GPS-Based Real-Time Orbit Determination of Low Earth Orbit Satellites Using Robust Unscented Kalman Filter
Publication: Journal of Aerospace Engineering
Volume 30, Issue 6
Abstract
In this research, a novel algorithm for real-time orbit determination (RTOD) is presented using the robust unscented Kalman filter (RUKF) with global positioning system (GPS) group and phase ionospheric correction (GRAPHIC) observables. To increase the reliability of the solution, a robust approach is included in the UKF to cope with the bad, invalid, or degraded measurements leading to the divergence or inaccurate output of the filter. Robustness is provided by making the filter less sensitive to faulty measurements using a scale matrix that is multiplied with the covariance matrix of the observation noises. Real data collected during a massive solar storm are used in the algorithm. For external validation, the outputs of RUKF and classical UKF are compared with the precision orbit ephemerides of the Challenging Minisatellite Payload (CHAMP). The results show that RUKF slightly outperforms classical UKF and possesses the capability to be used as an efficient and reliable algorithm in case of bad observations or malfunctioning of the system.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
GPS measurements evaluated in this study have been made available by the CHAMP project managed by GeoForschungsZentrum (GFZ) Potsdam. Precision orbit ephemerides have been acquired from NASA JPL, California Institute of Technology. Furthermore, the authors would like to thank the anonymous reviewers for valuable comments and suggestions.
References
Bock, H., Jäggi, A., Dach, R., Schaer, S., and Beutler, G. (2009). “GPS single-frequency orbit determination for low Earth orbiting satellites.” Adv. Sp. Res., 43(5), 783–791.
Chapra, S. C., and Canale, R. P. (2006). Numerical methods for engineers, 5th Ed., McGraw-Hill, New York.
Chiaradia, A., Kuga, H., and Prado, A. (2003). “Single frequency GPS measurements in real-time artificial satellite orbit determination.” Acta Astronaut., 53(2), 123–133.
Chiaradia, A. P. M., Gill, E., Montenbruck, O., and Kuga, H. K. (2000). Algorithms for on-board orbit determination using GPS OBODE-GPS, German Space Operations Center, DLR, Oberpfaffenhofen, Germany.
Choi, E.-J., Yoon, J.-C., Lee, B.-S., Park, S.-Y., and Choi, K.-H. (2010). “Onboard orbit determination using GPS observations based on the unscented Kalman filter.” Adv. Sp. Res., 46(11), 1440–1450.
GFZ (GeoForschungszentrum). (2012). “Information systems and data center: Global earth science data.” Helmholtz-Zentrum, Potsdam, Germany.
Gill, E., Montenbruck, O., Arichandran, K., Tan, S., and Bretschneider, T. (2004). “High-precision onboard orbit determination for small satellites–the GPS-based XNS on X-Sat.” Proc., Small Satellites Systems and Services, ESA, Paris.
Gill, E., Montenbruck, O., and Montenegro, S. (2002). “Flight results from the BIRD onboard navigation system.” Proc., 5th ESA Int. Conf. on Spacecraft Guidance, Navigation and Control System, ESA, Paris.
GIPSY [Computer software]. Jet Propulsion Laboratory, California Institute of Technology, CA.
Grewal, M. S., Weill, L. R., and Andrews, A. P. (2007). Global positioning systems, inertial navigation, and integration, 2nd Ed., Wiley, Hoboken, NJ.
Hajiyev, C., and Soken, H. E. (2012). “Robust estimation of UAV dynamics in the presence of measurement faults.” J. Aerosp. Eng., 80–89.
Hajiyev, C., and Soken, H. E. (2014). “Robust adaptive unscented Kalman filter for attitude estimation of pico satellites.” Int. J. Adapt. Control Signal Process., 28(2), 107–120.
Harris, I., and Priester, W. (1962). “Time-dependent structure of the upper atmosphere.” J. Atmos. Sci., 19(4), 286–301.
Julier, S. J., and Uhlmann, J. K. (1997). “A new extension of the Kalman filter to nonlinear systems.” Proc., SPIE, Signal Processing, Sensor Fusion, and Target Recognition VI, I. Kadar, ed., Vol. 3068, Society of Photo-optical Instrumentation Engineers, Bellingham, WA, 182–193.
Jwo, D.-J., and Lai, C.-N. (2008). “Unscented Kalman filter with nonlinear dynamic process modeling for GPS navigation.” GPS Solut., 12(4), 249–260.
Karslioglu, M. O. (2005). “An interactive program for GPS-based dynamic orbit determination of small satellites.” Comput. Geosci., 31(3), 309–317.
König, R., Michalak, G., Grunwaldt, L., and Reigber, C. (2005). “CHAMP clock characterization revisited.” Earth observation with CHAMP SE-28, 2nd Ed., C. Reigber, H. Lühr, P. Schwintzer, and J. Wickert, eds., Springer, Berlin, 175–180.
Lee, D.-J. J., and Alfriend, K. T. (2007). “Sigma point filtering for sequential orbit estimation and prediction.” J. Spacecr. Rockets, 44(2), 388–398.
Lucchesi, D. (2001). “Reassessment of the error modelling of non-gravitational perturbations on LAGEOS II and their impact in the Lense-Thirring determination.” Part I Planet. Space Sci., 49(5), 447–463.
Lundberg, J. B., and Schutz, B. E. (1988). “Recursion formulas of Legendre functions for use with nonsingular geopotential models.” J. Guid. Control. Dyn., 11(1), 31–38.
Marshall, J. A., and Luthcke, S. B. (1994). “Modeling radiation forces acting on Topex/Poseidon for precision orbit determination.” J. Spacecr. Rockets., 31(1), 99–105.
Montenbruck, O., and Gill, E. (2000). Satellite orbits: Models, methods and applications, Springer, Heidelberg, Germany.
Montenbruck, O., Gill, E., and Markgraf, M. (2006). “Phoenix-XNS-a miniature real-time navigation system for LEO satellites.” 3rd Workshop on Satellite Navigation User Equipment Technology, Navitec, ESA, Paris.
Montenbruck, O., and Ramos-Bosch, P. (2008). “Precision real-time navigation of LEO satellites using global positioning system measurements.” GPS Solut., 12(3), 187–198.
Montenbruck, O., van Helleputte, T., and Kroes, E. (2005). “Reduced dynamic orbit determination using GPS code and carrier measurements.” Aerosp. Sci. Technol., 9(3), 261–271.
Pardal, P. C. P. M., Kuga, H. K., and Vilhena de Morales, R. (2009). “Non linear sigma point Kalman filter applied to orbit determination using GPS measurements.” Proc., 22nd Int. Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2009), Institute of Navigation, Manassas, VA.
Park, E.-S., Park, S.-Y., Roh, K.-M., and Choi, K.-H. (2010). “Satellite orbit determination using a batch filter based on the unscented transformation.” Aerosp. Sci. Technol., 14(6), 387–396.
Pines, S. (1973). “Uniform representation of the gravitational potential and its derivatives.” AIAA J., 11(11), 1508–1511.
Ramos-Bosch, P. (2008). “Improvements in autonomous GPS navigation of low Earth orbit satellites.” Ph.D. dissertation, Universitat Politecnica de Catalunya, Barcelona, Spain.
Reichert, A., Meehan, T., and Munson, T. (2002). “Toward decimeter-level real-time orbit determination: A demonstration using the SAC-C and CHAMP Spacecraft.” Proc., 15th Int. Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 2002), Portland, OR.
Rizos, C., and Stolz, A. (1985). “Force modelling for GPS satellite orbits.” 1st Int. Symp. on Precise Positioning with the Global Positioning System, U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, Rockville, MD, 87–98.
Soken, H., and Hajiyev, C. (2010). “Robust UKF insensitive to measurement faults for pico satellite attitude estimation.” World Acad. Sci. Eng. Technol. Int. Sci. Index, 44(8), 1179–1184.
Soken, H., Hajiyev, C., and Sakai, S. (2014). “Robust Kalman filtering for small satellite attitude estimation in the presence of measurement faults.” Eur. J. Control, 20(2), 64–72.
Spencer, J. L. (1976). Nonsingular gravitational potential derivation, description and implementation, McDonnell Douglas Technical Services, St. Louis, MO.
Tapley, B., and Ingram, D. (1973). “Orbit determination in the presence of unmodeled accelerations.” IEEE Trans. Automat. Contr., 18(4), 369–373.
Tapley, B. D., Bob, E. S., and George, H. B. (2004). Statistical orbit determination, Elsevier, Cambridge, MA.
van der Merwe, R., Doucet, A., De Freitas, N., and Wan, E. (2000). “The unscented particle filter.”, Oregon Graduate Institute Electrical and Computer Engineering, OR.
Wan, E. A., and van der Merwe, R. (2000). “The unscented Kalman filter for nonlinear estimation.” Proc., IEEE Adaptive Systems Signal Processing Communication Control Symp., IEEE, Washington, DC, 153–158.
Wan, E. A., and van der Merwe, R. (2001). “The unscented Kalman filter.” Kalman filtering and neural networks, S. Haykin, ed., Wiley, New York.
Yoon, J.-C., et al. (2002). “Orbit determination of spacecraft using global positioning system single-frequency measurement.” J. Spacecr. Rockets, 39(5), 796–801.
Yunck, T. P. (1996). “Orbit determination.” Global positioning systems theory applied, B. W. Parkinson and J. J. Spilker, eds., AIAA, Reston, VA, 559–592.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 25, 2016
Accepted: Apr 17, 2017
Published online: Jul 21, 2017
Published in print: Nov 1, 2017
Discussion open until: Dec 21, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.