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Comparison of Linearized Kalman Filter and Extended Kalman Filter for Satellite Motion States Estimation

Ya-fei YANG(杨亚非)

 

(Control & Simulation Center, Harbin Institute of Technology, Harbin 150008, China)

 

Abstract-The performance of the conventional Kalman filter depends on process and measurement noise statistics given by the system model and measurements. The conventional Kalman filter is usually used for a linear system, but it should not be used for estimating the state of a nonlinear system such as a satellite motion because it is difficult to obtain the desired estimation results. The linearized Kalman filtering approach and the extended Kalman filtering approach have been proposed for a general nonlinear system. The equations of satellite motion are described. The satellite motion states are estimated, and the relevant estimation errors are calculated through the estimation algorithms of the both above mentioned  approaches implemented in Matlab are estimated. The performances of the extended Kalman filter and the linearized Kalman filter are compared. The simulation results show that the extended Kalman filter is much better than the linearized Kalman filter at the aspect of estimation effect.

 

Key words-nonlinear filtering approach; nonlinear system; satellite orbit; state space; state estimation

 

Manuscript Number: 1674-8042(2011)04-0307-05

 

doi: 10.3969/j.issn.1674-8042.2011.04.001

 

References

 

[1] R. E. Kalman, 1960. A new approach to linear filtering and prediction problems. Trans. ASME-Journal of Basic Engineering, 82: 34-35.
[2] R. E. Kalman, R. S. Bucy, 1961. New results in linear filtering and prediction. Trans. ASME, Journal of Basic Engineering, 83: 95-108.
[3] A. Jazwinski, 1970. Stochastic processes and filtering theory. Academic Press, New York.
[4] J. R. Forbes, 2010. Extended Kalman filter and sigman point filter approaches to adaptive filtering. AIAA Guaidance, Navigation, and Control Conference, 2-5, Toronto, Ontario Canada.
[5] S. Julier, J. K. Uhlmann, H. F. Durrant-Whyte, 1995. A new approach for filtering nonlinear system. Proceeding of the American Control Conference, Seattle, WA, USA, p.1628-1632.
[6] S. Julier, J. K. Uhlmann, 1997. A new extension of the Kalman filter to nonlinear system. Proceeding of the 11th International Symposium on Aerospace/ Deference Sensing Simulation and Controls, Orlando, FL, USA, p.182-193.
[7] S. Julier, J. K. Uhlmann, H. F. Durrant-Whyte, 2000. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. on Automatic Control, 45(3): 477-482.
[8] M. S. Arulampalam, S. Maskell, N. Gordon, et al., 2002. A Tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. on Signal Processing, 50(2): 174-185.
[9] J. L. Crassidis, F. L. Markley, Y. Cheng, 2007. Survey of nonlinear altitude estimation methods. Journal of Guidance, Control, and Dynamics, 30(1): 12-28.
[10] A. Gelb, 1974. Applied optimal estimation. the MIT press, Cambridge, MA, p.181-228.
[11] R. Brown, R. Hwang, 1997.  Introduction to random signals and applied Kalman filtering. John Wiley & Sons INC., New York, p.335-391.
[12] Dan Simon, 2006. Optimal state estimation: Kalman, H, and nonlinear approaches. John Wiley & Sons INC., New York, p.394-431.

 

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