×

Finite-horizon robust Kalman filter for uncertain attitude estimation system with star sensor measurement delays. (English) Zbl 1406.93349

Summary: This paper addresses the robust Kalman filtering problem for uncertain attitude estimation system with star sensor measurement delays. Combined with the misalignment errors and scale factor errors of gyros in the process model and the misalignment errors of star sensors in the measurement model, the uncertain attitude estimation model can be established, which indicates that uncertainties not only appear in the state and output matrices but also affect the statistic of the process noise. Meanwhile, the phenomenon of star sensor measurement delays is described by introducing Bernoulli random variables with different delay characteristics. The aim of the addressed attitude estimation problem is to design a filter such that, in the presence of model uncertainties and star sensors delays for the attitude estimation system, the optimized filter parameters can be obtained to minimize the upper bound on the estimation error covariance. Therefore, a finite-horizon robust Kalman filter is proposed to cope with this question. Compared with traditional attitude estimation algorithms, the designed robust filter takes into account the effects of star sensor measurement delays and model uncertainties. Simulation results illustrate the effectiveness of the developed robust filter.

MSC:

93E11 Filtering in stochastic control theory
93B35 Sensitivity (robustness)
93E10 Estimation and detection in stochastic control theory
93C41 Control/observation systems with incomplete information
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lefferts, E. J.; Markley, F. L.; Shuster, M. D., Kalman filtering for spacecraft attitude estimation, Journal of Guidance, Control, and Dynamics, 5, 5, 417-429 (1982)
[2] Markley, F. L., Attitude error representations for Kalman filtering, Journal of Guidance, Control, and Dynamics, 26, 2, 311-317 (2003)
[3] Crassidis, J. L.; Markley, F. L.; Cheng, Y., Survey of nonlinear attitude estimation methods, Journal of Guidance, Control, and Dynamics, 30, 1, 12-28 (2007) · doi:10.2514/1.22452
[4] Shuster, M. D.; Pitone, D. S.; Bierman, G. J., Batch estimation of spacecraft sensor alignments—relative alignment estimation, Journal of the Astronautical Sciences, 39, 4, 519-546 (1991)
[5] Pittelkau, M., Kalman filtering for spacecraft system alignment calibration, Journal of Guidance, Control, and Dynamics, 24, 6, 1187-1195 (2001)
[6] Pittelkau, M., Survey of calibration algorithms for spacecraft attitude sensors and gyros, Advances in the Astronautical Sciences, 129, 651-706 (2008)
[7] Lai, K. L.; Crassidis, J. L., In-space spacecraft alignment calibration using the unscented filter, Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit
[8] Vandersteen, J.; Diehl, M.; Aerts, C.; Swevers, J., Spacecraft attitude estimation and sensor calibration using moving horizon estimation, Journal of Guidance, Control, and Dynamics, 36, 3, 734-742 (2013) · doi:10.2514/1.58805
[9] Hmamed, A.; Kasri, C. E.; Tissir, E. H.; Alvarez, T.; Tadeo, F., Robust \(H_∞\) filtering for uncertain 2-D continuous systems with delays, International Journal of Innovative Computing, Information and Control, 9, 5, 2167-2183 (2013)
[10] Ahn, C. K.; Kim, P. S., New energy-to-peak FIR filter design for systems with disturbance: a convex optimization approach, International Journal of Innovative Computing, Information and Control, 9, 5, 1987-1993 (2013)
[11] Wu, L. G.; Ho, D. W. C., Fuzzy filter design for Itô stochastic systems with application to sensor fault detection, IEEE Transactions on Fuzzy Systems, 17, 1, 233-242 (2009) · doi:10.1109/TFUZZ.2008.2010867
[12] Hu, J.; Wang, Z. D.; Gao, H. J.; Stergioulas, L. K., Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements, Automatica, 48, 9, 2007-2015 (2012) · Zbl 1257.93099 · doi:10.1016/j.automatica.2012.03.027
[13] Hu, J.; Wang, Z. D.; Shen, B.; Gao, H. J., Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements, International Journal of Control, 86, 4, 650-663 (2013) · Zbl 1278.93269 · doi:10.1080/00207179.2012.756149
[14] Wang, J. Q.; He, Z. M.; Zhou, H. Y.; Jiao, Y. Y., Regularized robust filter for attitude determination system with relative installation error of star trackers, Acta Astronautica, 87, 88-95 (2013) · doi:10.1016/j.actaastro.2013.01.008
[15] Dong, Z.; You, Z., Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-covariance white noises, IEEE Signal Processing Letters, 13, 8, 493-496 (2006) · doi:10.1109/LSP.2006.873148
[16] Souto, R. F.; Ishihara, J. Y., Comments on ‘finite: horizon robust Kalman filtering for uncertain discrete time: varying systems with uncertain: covariance white noises’, IEEE Signal Processing Letters, 17, 2, 213-216 (2010) · doi:10.1109/LSP.2008.2005046
[17] Su, X.; Wu, L.; Shi, P., Sensor networks with random link failures: distributed filtering for T-S fuzzy systems, IEEE Transactions on Industrial Informatics, 9, 3, 1739-1750 (2013) · doi:10.1109/TII.2012.2231085
[18] Su, X.; Shi, P.; Wu, L.; Nguang, S. K., Induced \(l_2\) filtering of fuzzy stochastic systems with time-varying delays, IEEE Transactions on Cybernetics, 43, 4, 1251-1264 (2013) · doi:10.1109/TSMCB.2012.2227721
[19] Yang, R.; Shi, P.; Liu, G., Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts, IEEE Transactions on Automatic Control, 56, 11, 2655-2660 (2011) · Zbl 1368.93734 · doi:10.1109/TAC.2011.2166729
[20] Caballero-Aguila, R.; Hermoso-Carazo, A.; Jimenez-Lopez, J. D.; Linares-Perez, J.; Nakamori, S., Recursive estimation of discrete-time signals from nonlinear randomly delayed observations, Computers & Mathematics with Applications, 58, 6, 1160-1168 (2009) · Zbl 1189.93136 · doi:10.1016/j.camwa.2009.06.046
[21] Caballero-Aguilaa, R.; Hermoso-Carazo, A.; Jimenez-Lopez, J. D.; Linares-Perez, J.; Nakamori, S., Signal estimation with multiple delayed sensors using covariance information, Digital Signal Processing, 20, 2, 528-540 (2010) · doi:10.1016/j.dsp.2009.06.011
[22] Dam, H. H., Variable fractional delay filter with sub-expression coefficients, International Journal of Innovative Computing, Information and Control, 9, 7, 2995-3003 (2013)
[23] Hounkpevi, F. O.; Yaz, E., Minimum variance generalized state estimators for multiple sensors with different delay rates, Signal Processing, 87, 4, 602-613 (2007) · Zbl 1186.94148 · doi:10.1016/j.sigpro.2006.06.017
[24] Wang, X. X.; Liang, Y.; Pan, Q.; Zhao, C. H., Gaussian filter for nonlinear systems with one-step randomly delayed measurements, Automatica, 49, 4, 976-986 (2013) · Zbl 1284.93236 · doi:10.1016/j.automatica.2013.01.012
[25] Hu, J.; Wang, Z. D.; Shen, B.; Gao, H. J., Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays, IEEE Transactions on Signal Processing, 61, 5, 1230-1238 (2013) · Zbl 1393.94261 · doi:10.1109/TSP.2012.2232660
[26] Xie, L.; Soh, Y. C.; de Souza, C. E., Robust Kalman filtering for uncertain discrete-time systems, IEEE Transactions on Automatic Control, 39, 6, 1310-1314 (1994) · Zbl 0812.93069 · doi:10.1109/9.293203
[27] Horn, R. A.; Johnson, C. R., Topics in Matrix Analysis (1991), New York, NY, USA: Cambridge University Press, New York, NY, USA · Zbl 0729.15001 · doi:10.1017/CBO9780511840371
[28] Yao, X. M.; Guo, L., Composite anti-disturbance control for Markovian jump nonlinear systems via disturbance observer, Automatica, 49, 8, 2538-2545 (2013) · Zbl 1364.93102 · doi:10.1016/j.automatica.2013.05.002
[29] Yao, X. M.; Dong, Z.; Wang, D. F., Full-order disturbance-observer-based control for singular hybrid system, Mathematical Problems in Engineering (2013) · Zbl 1296.93032 · doi:10.1155/2013/352198
[30] Tang, X. J.; Liu, Z. B.; Zhang, J. S., Square-root quaternion cubature Kalman filtering for spacecraft attitude estimation, Acta Astronautica, 76, 84-94 (2012) · doi:10.1016/j.actaastro.2012.02.009
[31] Arasaratnam, I.; Haykin, S.; Hurd, T. R., Cubature Kalman filtering for continuous-discrete systems: theory and simulations, IEEE Transactions on Signal Processing, 58, 10, 4977-4993 (2010) · Zbl 1391.93223 · doi:10.1109/TSP.2010.2056923
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.