedback is not needed and noise associated with the readout electronics is minimal as the TDSMG is sensed using digital means. By using highly accurate time interval analyzers and knowledge of the position of the triggers, determining angular rate as well other parameters (i.e., frequency mismatch, time constant mismatch, etc.) can be formulated as a parametric system identification problem.

Unlike classically designed MEMS gyroscopes, timing jitter contributes to the ARW of the TDSMG. Effects due to thermomechanical noise also play a role, but time-domain switching aids in mitigating this effect as large-amplitude oscillations, which would typically introduce nonlinear effects with electrostatically transduced devices, can be used. Thus, with the combination of large-amplitude oscillations, particular conditions for how the signal processing should be implemented, and the low jitter metrics of modern time interval analyzers (<1 ps), navigation-grade performance is capable. Moreover, since the signal processing used to determine angular rate is independent of parameters that are known to be sensitive to temperature or other environmental factors (e.g., variability of the natural frequency of the resonator with respect to temperature), it is expected that the bias and scale factor instability performance will be very good.

The only parameter that is not directly estimated is the angular gain of the gyroscope. This parameter would need to be estimated with an initial calibration. Note that with structurally similar gyroscopes, such as the hemispherical resonator gyroscope, it was found that the angular gain was insensitive to temperature.

*This work was done by Andrew B. Sabater and Paul Swanson for the Space and Naval Warfare Systems Center Pacific (SPAWAR). SPAWAR-0006*

##### This Brief includes a Technical Support Package (TSP).

###### Angular Random Walk Estimation of a Time-Domain Switching Micromachined Gyroscope

(reference SPAWAR-006) is currently available for download from the TSP library.

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