An investigation on cubature Kalman filter performance for orbit determination application

  • Paula Cristiane Pinto Mesquita PardalEmail author
  • Roberta Veloso Garcia
  • Helio Koiti Kuga
  • William Reis Silva
Technical Paper


This work aims at discussing the cubature Kalman filter (CKF) performance when applied to a highly nonlinear problem: the artificial satellites orbit determination problem, using real global positioning system (GPS) data. The CKF is a nonlinear filter based on a third-degree spherical–radial cubature rule, which allows to numerically compute multivariate moment integrals in the Bayesian filter and also provides a set of cubature points scaling linearly with the state vector dimension. Therefore, CKF yields a systematic solution for high-dimensional nonlinear filtering problems, such as the orbit determination application addressed here. This application consists of determining the orbit of Jason-2 satellite, using real GPS data from its onboard receivers, which is a highly nonlinear problem, with respect to the dynamics and the observations equations. The standard differential equations that characterize the orbital motion and the GPS measurements are modified to accommodate the nonlinear filter, and the CKF algorithm is also used for estimating the state of the orbit. The assessment to be presented will be based on the robustness of the filter, concerning convergence speed when the measurements are scattered. The results from CKF will be compared with the unscented Kalman filter results for the same problem, in computational terms such as convergence and accuracy. According to the analysis of such criteria, the conclusions will be presented.


Orbit determination Estimation theory Cubature Kalman filter Unscented Kalman filter GPS measurements 



The authors wish to express their appreciation to Lorena School of Engineering/University of São Paulo (EEL/USP) that kindly provided everything necessary for this paper to be developed. The authors are also grateful to the Brazilian National Council for Scientific and Technological Development (CNPq), for the funding support under contracts # 407296/2016-6, 405468/2016-4, and 307255/2018-2.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.USP/EEL (University of São Paulo)LorenaBrazil
  2. 2.ITA/DCTA (Technological Institute of Aeronautics)São José dos CamposBrazil
  3. 3.UnB/FGA (University of Brasília)GamaBrazil

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