Advertisement

Nonlinear Dynamics

, Volume 98, Issue 1, pp 589–600 | Cite as

Robustness to measurement noise of a globally convergent attitude observer with topological relaxations

  • Pedro BatistaEmail author
Original paper
  • 69 Downloads

Abstract

In the past decade, substantial effort has been put in the design of attitude observers with bias estimation that present both stability and convergence guarantees. However, most theoretical results consider a noiseless setting, deferring the analysis of the effect of noise to simulation and experimental results. This paper addresses the robustness of an existing solution to noise in all measurements by considering two settings: (i) bounded noise and (ii) stochastic noise modeled by a Wiener process. The results are appealing in that they effectively show the robustness of the observer in both scenarios, thus complementing global exponential convergence in noiseless settings. In particular, for bounded noise, the estimation error remains bounded, whereas in the case of noise modeled by a Wiener process, the mean error converges to zero, with bounded covariance. Finally, an additional result regarding the computation of estimates on SO(3) is also included.

Keywords

Attitude estimation Robustness Bounded noise Stochastic noise Navigation systems 

Notes

Funding

This work was supported by the Fundação para a Ciência e a Tecnologia (FCT) through ISR under FCT [UID/EEA/50009/2019] and through the FCT project DECENTER [LISBOA-01-0145-FEDER-029605], funded by the Lisboa 2020 and PIDDAC programs.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no further conflict of interest concerning the publication of this manuscript.

References

  1. 1.
    Barrau, A., Bonnabel, S.: Intrinsic filtering on Lie groups with applications to attitude estimation. IEEE Trans. Autom. Control 60(2), 436–449 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Batista, P., Silvestre, C., Oliveira, P.: A GES attitude observer with single vector observations. Automatica 48(2), 388–395 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Batista, P., Silvestre, C., Oliveira, P.: Globally exponentially stable cascade observers for attitude estimation. Control Eng. Pract. 20(2), 148–155 (2012)CrossRefGoogle Scholar
  4. 4.
    Batista, P., Silvestre, C., Oliveira, P.: Sensor-based globally asymptotically stable filters for attitude estimation: analysis, design, and performance evaluation. IEEE Trans. Autom. Control 57(8), 2095–2100 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Belta, C., Kumar, V.: An SVD-based projection method for interpolation on SE(3). IEEE Trans. Robot. Autom. 18(3), 334–345 (2002)CrossRefGoogle Scholar
  6. 6.
    Berkane, S., Abdessameud, A., Tayebi, A.: Global hybrid attitude estimation on the special orthogonal group SO(3). In: Proceedings of the 2016 American Control Conference, pp. 113–118. Boston, USA (2016)Google Scholar
  7. 7.
    Berkane, S., Tayebi, A.: On deterministic attitude observers on the special orthogonal group SO(3). In: Proceedings of the 55th IEEE Conference on Decision and Control, pp. 1165–1170. Las Vegas, USA (2016)Google Scholar
  8. 8.
    Crassidis, J., Markley, F., Cheng, Y.: Survey of nonlinear attitude estimation methods. J Guid. Control Dyn. 30(1), 12–28 (2007)CrossRefGoogle Scholar
  9. 9.
    Geering, H., Dondi, G., Herzog, F., Keel, S.: Stochastic systems. Measurement and Control Laboratory, Swiss Federal Institute of Technology (ETH) (2011)Google Scholar
  10. 10.
    Grip, H., Fossen, T., Johansen, T., Saberi, A.: Attitude estimation using biased gyro and vector measurements with time-varying reference vectors. IEEE Trans. Autom. Control 57(5), 1332–1338 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Grip, H., Fossen, T., Johansen, T., Saberi, A.: Globally exponentially stable attitude and gyro bias estimation with application to GNSS/INS integration. Automatica 51, 158–166 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Hua, M.D.: Attitude estimation for accelerated vehicles using GPS/INS measurements. Control Eng. Pract. 18(7), 723–732 (2010)CrossRefGoogle Scholar
  13. 13.
    Izadi, M., Sanyal, A.: Rigid body attitude estimation based on the Lagrange-d’Alembert principle. Automatica 50(10), 2570–2577 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Izadi, M., Viswanathan, S., Sanyal, A., Silvestre, C., Oliveira, P.: The variational attitude estimator in the presence of bias in angular velocity measurements. In: Proceedings of the 2016 American Control Conference, pp. 4065–4070. Boston, USA (2016)Google Scholar
  15. 15.
    Khalil, H.: Nonlinear Systems, 2nd edn. Prentice-Hall, Upper Saddle River (1996)Google Scholar
  16. 16.
    Khalil, H.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2001)Google Scholar
  17. 17.
    Mahony, R., Hamel, T., Pflimlin, J.M.: Nonlinear complementary filters on the special orthogonal group. IEEE Trans. Autom. Control 53(5), 1203–1218 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Markley, F., Mortari, D.: How to estimate attitude from vector observations. Proc. AAS/AIAA Astrodyn. Spec. Conf. 103(3), 1979–1996 (1999)Google Scholar
  19. 19.
    Namvar, M., Safaei, F.: Adaptive compensation of gyro bias in rigid-body attitude estimation using a single vector measurement. IEEE Trans. Autom. Control 58(7), 1816–1822 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Rugh, W.: Linear system theory, 2nd edn. Prentice-Hall Inc, Upper Saddle River (1995)Google Scholar
  21. 21.
    Teel, A.R., Hespanha, J.: Examples of GES systems that can be driven to infinity by arbitrarily small additive decaying exponentials. IEEE Trans. Autom. Control 49(8), 1407–1410 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Trumpf, J., Mahony, R., Hamel, T., Lageman, C.: Analysis of non-linear attitude observers for time-varying reference measurements. IEEE Trans. Autom. Control 57(11), 2789–2800 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wu, T.H., Kaufman, E., Lee, T.: Globally asymptotically stable attitude observer on SO(3). In: Proceedings of the 54th IEEE Conference on Decision and Control, pp. 2164–2168. Osaka, Japan (2015)Google Scholar
  24. 24.
    Zamani, M., Trumpf, J., Mahony, R.: Minimum-energy filtering for attitude estimation. IEEE Trans. Autom. Control 58(11), 2917–2921 (2013)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute for Systems and Robotics, LARSyS Department of Electrical and Computer Engineering, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

Personalised recommendations