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According to the attitude estimation and three-axis magnetometer on-line calibration, a real time moving horizon estimation algorithm is presented in this paper. First, moving horizon estimation filter is designed since system constraints existing in most practical cases cannot be solved analytically in the framework of Kalman filter. Taking advantage of the optimal problem in dealing with constraints, the presented method converts the attitude estimation problem into an optimal one by which the quaternion normalization property can be solved analytically in smaller searching space with better efficiency and accuracy. Second, through a series of linearization of system equations, Gauss-Newton iterative method is applied in the horizon window composed of finite history information to obtain the best state estimation and meet the real time requirement at the same time. Once the newest best state estimation value is obtained, it will be sacked into the horizon window and the oldest one discarded. By this way, the filter is moving forward. Finally, based on the proposed method, the three-axis magnetometer parameter on-line calibration combined with attitude estimation is solved without adding any system state dimension, which can also make sure that the measurements with three-axis magnetometer are in the form of vector as its obvious benefits in the sense of ensuring information quantity. On considering the extreme environment such as great temperature gradient, mechanical pressure and complex electromagnetic fields, different from that of the off-line calibration, the calibration parameter is changed definitely. So the on-line calibration is necessary though neglected by most papers. Simulation results show that under the condition of small initial errors, the difference of accuracy among EKF, UKF and moving horizon estimation is small. But the computational burden of the last one is relatively large. The advantage of the described method is not so obvious in this case. But when the initial errors are large, the moving horizon estimation still can get the precise results no matter how great are the EKF (extended Kalman filter) and UKF (unscented Kalman filter) deviated from the true values. Thus the proposed method has its high accuracy and poor sensitivity of the initial and systematic errors along with fast convergence, all of which are vital in most actual environments.
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Keywords:
- attitude estimation /
- moving horizon estimation /
- three-axis magnetometer /
- on-line calibration
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[2] BarI I Y, Harman R R 1997 Gu. Contr. Dyn. 20 208
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[4] Chen W D, Liu Y L, Zhu Q G, Chen Y 2013 Acta Phys. Sin. 17 105 (in Chinese) [陈卫东, 刘要龙, 朱奇光, 陈颖 2013 物理学报 17 105]
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[10] Zu T Z, Jia S Z 2010 Chin. Phys. B 19 104601
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[14] Jyh C J, Yung F T, Chiu T T 2012 Aero. Sci. Techn. 21 47
[15] Inamori T, Nakasuka S, Sako N 2009 Proceedings of AIAA Guidance, Navigation, and Control Conference Chicago, USA, August 10-13, 2009 p1
[16] John C S, James W C 2012 IEEE Gu. Contr. Dyn. 35 1080
[17] John L C, Kok L L 2005 IEEE Gu. Contr. Dyn. 28 115
[18] Vasconcelos J F, Elkaim G, Silvestre C 2011 IEEE Aero. El. Syst. 47 1293
[19] Wu Z W, Yao M L, Ma H G 2013 IEEE Veh. Techn. 62 1084
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[21] Marsden J E, West M 2001 Acta Num. 10 357
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[23] Pang H, Li J, Chen D 2013 Measurement 46 1600
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[25] Rao C V, Rawlings J B 2002 IEEE Aich. E. 48 97
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[1] Goldenberg F 2006 Proceedings of IEEE/ION PLANS San Diego, Canada, April 25-27, 2001 p684
[2] BarI I Y, Harman R R 1997 Gu. Contr. Dyn. 20 208
[3] Markley F 1989 Acta Astro. S. 37 41
[4] Chen W D, Liu Y L, Zhu Q G, Chen Y 2013 Acta Phys. Sin. 17 105 (in Chinese) [陈卫东, 刘要龙, 朱奇光, 陈颖 2013 物理学报 17 105]
[5] Sheng Z 2011 Acta Phys. Sin. 11 820 (in Chinese) [盛峥 2011 物理学报 11 820]
[6] Zhao L 2012 Acta Phys. Sin. 10 231 (in Chinese) [赵龙 2012 物理学报 10 231]
[7] Huang X Y, Wang J M 2014 IEEE Veh. Techn. 63 4221
[8] Wu X D, Song Z H 2008 Chin. Phys. B 17 3241
[9] Liu Y, Wang H, Hou C H 2013 IEEE Sign. Proc. 61 4988
[10] Zu T Z, Jia S Z 2010 Chin. Phys. B 19 104601
[11] Canale M, Fagiano L, Novara C 2014 IEEE Contr. Syst. Techn. 22 2048
[12] Tor A J, Dan S, Roar N 2013 IEEE Contr. Syst. Techn. 21 2114
[13] Rao C V, Rawlings J B, Mayne D Q 2003 IEEE Aut. Contr. 48 246
[14] Jyh C J, Yung F T, Chiu T T 2012 Aero. Sci. Techn. 21 47
[15] Inamori T, Nakasuka S, Sako N 2009 Proceedings of AIAA Guidance, Navigation, and Control Conference Chicago, USA, August 10-13, 2009 p1
[16] John C S, James W C 2012 IEEE Gu. Contr. Dyn. 35 1080
[17] John L C, Kok L L 2005 IEEE Gu. Contr. Dyn. 28 115
[18] Vasconcelos J F, Elkaim G, Silvestre C 2011 IEEE Aero. El. Syst. 47 1293
[19] Wu Z W, Yao M L, Ma H G 2013 IEEE Veh. Techn. 62 1084
[20] Wertz J R 2012 Spacecraft attitude determination and control (Vol. 73) (Berlin: Springer Science & Business Media) p342-345
[21] Marsden J E, West M 2001 Acta Num. 10 357
[22] Zhao H Y 2007 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [赵海燕 2007 博士学位论文(长春: 吉林大学)]
[23] Pang H, Li J, Chen D 2013 Measurement 46 1600
[24] Alonso R, Shuster M D 2002 IEEE Astro. S. 50 477
[25] Rao C V, Rawlings J B 2002 IEEE Aich. E. 48 97
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