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


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.


Attitude estimation Robustness Bounded noise Stochastic noise Navigation systems 



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.


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© 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

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