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Spacecraft Large Attitude Estimation Using a Navigation Sensor

Published online by Cambridge University Press:  01 December 2009

Ranjan Vepa
Ranjan Vepa*
Affiliation:
(Queen Mary, University of London)
*
(Email: r.vepa@qmul.ac.uk)
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Abstract

In this paper we assume that we have measurements of a first difference of a typical satellite navigation carrier phase differential, which is a homogeneous quadratic function of the components of the attitude quaternion. We illustrate the determination of large or sustained attitudes using a dedicated unscented Kalman filter. The unscented Kalman filter structure was chosen for the dedicated filter because of its derivative free nature and other advantages. When a Gaussian distributed vector random variable is transformed to an equivalent quaternion it does not continue to be Gaussian distributed. For this reason, a new predictor-corrector form of the unscented Kalman filter is proposed to maintain the normalization of the unscented mean quaternion estimate in the presence of additive disturbances. The results from our realistic simulations indicate that the large attitude of a spacecraft can be estimated to within 0·1% accuracy over large time frames. The filter is particularly useful for autonomous operations of spacecraft as well as in other applications where the process model is bilinear or second order in the states.

Keywords

Unscented Kalman FilterSpacecraft attitude
Type
Research Article
Information
The Journal of Navigation , Volume 63 , Issue 1 , January 2010 , pp. 89 - 104
Copyright
Copyright © The Royal Institute of Navigation 2009

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References

REFERENCES

Cheon, Y-J., and Kim, J-H. (2007). Unscented Filtering in a Unit Quaternion Space for Spacecraft Attitude Estimation, Proceedings of the IEEE International Symposium on Industrial Electronics, 2007, ISIE 2007, 66–71.CrossRefGoogle Scholar
Creamer, G. (1996). Spacecraft Attitude Determination Using Gyros and Quaternion Measurements, The Journal of the Astronautical Sciences, Vol. 44, No. 3, 357–371.Google Scholar
Crassidis, J.L., and Markley, F.L. (1997a). Predictive Filtering for Attitude Estimation Without Rate Sensors, Journal of Guidance Control and Dynamics, Vol. 20, No. 3, 522–527.CrossRefGoogle Scholar
Crassidis, J.L., and Markley, F.L. (1997b). Predictive Filtering for Nonlinear Systems,” Journal of Guidance Control and Dynamics, Vol. 20, No. 4, 566–572.CrossRefGoogle Scholar
Crassidis, J.L., and Markley, F.L. (2003). Unscented Filtering for Spacecraft Attitude Estimation,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 4, 536–542.CrossRefGoogle Scholar
de Ruiter, A.H.J. and Damaren, C.J. (2002). Extended Kalman Filtering and Nonlinear Predictive Filtering for Spacecraft Attitude Determination, Canadian Aeronautics and Space Journal, Vol. 48, No. 1,13–23.CrossRefGoogle Scholar
Farrell, J.L. (1970). Attitude Determination by Kalman Filtering, Automatica, Vol. 6, 419–430.CrossRefGoogle Scholar
Farrenkopf, R.L. (1978). Analytic Steady-State Accuracy Solutions for Two Common Spacecraft Attitude Estimators, Journal of Guidance, Control and Dynamics, Vol. 1, No. 4, 282–284.CrossRefGoogle Scholar
Fujikawa, S.J. and Zimbelman, D.F. (1995). Spacecraft Attitude Determination by Kalman Filtering of Global positioning System Signals, Journal of Guidance, Control and Dynamics, Vol. 18, No. 6, 1365–1371.CrossRefGoogle Scholar
Hatch, R.R. and Sharpe, T. (2001). A Computationally Efficient Ambiguity Resolution Technique, Proceeding of ION GPS 2001, Salt Lake City, UT, USA, 11–14 Sept. 2001.Google Scholar
Hoots, F.R., Schumacher, P.W. Jr., and Glover, R.A. (2004). History of Analytical Orbit Modeling in the U.S. Space Surveillance System, Journal of Guidance, Control and Dynamics, Vol. 27, No. 2, 174–185.CrossRefGoogle Scholar
Huang, G.-S. and Juang, J.-C. (1997). Application of Nonlinear Kalman Filter Approach in Dynamic GPS-Based Attitude Determination, Proceedings of the 40th Midwest Symposium on Circuits and Systems, 1997, Vol. 2, pp. 1440–1444.Google Scholar
Jazwinski, A.H. (1970). Stochastic Processes and Filtering Theory, Academic Press, London, England.Google Scholar
Julier, S.J. (2002). The Scaled Unscented Transformation, Proceedings of the American Control Conference, Vol. 6, 4555–4559.Google Scholar
Julier, S.J. and Uhlmann, J.K. (2000). Unscented Filtering and Nonlinear estimation, Proceedings of the IEEE, 92, 401–422.CrossRefGoogle Scholar
Julier, S.J., Uhlmann, J., and Durrant-Whyte, H.F. (2000). A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators, IEEE Transactions on Automatic Control, Vol. 45, No. 3, 477–482.CrossRefGoogle Scholar
Kingston, D.B. and Beard, R.W. (2004). Real-Time Attitude and Position Estimation for Small UAVs Using Low-Cost Sensors, AIAA 3rd Unmanned Unlimited Systems Conference and Workshop, September, 2004, Paper no. AIAA-2004-6488.Google Scholar
Kraft, E. (2003). A Quaternion-based Unscented Kalman Filter for Orientation Tracking, Proceedings of the Sixth International Conference of Information Fusion, 2003, Vol. 1, 47–54.CrossRefGoogle Scholar
Lefferts, E.J., Markley, F.L., and Schuster, M.D. (1982). Kalman Filtering for Spacecraft Attitude Estimation, Journal of Guidance, Control and Dynamics, Vol. 5, No. 5, 417–429.CrossRefGoogle Scholar
Lerner, G.M. (1978). Three-Axis Attitude Determination, Spacecraft Attitude Determination and Control, edited by Wertz, J.R., Reidel, D.Publishing Co., Dordrecht, The Netherlands, 420–428.Google Scholar
Markley, F.L. (1978) Matrix and Vector Algebra, Spacecraft Attitude Determination and Control, edited by Wertz, J.R., Reidel, D.Publishing Co., Dordrecht, The Netherlands, pp. 754–755.Google Scholar
Marins, J.L., Yun, X., Bachmann, E.R., McGhee, R.B. and Zyda, M.J. (2001). An Extended Kalman Filter for Quaternion-Based Orientation Estimation Using MARG Sensors, Proceedings of the 2001 IEEE/RSJ, International Conference on Intelligent Robots and Systems, Maui, Hawaii, USA, Oct. 29 – Nov. 03, 2001.Google Scholar
Pervan, B.Cohen, C. and Parkinson, B. (1994). Integrity Monitoring for Precision Approach Using Kinematic GPS and a Ground-Based Pseudolite, Navigation, Vol. 41, No. 2, 159–174.CrossRefGoogle Scholar
Potter, J.E. and Vander Velde, W.E. (1968). Optimum Mixing of Gyroscope and Star Tracker Data, Journal of Spacecraft and Rockets, Vol. 5, No. 5, 536–540.CrossRefGoogle Scholar
Sage, A.P. and Melsa, J.L. (1971). Estimation Theory with Applications to Communications and Control, McGraw-Hill, New York, pp. 106–156.Google Scholar
VanDyke, M.C., Schwartz, J.L. and Hall, C.D. (2004). Unscented Kalman Filtering For Spacecraft Attitude State And Parameter Estimation, The American Astronautical Society, Paper AAS-04-115.Google Scholar
Vathsal, S. (1987). Spacecraft Attitude Determination Using a Second-Order Nonlinear Filter, Journal of Guidance, Control and Dynamics, Vol. 10, No. 6, 559–566.CrossRefGoogle Scholar
Wahba, G. (1965). A Least-Squares Estimate of Satellite Attitude, Problem 65-1, SIAM Review, Vol. 7, No. 3, 409.CrossRefGoogle Scholar