This paper presents four innovative techniques, three Kalman-based and one observer-based, to estimate environmental perturbation torques acting on an Earth-orbiting spacecraft. The Kalman-based techniques all use simple generic models for the state dependence of the perturbation, and for estimating the unknown coefficients included in these generic mathematical formulations. The observer-based technique is developed with the nonlinear disturbance observer theory. The proposed strategies are validated in numerical simulations and are traded-off in terms of estimation accuracy and computational load requirement. Then, the most suitable estimation technique is combined with a batch least square filter algorithm to yield a perturbation estimation system with low computational load, which can be implemented onboard a spacecraft. Finally, the proposed estimation strategy is applied to a realistic gyroless Earth-orbiting spacecraft mission: the European Space Agency’s Project for Onboard Autonomy (PROBA)-2 mission. Ultimately, the selected estimation strategy will be implemented onboard the PROBA-2 spacecraft for in-flight validation. All strategies proposed in this article are general and are applicable to any Earth-orbiting spacecraft.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Johnson, C. “Accommodation of External Disturbances in Linear Regulator and Servomechanism Problems,” IEEE Transactions on Automatic Control, Vol. AC-16, No. 6, 1971, pp. 635–644.
Johnson, C. “Accommodation of Disturbances in Optimal Control Problems,” International Journal of Control, Vol. 15, Issue 2, 1972, pp. 209–231.
Johnson, C. and Kelly, W. “Theory of Disturbance-Utilizing Control: Some Recent Developments,” Proceedings of IEEE Southeast Conference, Huntsville, AL, April 5–8, 1981, pp. 614–620.
George, J. and Crassidis, J. “Sensitivity Analysis of Disturbance Accommodating Control with Kaiman Filter Estimation,” Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, SC, Aug. 20–23, 2007.
Hoefer, S., Kumaresan, R., Pandit, M., and Stollhof, T. “Adaptive FIR-Filter for Control Systems with Periodic Disturbances,” Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 5, 1991, pp. 3241–3244.
Hu, J. and Tomizuka, M. “A New Plug-In Adaptive Controller for Rejection of Periodic Disturbances,” Journal of Dynamic Systems, Measurement, and Control, Vol. 115, No. 3, 1993, pp. 543–546.
Hillerstrom, G. and Sternby, J. “Rejection of Periodic Disturbances with Unknown Period—A Frequency Domain Approach,” Proceedings of the American Control Conference, Baltimore, MD, June 29–July 1, 1994, Vol. 2, 1994, pp. 1626–1631.
Hyland, D.C., Davis, L., DAS, A., and Yen, G. “Autonomous Neural Control for Structure Vibration Suppression,” Proceedings of the AIAA Guidance, Navigation, and Control Conference, San Diego, CA, July 29–31, 1996.
Chan, S.P. “A Disturbance Observer for Robot Manipulators with Application to Electronic Components Assembly,” IEEE Transactions of Industrial Electronics, Vol. 42, No. 5, 1995, pp. 487–493.
Eom, K.S., Suh, I.H., Chung, W.K., and Oh, S.-R. “Disturbance Observer Based Force Control of Robot Manipulator without Force Sensor,” Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, May 16–20, 1998, Vol. 4, pp. 3012–3017.
Oh, Y. and Chung, W.K. “Disturbance-Observer-Based Motion Control of Redundant Manipulators Using Inertially Decoupled Dynamics,” IEEE/ASME Transactions on Mechatronics, Vol. 4, No. 2, 1999, pp. 133–146.
Liu, C.S. and Peng, H. “Disturbance Observer Based Tracking Control,” Journal of Dynamic Systems, Measurement, and Control, Vol. 122, Issue 2, 2000, pp. 332–335.
Chen, W.H., Ballance, D.J., Gawthrop, P.J., and O’reilly, J. “A Nonlinear Disturbance Observer for Robotic Manipulators,” IEEE Transactions on Industrial Electronics, Vol. 47, No. 4, 2000, pp. 932–938.
Chen, W.H. “Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, 2003, pp. 161–166.
Claveau, F. and De Lafontaine, J. “Innovative Nonlinear Predictive Control of Spacecraft Improved by Disturbance Observer,” Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Mackinac Island, MI, Aug. 19–23, 2007.
Chen, W.H. “Harmonic Disturbance Observer for Nonlinear System,” Journal of Dynamic Systems, Measurement, and Control, Vol. 125, Issue 1, 2003, pp. 114–117.
Crassidis, J.L. and Junkins, J.L. Optimal Estimation of Dynamic Systems, Chapman & Hall/CRC, Boca Raton, FL, 2004.
Savonof, M. and Athans, M. “Robustness and Computational Aspects of Nonlinear Stochastic Estimators and Regulators,” IEEE Transactions on Automatic Control, Vol. 23, Issue 4, 1978, pp. 717–725.
Sugiyama, N. “System Identification of Jet Engines,” Journal of Engineering for Gas Turbines and Power, Vol. 122, Issue 1, 2000, pp. 19–26.
Kobayashi, T., Simon, D.L., and Litt, J.S. “Applications of a Constant Gain Extended Kaiman Filter for In-Flight Estimation of Aircraft Engine Performance Parameters,” Technical Report TM-2005-213865, NASA, Sept. 2005.
Julier, S.J., Uhlmann J.K., and Durrant-Whyte, H.F. “A New Approach for Filtering Nonlinear Systems,” Proceedings of the American Control Conference, Seattle, WA, Jun. 21–23, 1995.
Julier, S.J. and Uhlmann, J.K. “A New Extension of the Kaiman Filter to Nonlinear Systems,” Proceedings of the 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Multi Sensor Fusion, Tracking and Resource Management II, Orlando, FL, Apr. 21–24, 1997.
Crassidis, J.L., Markley, F.L., and Cheng, Y. “Survey of Nonlinear Estimation Methods,” Journal of Guidance, Control and Dynamics, Vol. 30, No. 1, 2007, pp. 12–28.
De Lafontaine, J. “Orbital Dynamics in a Stochastic Atmosphere and a Non-Spherical Gravity Field,” Ph.D. Thesis, University of Toronto Institute of Aerospace Studies, Toronto, ON, Canada. 1986.
Plett, M., Aiello, J., Yong, K., and Gottlieb, D.M. “Modeling the space Environment,” Spacecraft Attitude Determination and Control, ed. Wertz, J.R., Riedel Publishing Co., Dordrecht, The Netherlands, 1980, pp. 113–132.
Bate, R.R., Mueller, D.D., and White, J.E. Fundamental of Astrodynamics, Dover Publications, Mineola, NY, 1971.
Schmidt, S.F. “The Kaiman Filter: Its Recognition and Development for Aerospace Applications,” Journal of Guidance, Control and Dynamics, Vol. 4, No. 1, 1981, pp. 4–7.
Sorensen, J.A., Schmidt, S.F., and Gota, T. “Application of Square-Root Filtering for Spacecraft Attitude Control,” Journal of Guidance, Control and Dynamics, Vol. 2, No. 1, 1979, pp. 426–433.
Lefferts, E.J., Markley, F.L., and Shuster, M.D. “Kaiman Filtering for Spacecraft Attitude Estimation,” Journal of Guidance, Control and Dynamics, Vol. 5, No. 5, 1982, pp. 417–429.
Wiegand, M. “Autonomous Satellite Navigation via Kaiman Filtering of Magnetometer Data,” Acta Astronautica, Vol. 38, No. 4, 1996, pp. 395–403.
Chodas, P.W. “Combined Satellite Attitude and Orbit Determination with Dynamic Coupling,” Proceedings of the ALAA/AAS Astrodynamics Conference, San Diego, CA, Aug, 9–11, 1982.
Fosbury, A.M. “Satellite Position and Attitude Estimation Using an Extended Kaiman Filter,” Proceedings of the AIAA Guidance, Navigation and Control Conference and Exhibit, Hilton Head, SC, Aug. 20–23, 2007.
De Lafontaine, J., Buijs, J., Vuilleumier, P., Van Den Braembussche, P., and Mellab, K. “Development of the PROBA Attitude Control and Navigation Software,” Proceedings of the 4th International ESA Conference on Guidance, Navigation and Control Systems, Noordwijk, The Netherlands, Oct. 18–21, 1999.
Côt, J. and De Lafontaine, J. “Magnetic-Only Orbit and Attitude Estimation Using the Square-Root Unscented Kaiman Filter: Application to the PROBA-2 Spacecraft,” Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit, Honolulu, HI, Aug. 18–21, 2008.
Van Der Merwe, R. and Wan, E. “The Square-Root Unscented Kaiman Filter for State and Parameter-Estimation,” Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, UT, May 2001.
Valado, D.A. Fundamentals of Astrodynamics and Applications, 2nd Ed., Kluwer Academic Publications, Dordrecht, The Netherlands, 2001.
Hostetter, G.H. “Recursive Discrete Fourier Transform,” IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. 28, Issue 4, 1980, pp. 183–190.
Peceli, G. “A Common Structure for Recursive Discrete Transforms,” IEEE Transactions on Circuits and Systems, Vol. 33, Issue 10, 1986, pp. 1035–1036.
Baudrenghien, P. The Adaptive Spectrum Analyzer, Standford University Press, Standford, CA, 1984.
Bitmead, R.R., Tsoi, A.C., and Parker, P.J. “A Kaiman Filtering Approach to Short-Time Fourier Analysis,” IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 34, Issue 6, 1986, pp. 1493–1501.
M’sirdi, N.K., Tjokronegoro, H.R., and Landau, I.D. “An RML Algorithm for Retrieval of Sinusoids with Cascaded Notch Filters,” Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, New York, NY, April 11–14, 1988, Vol. 4, pp. 2484–2487.
Xiao, Y., Tadokoro, Y., Shida, K., and Iwamoto, K. “Performance Analysis of a Simplified RLS Algorithm for the Estimation of Sinusoidal Signals in Additive Noise,” IEICE Transactions Fundamentals of Electronics, Communications and Computer Sciences, Vol. E81-A, Issue 8, 1998, pp.1703–1712.
Xiao, Y., Ma, L., and Ward, R. K. “Fast RLS Fourier Analyzers Capable of Accommodating Frequency Mismatch,” Signal Processing, Vol. 87, Issue 9, 2007, pp. 2197–2212.
Biqing W. and Bodson, M. “A Magnitude/Phase-Locked Loop Approach to Parameter Estimation of Periodic Signals,” IEEE Transactions on Automatic Control, Vol. 48, Issue 4, 2003, pp. 612–618.
Kay, S.M. and Marple, S.L. Jr. “Spectrum Analysis—A Modern Perspective,” Proceedings of IEEE, Vol. 69, Nov. 1981, pp. 1380–1419.
Kaiser, J.F. “On a Simple Algorithm to Calculate the ‘Energy’ of a Signal,” Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 1, pp. 381–384, 1990.
Hughes, P.C. Spacecraft Attitude Dynamics, Wiley, New York, 1986.
Lewis, F.L. Optimal Estimation with an Introduction to Stochastic Control Theory, Wiley, New York, 1986, Chap. 2.4, pp. 88–94.
De Lafontaine, J., Côt, J., Kron, A., Vuilleumier, P., Santandrea, S., and Van Den Braembussche, P. “Validation of Innovative State Estimation and Control Techniques on PROBA-2,” Proceedings of the 6th ESA International Conference on Guidance, Navigation and Control Systems, Loutraki, Greece, Oct. 17–20, 2005.
De Lafontaine, J., Côt, J., Kron, A., Vuilleumier, P., Santandrea, S., and Van Den Braembussche, P. “Innovative Autonomous Navigation and Control Functions Onboard the Mini-Satellite PROBA-2,” Proceedings of the 13th CASI Conference on Astronautics, Montreal, QC, Canada, Apr. 25–28, 2006.
About this article
Cite this article
Ulrich, S., Côté, J. & de Lafontaine, J. In-Flight Attitude Perturbation Estimation for Earth-Orbiting Spacecraft. J of Astronaut Sci 57, 633–665 (2009). https://doi.org/10.1007/BF03321520