Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 55–64 | Cite as

Unscented Kalman filter and smoothing applied to attitude estimation of artificial satellites

  • Roberta Veloso GarciaEmail author
  • Hélio Koiti Kuga
  • William Reis Silva
  • Maria Cecília Zanardi


This article uses the state smoothing methodology applied to nonlinear systems to refine the attitude of artificial satellites. In this paper, simulated data of telemetry and ephemeris of a satellite with the specifications of China Brazil Earth Resources Satellite are considered and the dynamic system is described by the set of kinematic equations in terms of the Euler angles and the bias vector of gyroscope. The estimator used to determine the forward estimates in time is the Unscented Kalman filter, while the Rauch–Tung–Striebel fixed interval estimator makes the estimate backward time. The results show that, although the time of the estimation process is slightly increased, the smoother presents estimated attitude and bias closer to the real values than the estimated values when using only the Unscented Kalman filter. Therefore, the smoother can be considered as a technique that provides refined measurements of the attitude and bias of the gyroscope that may serve to calibrate the Kalman filter for next estimates.


Rauch–Tung–Striebel smoother Unscented Kalman filter Attitude estimation Euler angles 

Mathematics Subject Classification

60G25 60-xx 60G-xx 60G-25 



The authors would like to thank the financial support received by CNPq and CAPES.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  • Roberta Veloso Garcia
    • 1
    Email author
  • Hélio Koiti Kuga
    • 2
  • William Reis Silva
    • 2
  • Maria Cecília Zanardi
    • 3
  1. 1.Lorena School of EngineeringSao Paulo UniversityLorenaBrazil
  2. 2.Technological Institute of AeronauticsSão José dos CamposBrazil
  3. 3.Federal University of ABCSanto AndréBrazil

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