Nonlinear Operation of Inertial Sensors

  • Andrew B. SabaterEmail author
  • Kari M. Moran
  • Eric Bozeman
  • Andrew Wang
  • Kevin Stanzione
Conference paper
Part of the Understanding Complex Systems book series (UCS)


It is often assumed, and has been shown experimentally, that nonlinear operation of inertial sensors–in particular gyroscopes–can degrade or trivially improve performance. As such, the standard practice is to operate below or near the threshold where nonlinear effects become significant. The limitation with this method is that the dynamic range, or the range of excitations where the sensor behaves linearly, shrinks as the dimensions of the sensor decrease. Thus, while relatively large mechanical gyroscopes, such as hemispherical resonator gyroscopes (HRGs), can achieve navigation-grade performance, microelectromechanical system (MEMS) gyroscopes, being orders of magnitude smaller, have orders of magnitude worse performance. A relatively new class mechanical gyroscope, the frequency modulated (FM) gyroscope, is able to address long-term noise performance issues. The trade-off with FM gyroscopes, compared to the standard amplitude modulated ones, is that short-term noise can be elevated. One means of improving short-term gyroscope performance is improving short-term frequency stability. It has been shown theoretically and experimentally that while most states within the nonlinear regime of an oscillator degrade frequency stability, a select few allow operation at a lower fundamental limit. This work describes and provides some preliminary experimental work on the constructive exploitation of nonlinear operation with FM gyroscopes.


  1. 1.
    I.P. Prikhodko, B. Bearss, C. Merritt, J. Bergeron, C. Blackmer, Towards self-navigating cars using MEMS IMU: challenges and opportunities, in Proceedings of 2018 IEEE INERTIAL (IEEE, Moltrasio, 2018), pp. 1–4Google Scholar
  2. 2.
    B. Eminoglu, Y.-C. Yeh, I.I. Izyumin, I. Nacita, M. Wireman, A. Reinelt, B.E. Boser, Comparison of long-term stability of AM versus FM gyroscopes. In: Proceedings of 2016 IEEE MEMS (IEEE, Shanghai, 2016), pp. 954–957Google Scholar
  3. 3.
    I.P. Prikhodko, S. Nadig, J.A. Gregory, W.A. Clark, M.W. Judy, Half-a-month stable 0.2 degree-per-hour mode-matched MEMS gyroscope, in Proceedings of IEEE MEMS (IEEE, Kauai, 2017), pp. 1–4Google Scholar
  4. 4.
    R.P. Leland, Mechanical-thermal noise in MEMS gyroscopes. IEEE Sens. J. 5(3), 493–500 (2005)CrossRefGoogle Scholar
  5. 5.
    B. Eminoglu, B.E. Boser, (2018) Chopped rate-to-digital FM gyroscope with 40 ppm scale factor accuracy and 1.2 dph bias. In: Proceedings of 2018 IEEE ISSCC (IEEE, San Francisco, 2018), pp. 178–180Google Scholar
  6. 6.
    P. Taheri-Tehrani, M. Defoort, D.A. Horsley, Operation of a high quality-factor gyroscope in electromechanical nonlinearities regime. J. Micromech. Microeng. 27, 075015 (2017)CrossRefGoogle Scholar
  7. 7.
    IEEE Standard Specification Format Guide and Test Procedure for Coriolis Vibratory Gyros. IEEE Standard 1431-2004 (2004)Google Scholar
  8. 8.
    I.I. Izyumin, M.H. Kline, Y.-C. Yeh, B. Eminoglu, C.H. Ahn, V.A. Hong, Y. Yang, E.J. Ng, T.W. Kenny, B.E. Boser, A 7ppm, 6 deg/hr frequency-output MEMS gyroscope, in Proceedings of 2015 IEEE MEMS (IEEE, Estoril, 2015), pp. 33–36Google Scholar
  9. 9.
    D.D. Lynch, Vibratory Gyro Analysis by the Method of Averaging (1995), pp. 26–34Google Scholar
  10. 10.
    B.R. Simon, S. Khan, A.A. Trusov, A.M. Shkel, mode ordering in tuning fork structures with negative structural coupling for mitigation of common-mode g-sensitivity, in Proceedings of 2015 IEEE SENSORS (IEEE, Busan, 2015), pp. 1–4Google Scholar
  11. 11.
    R.N. Candler, M.A. Hopcroft, B. Kim, W.-T. Park, R. Melamud, M. Agarwal, G. Yama, A. Partridge, M. Lutz, T.W. Kenny, Long-Term and accelerated life testing of a novel single-wafer vacuum encapsulation for MEMS resonators. J. Microelectromech. Syst. 15(6), 1446–1456 (2006)CrossRefGoogle Scholar
  12. 12.
    D.S. Greywall, B. Yurke, P.A. Busch, A.N. Pargellis, R.L. Willett, Evading amplifier noise in nonlinear oscillators. Phys. Rev. Lett. 72(19), 2992–2995 (1994)CrossRefGoogle Scholar
  13. 13.
    J. Juillard, A. Brenes, Impact of excitation waveform on the frequency stability of electrostatically-actuated micro-electromechanical oscillators. J. Sound Vib. 422, 79–91 (2018)CrossRefGoogle Scholar
  14. 14.
    L.G. Villanueva, E. Kenig, R.B. Karabalin, M.H. Matheny, R. Lifshitz, M.C. Cross, M.L. Roukes, Surpassing fundamental limits of oscillators using nonlinear resonators. Phys. Rev. Lett. 110, 177208 (2013)CrossRefGoogle Scholar
  15. 15.
    N. Miller, Noise in nonlinear micro-resonators. Ph.D. Thesis, Michigan State University, Lansing, Michigan, (2012)Google Scholar
  16. 16.
    J. Sieber, A. Gonzalez-Buelga, S.A. Neild, D.J. Wagg, B. Krauskopf, Experimental continuation of periodic orbits through a fold. Phys. Rev. Lett. 100, 244101 (2008)CrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2019

Authors and Affiliations

  • Andrew B. Sabater
    • 1
    Email author
  • Kari M. Moran
    • 1
  • Eric Bozeman
    • 1
  • Andrew Wang
    • 1
  • Kevin Stanzione
    • 1
  1. 1.SPAWAR Systems Center PacificSan DiegoUSA

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