Analyzing the Unscented Kalman Filter Robustness for Orbit Determination Through Global Positioning System Signals

Pardal, Paula Cristiane Pinto Mesquita; Kuga, Hélio Koiti; Moraes, Rodolpho Vilhena de

doi:10.5028/jatm.v5i4.252

ABSTRACT:

The nonlinear unscented Kalman filter (UKF) is evaluated for the satellite orbit determination problem, using Global Positioning System (GPS) measurements. The assessment is based on the robustness of the filter. The main subjects for the evaluation are convergence speed and dynamical model complexity. Such assessment is based on comparing the UKF results with the extended Kalman filter (EKF) results for the solution of the same problem. Based on the analysis of such criteria, the advantages and drawbacks of the implementations are presented. In this orbit determination problem, the focus is to analyze UKF convergence behavior using different sampling rates for the GPS signals, where scattering of measurements will be taken into account. A second aim is to evaluate how the dynamical model complexity affects the performance of the estimators in such adverse situation. After solving the real-time satellite orbit determination problem using actual GPS measurements, through EKF and UKF algorithms, the results obtained are compared in computational terms such as complexity, convergence, and accuracy.

KEYWORDS:
Orbit determination; Nonlinear Kalman filters; GPS measurements; Real time

Full text is available only in PDF.

REFERENCES

Brown, R. G. and Hwang, P. Y. C., 1984, A Kalman filter approach to precision GPS geodesy, Navigation: Global Positioning System, Vol. II, pp. 155-166.
Brown, R. G. and Hwang, P. Y. C., 1985, Introduction to random signals and applied Kalman filtering, 3rd ed. New York: John Wiley & Sons. 502 p.
Chiaradia, A. P. M., Kuga, H. K. Kuga and Prado, A. F. B. A., 2003, Single frequency GPS measurements in real-time artificial satellite orbit determination, Acta Astronautica, Vol. 53, n. 2, pp. 123-133.
El-Sheimy, N., Shin, E-H. and Niu, X., 2006, Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial. Available from: http://www.insidegnss.com/auto/0306%20Kalman.pdf
» http://www.insidegnss.com/auto/0306%20Kalman.pdf
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» http://inside.mines.edu/fs_home/tohno/teaching/PH505_2011/Paper_TianyuanGuan.pdf
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» http://epubl.ltu.se/1653-0187/2009/095/LTUPB-EX-09095-SE.pdf
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Kaula, W.M., 1966, Theory of Satellite Geodesy. Blasdell Pub. Co. Walthmam, Mass.
Maybeck, P.S., 1982, Stochastic models, estimation, and control. Vol. 2, Academic Press, NY.
Montenbruck, O. and Gill, E., 2001, Satellite orbits: models, methods, and applications, Springer-Verlag, Berlin Heidelberg NewYork. 369 p.
Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2009a, A discussion related to orbit determination using nonlinear sigma point Kalman filter, Mathematical Problems in Engineering, v. 2009, 12 p. Hindawi Publishing Corporation, doi:10.1155/2009/140963.
» https://doi.org/10.1155/2009/140963
Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2009b, Non linear sigma point Kalman filter applied to orbit determination using GPS measurements, 22nd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), 22-25 Sept., Savannah, USA.
Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2010, Comparing the extended and the sigma point Kalman filters for orbit determination modeling using GPS measurements,23rd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), 21-24 Sept., Portland, USA.
Pardal, P. C. P. M., Real time orbit determination through non linear sigma-point Kalman filter, 2011, Ph.D thesis, National Institute for Space Research (INPE), São José dos Campos. (In Portuguese).
Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2011, Robustness assessment between sigma point and extended Kalman filter for orbit determination,. Journal of Aerospace Engineering, Sciences and Applications, v. III, pp. 35-44. doi: 10.7446/jaesa.0303.04
» https://doi.org/10.7446/jaesa.0303.04
Prado, A. F. B. A. and Kuga, H. K. (Eds.), 2001, Space Technology Fundaments, São José dos Campos: INPE. 220 p. (In Portuguese).
Soken, H. E. and Hajiyev, C., 2011, REKF and RUKF Development for Pico Satellite Attitude Estimation in the Presence of Measurement Faults, 5th International Conference on Recent Advances in Space Technologies (RAST), 9-11 June 2011. pp. 891-896. doi: 10.1109/RAST.2011.5966972
» https://doi.org/10.1109/RAST.2011.5966972
van der Merwe, R., 2004, Sigma-Point Kalman filters for probabilistic inference in dynamic state-space models, Ph.D thesis. Oregon Health & Science University, Portland.
van der Merwe, R., Wan, E.A. and Julier, S.J., 2004, Sigma-point Kalman filters for nonlinear estimation and sensor-fusion applications to integrated navigation, AIAA Guidance, Navigation, and Control Conference and Exhibit, 16-19 Aug. 2004, Rhode Island.
Wan, E. A. and van der Merwe, R., 2001, The unscented Kalman filter, Kalman Filtering and Neural Networks. Haykins, S. (Ed.), John Wiley & Sons, New York, Chap. 7.

Publication Dates

Publication in this collection
Oct-Dec 2013

History

Received
27 May 2013
Accepted
18 Aug 2013

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Brown, R. G. and Hwang, P. Y. C., 1984, A Kalman filter approach to precision GPS geodesy, Navigation: Global Positioning System, Vol. II, pp. 155-166.

[2] Brown, R. G. and Hwang, P. Y. C., 1985, Introduction to random signals and applied Kalman filtering, 3rd ed. New York: John Wiley & Sons. 502 p.

[3] Chiaradia, A. P. M., Kuga, H. K. Kuga and Prado, A. F. B. A., 2003, Single frequency GPS measurements in real-time artificial satellite orbit determination, Acta Astronautica, Vol. 53, n. 2, pp. 123-133.

[4] El-Sheimy, N., Shin, E-H. and Niu, X., 2006, Extended vs. Unscented Kalman Filters for Integrated GPS and MEMS Inertial. Available from: http://www.insidegnss.com/auto/0306%20Kalman.pdf
» http://www.insidegnss.com/auto/0306%20Kalman.pdf

[5] Guan, T., 2013, Special cases of the three body problem, [online Colorado University database]. Available from: http://inside.mines.edu/fs_home/tohno/teaching/PH505_2011/Paper_TianyuanGuan.pdf
» http://inside.mines.edu/fs_home/tohno/teaching/PH505_2011/Paper_TianyuanGuan.pdf

[6] Jose, J. M., 2009, Performance comparison of Extended and Unscented Kalman Filter implementation in INS-GPS integration, Ph.D thesis. Czech Technical University in Prague, Prague (in English). Available from: http://epubl.ltu.se/1653-0187/2009/095/LTUPB-EX-09095-SE.pdf
» http://epubl.ltu.se/1653-0187/2009/095/LTUPB-EX-09095-SE.pdf

[7] Julier, S. J. and Uhlmann, J. K., 1997, A new extension of the Kalman filter for nonlinear systems, International Symposium on Aerospace/Defense Sensing, Simulation and Controls. SPIE.

[8] Julier, S. J. and Uhlmann, J. K., 2004, Unscented filtering and nonlinear estimation. IEEE Transactions on Automatic Control, Vol. 92, n. 3, Mar 2004.

[9] Kaula, W.M., 1966, Theory of Satellite Geodesy. Blasdell Pub. Co. Walthmam, Mass.

[10] Maybeck, P.S., 1982, Stochastic models, estimation, and control. Vol. 2, Academic Press, NY.

[11] Montenbruck, O. and Gill, E., 2001, Satellite orbits: models, methods, and applications, Springer-Verlag, Berlin Heidelberg NewYork. 369 p.

[12] Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2009a, A discussion related to orbit determination using nonlinear sigma point Kalman filter, Mathematical Problems in Engineering, v. 2009, 12 p. Hindawi Publishing Corporation, doi:10.1155/2009/140963.
» https://doi.org/10.1155/2009/140963

[13] Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2009b, Non linear sigma point Kalman filter applied to orbit determination using GPS measurements, 22nd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), 22-25 Sept., Savannah, USA.

[14] Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2010, Comparing the extended and the sigma point Kalman filters for orbit determination modeling using GPS measurements,23rd International Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), 21-24 Sept., Portland, USA.

[15] Pardal, P. C. P. M., Real time orbit determination through non linear sigma-point Kalman filter, 2011, Ph.D thesis, National Institute for Space Research (INPE), São José dos Campos. (In Portuguese).

[16] Pardal, P. C. P. M., Kuga, H. K. and Vilhena de Moraes, R., 2011, Robustness assessment between sigma point and extended Kalman filter for orbit determination,. Journal of Aerospace Engineering, Sciences and Applications, v. III, pp. 35-44. doi: 10.7446/jaesa.0303.04
» https://doi.org/10.7446/jaesa.0303.04

[17] Prado, A. F. B. A. and Kuga, H. K. (Eds.), 2001, Space Technology Fundaments, São José dos Campos: INPE. 220 p. (In Portuguese).

[18] Soken, H. E. and Hajiyev, C., 2011, REKF and RUKF Development for Pico Satellite Attitude Estimation in the Presence of Measurement Faults, 5th International Conference on Recent Advances in Space Technologies (RAST), 9-11 June 2011. pp. 891-896. doi: 10.1109/RAST.2011.5966972
» https://doi.org/10.1109/RAST.2011.5966972

[19] van der Merwe, R., 2004, Sigma-Point Kalman filters for probabilistic inference in dynamic state-space models, Ph.D thesis. Oregon Health & Science University, Portland.

[20] van der Merwe, R., Wan, E.A. and Julier, S.J., 2004, Sigma-point Kalman filters for nonlinear estimation and sensor-fusion applications to integrated navigation, AIAA Guidance, Navigation, and Control Conference and Exhibit, 16-19 Aug. 2004, Rhode Island.

[21] Wan, E. A. and van der Merwe, R., 2001, The unscented Kalman filter, Kalman Filtering and Neural Networks. Haykins, S. (Ed.), John Wiley & Sons, New York, Chap. 7.

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