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Mathematical Problems in Engineering
Volume 2015, Article ID 168045, 9 pages
Research Article

The Particle Filter Sample Impoverishment Problem in the Orbit Determination Application

1University of São Paulo (USP)-EEL/LOB, Estrada Municipal do Campinho, s/n, 12602-810 Lorena, SP, Brazil
2National Institute for Space Research (INPE)-DMC, Avenida dos Astronautas, 1758 Jardim da Granja, 12227-010 São José dos Campos, SP, Brazil
3São Paulo Federal University (UNIFESP)-ICT/UNIFESP, Rua Talim, 330 Vila Nair, 12231-280 São José dos Campos, SP, Brazil

Received 11 February 2015; Accepted 6 May 2015

Academic Editor: Ruihua Liu

Copyright © 2015 Paula Cristiane Pinto Mesquita Pardal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper aims at discussing techniques for administering one implementation issue that often arises in the application of particle filters: sample impoverishment. Dealing with such problem can significantly improve the performance of particle filters and can make the difference between success and failure. Sample impoverishment occurs because of the reduction in the number of truly distinct sample values. A simple solution can be to increase the number of particles, which can quickly lead to unreasonable computational demands, which only delays the inevitable sample impoverishment. There are more intelligent ways of dealing with this problem, such as roughening and prior editing, procedures to be discussed herein. The nonlinear particle filter is based on the bootstrap filter for implementing recursive Bayesian filters. The application consists of determining the orbit of an artificial satellite using real data from the GPS receivers. The standard differential equations describing the orbital motion and the GPS measurements equations are adapted for the nonlinear particle filter, so that the bootstrap algorithm is also used for estimating the orbital state. The evaluation will be done through convergence speed and computational implementation complexity, comparing the bootstrap algorithm results obtained for each technique that deals with sample impoverishment.