Skip to main content
Springer Nature Link
Log in

Global Exponential Attitude and Gyro Bias Estimation from Vector Measurements

  • Conference paper
  • First Online:
Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

Included in the following conference series:

Abstract

We consider the classical problem of estimating the attitude and gyro biases of a rigid body from at least two vector measurements and a triaxial rate gyro. We propose a solution based on a dynamic nonlinear estimator designed without respecting the geometry of \(\mathrm {SO(3)}\), which achieves uniform global exponential convergence. The convergence is established thanks to a dynamically scaled Lyapunov function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Astolfi, A., Karagiannis, D., Ortega, R.: Nonlinear and Adaptive Control with Applications. Springer, London (2008)

    Book  MATH  Google Scholar 

  2. Batista, P., Silvestre, C., Oliveira, P.: A GES attitude observer with single vector observations. Automatica 48(2), 388–395 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Batista, P., Silvestre, C., Oliveira, P.: Globally exponentially stable cascade observers for attitude estimation. Control Eng. Pract. 20(2), 148–155 (2012)

    Article  Google Scholar 

  4. Benziane, L., Benallegue, A., Chitour, Y., Tayebi, A.: Velocity-free attitude stabilization with inertial vector measurements. Int. J. Robust Nonlinear Control 26, 2478–2493 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bonnabel, S., Martin, P., Rouchon, P.: Symmetry-preserving observers. IEEE Trans. Autom. Control 53(11), 2514–2526 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Crassidis, J.L., Markley, F.L., Cheng, Y.: Survey of nonlinear attitude estimation methods. J. Guidance Control Dyn. 30(1), 12–28 (2007)

    Article  Google Scholar 

  7. Grip, H.F., Fossen, T.I., Johansen, T.A., Saberi, A.: Attitude estimation using biased gyro and vector measurements with time-varying reference vectors. IEEE Trans. Autom. Control 57(5), 1332–1338 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grip, H.F., Fossen, T.I., Johansen, T.A., Saberi, A.: Globally exponentially stable attitude and gyro bias estimation with application to GNSS/INS integration. Automatica 51, 158–166 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  9. Karagiannis, D., Sassano, M., Astolfi, A.: Dynamic scaling and observer design with application to adaptive control. Automatica 45(12), 2883–2889 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mahony, R., Hamel, T., Pflimlin, J.M.: Nonlinear complementary filters on the special orthogonal group. IEEE Trans. Autom. Control 53(5), 1203–1218 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Martin, P., Salaün, E.: Invariant observers for attitude and heading estimation from low-cost inertial and magnetic sensors. In: IEEE Conference on Decision and Control, pp. 1039–1045 (2007)

    Google Scholar 

  12. Martin, P., Salaün, E.: Design and implementation of a low-cost observer-based attitude and heading reference system. Control Eng. Pract. 18(7), 712–722 (2010)

    Article  Google Scholar 

  13. Martin, P., Salaün, E.: The true role of accelerometer feedback in quadrotor control. In: IEEE International Conference on Robotics and Automation, pp. 1623–1629 (2010)

    Google Scholar 

  14. Martin, P., Sarras, I.: A global attitude and gyro bias observer from vector measurements. IFAC-PapersOnLine, vol. 50, IFAC 2017 World Congress (2014)

    Google Scholar 

  15. Tayebi, A., Roberts, A., Benallegue, A.: Inertial vector measurements based velocity-free attitude stabilization. IEEE Trans. Autom. Control 58(11), 2893–2898 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Vasconcelos, J.F., Silvestre, C., Oliveira, P.: A nonlinear observer for rigid body attitude estimation using vector observations. IFAC Proc. Vol. 41(2), 8599–8604 (2008)

    Article  Google Scholar 

  17. Zamani, M., Trumpf, J., Mahony, R., Filtering, N.A.: A comparison study. ArXiv e-prints, arXiv:1502.03990 [cs.SY] (2015)

Download references

Author information

Authors and Affiliations

  1. Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 75006, Paris, France

    Philippe Martin

  2. ONERA – The French Aerospace Lab, 91123, Palaiseau, France

    Ioannis Sarras

Authors
  1. Philippe Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ioannis Sarras
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Martin .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Martin, P., Sarras, I. (2017). Global Exponential Attitude and Gyro Bias Estimation from Vector Measurements. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-68445-1_40

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics