Document Type : Research Paper

Authors

1 Department of Information and Communication Technology, Imam Hossein University, Tehran, Iran

2 Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

Abstract

For the detection of and tracking thelow earth orbit Satellites (LEO), there are different methods such as optic, laser and radar tracking, among which radar tracking is the best. Since the common linear tracking filters deployed in available radars are not able to estimate the position of the non-linear dynamic satellites, it is advisable to use non-linear filters. In this paper, firstly, the satellite motion path around the earth as well as radar observations are produced by the STK software. Accordingly, the samples are fed to non-linear Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Finally, the performance of the aforementioned filters is studied through evaluation of RMS position and estimation errors. Simulation results demonstrate that the Unscented Kalman filter has a better performance in terms of accuracy with respect to the Extended Kalman filter. In addition, using this method, theerror of observations decreases 50% along the range and 70% along the azimuth and elevation.

Keywords

[1]    Salem, J., Zeighami, M., and Alavi, S.M., Estimation of LEO Satellites Position and their Tracking with Extended Kalman Filter & Unscented Kalman Filter, (M. Sc. Thesis), Imam Hossein University, 2014 (In Persian).
[2]    Montenbruck, O. and Gill, E., Satellite Orbits. Models, Methods and Applications, Springer, 2001.
[3]    Salem, J., Zeighami, M. and Alavi, S.M., “Modelling of LEO Satellites Trajectories and Their Tracking With Extended Kalman Filter (EKF) & Unscented Kalman Filter(UKF),” Radar journal of  Imam HosseinUniversity, Vol. 2, No. 2 (No. 4), 2014, pp. 39-48.
[4]    Vergez, P., Sauter, L. and Dahlke, S., “An  ImprovedKalman Filter for Satellite Orbit Predictions,” The Journal of the Astronautical Sciences, Vol. 52, No. 3, 2004, pp. 1–22.
[5]    Sidi, M.J., Spacecraft Dynamic and Control, A Practical Engineering Approach, Cambridge Aerospace Series 7, 1997.
[6]    Benavoli, A., Chisci1, L. and Farina, A., ‘‘Tracking of a Ballistic Missile with A-Priori Information,” IEEE Trans. On Aerospace and Electronic Systems, Vol. 43, No. 3, 2007, pp. 1000-1016.
[7]    Wu, P., Kong, J. and Bo, Y., “Modified Iterated Extended KalmanParticle Filter for Single Satellite Passive Tracking,” Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 21, 2013, pp. 120 – 130.
[8]    Rohde, J., Kalman Filter for Attitude Determination of Student Satellite, (M. Sc. Thesis), Department of Engineering Cybernetics, Norwegian University of Science and Technology, 2007
[9]    Eric, W. A. and Van Der Merwe,  R., Kalman Filtering and Neural Networks, Edited by Simon Haykin, Department of Electrical and Computer Engineering, Oregon Graduate Institute of Science and Technology, Beaverton, Oregon, U.S.A. Copyright 2001.
[10] Julier, S. J. and Uhlmann, J. K., “A New Extension of the Kalman Filter to Nonlinear Systems,” Proceedings of the SPIE AeroSense International Symposium on Aerospace/ Defense Sensing, Simulation and Controls, Orlando, Florida,  April 20–25, 1997.
[11] Ilyas, M., Lim, J., Gyu Lee, J. and Gook Park, C., “Federated Unscented Kalman Filter Design for Multiple Satellites Formation Flying in LEO,” International Conference on Control, Automation and Systems, COEX, Seoul, Korea, Oct. 14-17, 2008.
[12] Van Dyke, M.C., Schwartz, J.L. and Hall, C.D., “Unscented Kalman Filtering for Spacecraft Attitude State and Parameter Estimation,” American Astronautical Society Journal (AAS-04-115), Vol. 115, No. 04, 2004.
[13] Forghani, M. and Farrokhi, M., Satellite Orbit Estimation Using On-Line Neural Networks, Department of Electrical Engineering Center of Excellence for Power System Automation and Operation Iran University of Science and Technology, 2002 IFAC.
[14] Lan H. , Liang, Y., Zhang, W.  and et.al., “Iterated Minimum Upper Bound Filter for Tracking Orbit Maneuvering Targets,” Information Fusion (FUSION) 16th International Conference, Istanbul, Turkey, 2013.
[15] Chen, H., Chen, G., Blasch, E. and Pham, K. “Comparison of Several Space Target Tracking Filters,” Sensors and Systems for Space Applications III, Proceedings of SPIE Conference, Vol. 7330, 73300I·May 2009.
[16] Giannitrapani, A. and Scortecci, F., “Comparison of EKF and UKF for Spacecraft Localization Via Angle Measurements,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, Issue. 1, 2011, pp. 75-84.