基于陀螺和星敏感器的卫星姿态确定研究
|
摘要
卫星姿态确定系统是卫星姿态控制系统中的重要组成部分,其精度是影响姿态控制系统精度水平的决定性因素。姿态确定的精度不仅取决于姿态测量系统硬件配置的性能与精度,还与所采用的姿态确定算法密切相关。本文针对基于矢量观测的三轴稳定对地定向卫星的姿态确定问题,从理论和应用两个方面对卫星姿态确定的非线性滤波技术作了深入和细致的研究。并且针对采用扩展卡尔曼滤波(Extended Kalman Filter,简称EKF)确定姿态的方法的不足,提出了改进方案。主要完成了以下几方面的工作:
首先,对姿态敏感器建立准确的测量模型,用四元数的方法建立卫星姿态确定模型,并采用EKF姿态确定算法,对得到的卫星姿态误差和陀螺漂移误差信息进行信息融合和相应的修正。当卫星的姿态角速度较小时,采用三轴解耦的扩展卡尔曼滤波(Uncoupled EKF,简称UEKF)算法,通过对滤波器的状态方程作近似处理,状态方程从每个轴上解耦,因此卡尔曼滤波增益的数量从18个降到了6个。EKF的核心是对卡尔曼滤波增益K的递推计算,定常增益的卡尔曼滤波(Constant gain KF,简称CGKF)用一常值矩阵代替对此增益的递推计算,这样不用对状态方差阵进行递推更新,增强了实时性。对EKF、UEKF和CGKF进行了仿真分析比较,结果表明在一定条件下,都能达到较高的滤波精度,使测量精度大幅提高;并且后两种滤波器在保证精度的同时,大大减少了计算量。
其次,在不能准确建立陀螺的测量模型,以及敏感器测量值的先验统计知识未知的情况下,研究了基于最小模型误差(Minimum Model Error,简称MME)准则的非线性预测滤波方法。该方法以星敏感器输出的姿态四元数信息直接作为观测方程,对由陀螺漂移造成的姿态角速度误差进行了预测和估计,从而得到较为准确的三轴稳定卫星的姿态信息。另外,还提出了一种改进的预测滤波算法,该算法将偏差四元数作为测量误差引入指标函数,估计出系统模型误差,从而估计出卫星的姿态角和姿态角速度。仿真结果和计算量统计表明,以上两种算法可以对卫星姿态角以及姿态角速度误差实现有效的估计和补偿,同时与EKF及两种简化的EKF算法相比计算量有不同程度的降低。
最后,介绍了利用RT-LAB建立包括一台宿主机和两台目标机的卫星GNC(Guidance, Navigation and Control)系统实时半物理仿真平台的方法。并搭建了基于RT-LAB的超实时仿真平台,该试验平台克服了在试验过程中由于软件编程带来的瓶颈问题。对姿态确定算法进行了超实时仿真,仿真结果表明算法的实时性符合要求。该平台不但适用于系统的全数学实时仿真,扩展相应硬件后还可用于卫星GNC系统的半物理实时仿真。
Satellite attitude determination system is an important part of the attitude control system (ACS), and its accuracy is the key factor for the stabilization of the ACS. In general, the estimation accuracy not only lies on the performance of the hardware of the measurement devices, such as star sensor, gyro, etc, but also the attitude estimation algorithm. In this dissertation, the nonlinear filter methods are deeply investigated on theory and application for the attitude estimation from vector observations of the three-axis stabilized satellite attitude measurement system. Furthermore, to avoid the shortages existed in extended Kalman filter (EKF), several improved schemes are presented. The main contents of this thesis are as follows.
Firstly, the model used for the satellite determination is set up by the accurate attitude sensor models and using quaternion. EKF algorithm is applied to modify the estimation error of satellite attitude and estimation error of gyroscope drift and information fusion. When the body rates are small, the state equation of the filter can be approximately disposed by using UEKF algorithm. The equations are uncoupled from the three-axis, as a consequence, the number of Kalman filter gains in this algorithm decreases from 18 to 6. The intention of EKF algorithm is the computation of Kalman filter gains. CGKF using a constant matrix to replace the computation of Kalman filter gains, no need to perform the calculation of state error covariance, with the obvious savings in computational effort. Finally, through analysis and comparison from the simulaton results, the above three algorithms all can gauge the performance in some conditions. Moreover, the last two algorithms can reduce large number of computation.
When we can’t get the exact measurement model of the gyro, or don’t know the pre-examination knowledge about the sensors, an approach of nonlinear predictive filter based on minimum model error (MME) rule is proposed. This approach uses the quaternion which output from star-sensor to be an observation equation, forecasted and estimated the angle velocity error caused by gyro drift, then get more accurate three-axis attitude information of satellite. In addition, a modified algorithm is presented. By incorporating error quaternion into the cost function, we can estimate the system model error, and therefore the accurate attitude and angular velocities are acquired. The simulation result and the statistic of computation shows that the two algorithms all can estimate the attitude angle and compensate the error of attitude angle velocity, and compared with above, the number of computation has reduced in different degree.
At last, this dissertation introduces a method of building a real-time simulation platform for satellite Guidance, Navigation and Control (GNC) system, including one host PC and two target PCs based on RT-LAB. And a super real-time simulation platform is put up to solve the bottleneck problem, which bring from software programme in the system examination. The super real-time simulation results show that the attitudue determination algorithm satisfy the real-time characteristic. This method is not only suitable for the digital real-time simulation test, but also can be extended to the semi-phsical real-time simulation test of satellite GNC system by adding some corresponding hardwares.
首先,对姿态敏感器建立准确的测量模型,用四元数的方法建立卫星姿态确定模型,并采用EKF姿态确定算法,对得到的卫星姿态误差和陀螺漂移误差信息进行信息融合和相应的修正。当卫星的姿态角速度较小时,采用三轴解耦的扩展卡尔曼滤波(Uncoupled EKF,简称UEKF)算法,通过对滤波器的状态方程作近似处理,状态方程从每个轴上解耦,因此卡尔曼滤波增益的数量从18个降到了6个。EKF的核心是对卡尔曼滤波增益K的递推计算,定常增益的卡尔曼滤波(Constant gain KF,简称CGKF)用一常值矩阵代替对此增益的递推计算,这样不用对状态方差阵进行递推更新,增强了实时性。对EKF、UEKF和CGKF进行了仿真分析比较,结果表明在一定条件下,都能达到较高的滤波精度,使测量精度大幅提高;并且后两种滤波器在保证精度的同时,大大减少了计算量。
其次,在不能准确建立陀螺的测量模型,以及敏感器测量值的先验统计知识未知的情况下,研究了基于最小模型误差(Minimum Model Error,简称MME)准则的非线性预测滤波方法。该方法以星敏感器输出的姿态四元数信息直接作为观测方程,对由陀螺漂移造成的姿态角速度误差进行了预测和估计,从而得到较为准确的三轴稳定卫星的姿态信息。另外,还提出了一种改进的预测滤波算法,该算法将偏差四元数作为测量误差引入指标函数,估计出系统模型误差,从而估计出卫星的姿态角和姿态角速度。仿真结果和计算量统计表明,以上两种算法可以对卫星姿态角以及姿态角速度误差实现有效的估计和补偿,同时与EKF及两种简化的EKF算法相比计算量有不同程度的降低。
最后,介绍了利用RT-LAB建立包括一台宿主机和两台目标机的卫星GNC(Guidance, Navigation and Control)系统实时半物理仿真平台的方法。并搭建了基于RT-LAB的超实时仿真平台,该试验平台克服了在试验过程中由于软件编程带来的瓶颈问题。对姿态确定算法进行了超实时仿真,仿真结果表明算法的实时性符合要求。该平台不但适用于系统的全数学实时仿真,扩展相应硬件后还可用于卫星GNC系统的半物理实时仿真。
Satellite attitude determination system is an important part of the attitude control system (ACS), and its accuracy is the key factor for the stabilization of the ACS. In general, the estimation accuracy not only lies on the performance of the hardware of the measurement devices, such as star sensor, gyro, etc, but also the attitude estimation algorithm. In this dissertation, the nonlinear filter methods are deeply investigated on theory and application for the attitude estimation from vector observations of the three-axis stabilized satellite attitude measurement system. Furthermore, to avoid the shortages existed in extended Kalman filter (EKF), several improved schemes are presented. The main contents of this thesis are as follows.
Firstly, the model used for the satellite determination is set up by the accurate attitude sensor models and using quaternion. EKF algorithm is applied to modify the estimation error of satellite attitude and estimation error of gyroscope drift and information fusion. When the body rates are small, the state equation of the filter can be approximately disposed by using UEKF algorithm. The equations are uncoupled from the three-axis, as a consequence, the number of Kalman filter gains in this algorithm decreases from 18 to 6. The intention of EKF algorithm is the computation of Kalman filter gains. CGKF using a constant matrix to replace the computation of Kalman filter gains, no need to perform the calculation of state error covariance, with the obvious savings in computational effort. Finally, through analysis and comparison from the simulaton results, the above three algorithms all can gauge the performance in some conditions. Moreover, the last two algorithms can reduce large number of computation.
When we can’t get the exact measurement model of the gyro, or don’t know the pre-examination knowledge about the sensors, an approach of nonlinear predictive filter based on minimum model error (MME) rule is proposed. This approach uses the quaternion which output from star-sensor to be an observation equation, forecasted and estimated the angle velocity error caused by gyro drift, then get more accurate three-axis attitude information of satellite. In addition, a modified algorithm is presented. By incorporating error quaternion into the cost function, we can estimate the system model error, and therefore the accurate attitude and angular velocities are acquired. The simulation result and the statistic of computation shows that the two algorithms all can estimate the attitude angle and compensate the error of attitude angle velocity, and compared with above, the number of computation has reduced in different degree.
At last, this dissertation introduces a method of building a real-time simulation platform for satellite Guidance, Navigation and Control (GNC) system, including one host PC and two target PCs based on RT-LAB. And a super real-time simulation platform is put up to solve the bottleneck problem, which bring from software programme in the system examination. The super real-time simulation results show that the attitudue determination algorithm satisfy the real-time characteristic. This method is not only suitable for the digital real-time simulation test, but also can be extended to the semi-phsical real-time simulation test of satellite GNC system by adding some corresponding hardwares.
引文
1施少范.国外对地观测卫星高精度姿态控制系统研究.上海航天, 2000,6: 49~53
2 G. M. Brown, S. A. Johnson. An Overview of the Fault Protection Design for the Attitude Control Subsystem of the Cassini Spacecraft. Proceedings of American Control Conference. Philadelphia, Pennsylvania, June 1998:884~898
3 W. D. Deininger, et al. Space Technology Three: Mission Overview and Spacecraft Concept Description. Acta Astronautica. 2003,52:455~465
4姜雪原.卫星姿态确定及敏感器误差修正的滤波算法研究.哈尔滨工业大学工学博士学位论文. 2006,2~6
5杨大明.空间飞行器姿态控制系统.哈尔滨工业大学出版社, 2000:100~158
6钱勇.高精度三轴稳定卫星姿态确定和控制系统研究.西北工业大学工学博士学位论文. 2002:94~96
7杨锋,周宗锡,刘曙光.基于星敏感器/光纤陀螺的卫星定姿算法.控制工程. 2006,13(4):374~376
8周山,王战军,孙艳华等.陀螺/星敏感器组合技术在卫星姿态确定系统中的应用[J].情报指挥控制系统与仿真技术. 2005,27(2):93~96
9杨锋.三轴稳定卫星姿态确定及控制系统研究.西北工业大学工学硕士学位论文. 2006: 32~45
10刘志俭,吴美平,胡小平.多敏感器卫星姿态确定的卡尔曼滤波器设计.国防科技大学学报. 2001,23(6): 28~32
11廖晖,周军,周凤崎.卫星正常模式姿态确定算法研究.航天控制. 2001,(1):17~22
12潘旺华,廖瑛,赵健康.基于红外地平仪的航天器姿态确定技术.计算机仿真. 2005,22(9): 40~43
13 John L. Crassidis, F. Landis Markley. Predictive Filtering for Attitude Estimation without Rate Sensors. Journal of Guidance, Control, and Dynamics. 1997, 20(3): 522~527
14刘一武,陈义庆.星敏感器测量模型及其在卫星姿态确定系统中的应用.宇航学报.2003,24(2): 162~167
15段方,刘建业,李荣冰.基于平淡卡尔曼滤波器的微小卫星姿态确定算法.上海交通大学学报. 2005,39(11):1899~1903
16姚静,易东云,聂鹏程等.三轴稳定卫星的星敏感器对地定姿精度分析.飞行器测控学报. 2006,25(5):27~31
17 F.L.Markley, D.Mortari. Quaternion Attitude Estimation Using Vector Observations. The Journal of the Astronautical Sciences, 2000,48(2,3):359~380
18 M. D. Shuster. Apptoximate Algorithms for Fast Optimal Attitude Computation. AIAA 78-1249, AIAA Guidance and Control Conference, Palo Alto, CA, 1978
19 M. D. Shuster, S. D. Oh. Three-Axis Attitude Determination from Vector Observations. Journal of Guidance and Control, 1981, 4(1): 70~77
20 F. L. Markley. Attitude Determination Using Vector Observations: A Fast Optimal Matrix Algorithm. The Journal of the Astronautical Sciences, 1993, 41(2): 261~280
21 F. L. Markley. Attitude Determination Using Vector Observations and the Singular Value Decomposition. The journal of the Astronautical Sciences, 1988,36(3):245~258
22 I. Y. Bar-Itzhack, P. Y. Montgomery, J. C. Garrick. Algorithms for Attitude Determination Using the Global Positioning Systerm. Journal of Guidance, Control, and Dynamics, 1998, 21(6): 846~852
23 J. L. Crassidis, F. L. Markley. New Algorithm for Attitude Determination Using Global Positioning System Signals. Journal of Guidance, Control, and Dynamics, 1997, 20(5): 891~896
24 F. C. Park, J. Kim, C. Kee. Geometric Descent Algorithms for Attitude Determination Using the Global Positioning System. Journal of Guidance, Control, and Dynamics, 2000, 23(1): 26~33
25 A. Nadler, I. Y. Bar-Itzhack, H. Weiss. Iterative Algorihms for Attitude Estimation Using Global Positioning System Phase Measurements. Journal of Guidance, Control, and Dynamics, 2001, 24(5): 983~990
26刘良栋等.卫星控制系统仿真技术.宇航出版社, 2003:34~45
27 A. H. Jazwinski. Stochastic Processes and Filtering Theory. New York: Academic Press, 1970: 142~360
28 R. E. Kalman. A New Approach to Linear Filtering and Prediction Problem. Journal of Basic Eng. (ASME). 1960, 82: 35~46
29 S. M. Joshi. On Attitude Estimation Schemes for Fine-Pointing Control. IEEETrans. on Aerospace and Electronic. 1978, 14(2): 258~265
30 T. W. Flatley, J. K. Forden, et al. On-board Attitude Determination and Control Algorithms for SAMPEX. Proc. of Flight Mechanics/Estimation Theory Symposium. NASA CP 3102, NASA Goddard Space Flight Center, Greenbelt, MD, 1990: 379~398
31 Y. J. Yoon, J. W. Choi, et al. An Attitude Determination Algorithm for a Spacecraft Using Nonlinear Filter. KSME International Journal. 1999, 13(2): 130~143
32 I. Y. Bar-itzhack, J. Oshman. Attitude Determination from Vector Observations: Quaternion Estimation. IEEE Trans. on AES. 1985, 21(1): 128~135
33 Thompson, I. C. and Quasuis, G. R.,”Attitude Determination for the P80-1 Satellite”AIAA Paper No.80-001, AAS Guidance and Control Conference, Keystone, CO,1980:17~21,
34 Lefferts, E. J., Markleyy, F. L., and Shuster, M. D.,”Kalman Filtering for Spacecraft Attitude Estimation”Journal of Guidance and Control, 1982, 5(5):417~429
35 Glenn Creamer, Spacecraft Attitude Determination Using Gyros and Quaternion Measurements. The Journal of the Astronautical Sciences, 1996, 44(3):357~371
36西蒙.赫金.自适应滤波器原理.第四版.郑宝玉等译.电子工业出版社, 2003: 613~617
37武廷鹏,尤政,任大海.采样Kalman滤波器在天文卫星定姿滤波中的应用.清华大学学报(自然科学版). 2003,43(8): 1013~1016
38 Ping Lu. Optimal predictive control of continuous nonlinear systems. International Journal of Control, 1995,62(3): 633~649
39 John L. Crassidis, F. Landis Markley. Predictie Filtering for Nonlinear System. Journal of Guidance, Control, and Dynamics, 1997,20(3): 566~572
40廖晖,周凤岐等.利用预测滤波法估计小卫星姿态角速度.西北工业大学学报. 2001, 19(1): 84~87
41屠善澄.卫星姿态动力学与控制.北京:宇航出版社,1998: 22~45
42 Joshua Cemenska. Sensor Modeling and Kalman Filtering Applied to Satellite Attetude Determination. Master’s thesis, The University of California at Berkeley, 2004:11~16
43 J. L. Crassidis. Sigma-Point Kalman Filtering for Integrated GPS and InertialNavigation. AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, 2005, AIAA-2005-6052
44何炬.国外天文导航技术发展综述.舰船科学技术. 2005,27(5):91~96
45李勇,魏春岭.卫星自主导航技术发展综述.航天控制. 2002,(2):70~74
46朱庆华,李英波.基于陀螺和四元数的EKF卫星姿态确定算法.上海航天[J]. 2005,(4): 1~5
47 Henry D. Travis. Attitude Determination Using Star Tracker Data with Kalman Filters. Master’s thesis, Naval Postgraduate School,2001:9~11
48林玉荣,邓正隆.基于模型误差确定卫星姿态的预测滤波算法.宇航学报. 2001, 22(1): 79~83
49林玉荣,邓正隆.基于MME准则估计卫星姿态的非线性滤波算法.哈尔滨工业大学学报. 2002,34(1): 14~18
50朱庆华,李英波.基于星敏感器四元数的卫星角速度预测滤波算法.上海航天. 2005,5: 14~18
51孙兆伟,耿云海,何平.小卫星大角度姿态机动研究及半实物仿真验证.航天控制. 2000, 2: 28~33
52王宁强,刘向东,陈振等.基于MATLAB的卫星姿态控制半物理实时仿真平台.系统仿真学报. 2005, 17(7): 1617~1620
53 Zhou Yijun. RT-LAB Training for 812. PowerPoint presentation, Dec. 2006. www.opal-rt.com
2 G. M. Brown, S. A. Johnson. An Overview of the Fault Protection Design for the Attitude Control Subsystem of the Cassini Spacecraft. Proceedings of American Control Conference. Philadelphia, Pennsylvania, June 1998:884~898
3 W. D. Deininger, et al. Space Technology Three: Mission Overview and Spacecraft Concept Description. Acta Astronautica. 2003,52:455~465
4姜雪原.卫星姿态确定及敏感器误差修正的滤波算法研究.哈尔滨工业大学工学博士学位论文. 2006,2~6
5杨大明.空间飞行器姿态控制系统.哈尔滨工业大学出版社, 2000:100~158
6钱勇.高精度三轴稳定卫星姿态确定和控制系统研究.西北工业大学工学博士学位论文. 2002:94~96
7杨锋,周宗锡,刘曙光.基于星敏感器/光纤陀螺的卫星定姿算法.控制工程. 2006,13(4):374~376
8周山,王战军,孙艳华等.陀螺/星敏感器组合技术在卫星姿态确定系统中的应用[J].情报指挥控制系统与仿真技术. 2005,27(2):93~96
9杨锋.三轴稳定卫星姿态确定及控制系统研究.西北工业大学工学硕士学位论文. 2006: 32~45
10刘志俭,吴美平,胡小平.多敏感器卫星姿态确定的卡尔曼滤波器设计.国防科技大学学报. 2001,23(6): 28~32
11廖晖,周军,周凤崎.卫星正常模式姿态确定算法研究.航天控制. 2001,(1):17~22
12潘旺华,廖瑛,赵健康.基于红外地平仪的航天器姿态确定技术.计算机仿真. 2005,22(9): 40~43
13 John L. Crassidis, F. Landis Markley. Predictive Filtering for Attitude Estimation without Rate Sensors. Journal of Guidance, Control, and Dynamics. 1997, 20(3): 522~527
14刘一武,陈义庆.星敏感器测量模型及其在卫星姿态确定系统中的应用.宇航学报.2003,24(2): 162~167
15段方,刘建业,李荣冰.基于平淡卡尔曼滤波器的微小卫星姿态确定算法.上海交通大学学报. 2005,39(11):1899~1903
16姚静,易东云,聂鹏程等.三轴稳定卫星的星敏感器对地定姿精度分析.飞行器测控学报. 2006,25(5):27~31
17 F.L.Markley, D.Mortari. Quaternion Attitude Estimation Using Vector Observations. The Journal of the Astronautical Sciences, 2000,48(2,3):359~380
18 M. D. Shuster. Apptoximate Algorithms for Fast Optimal Attitude Computation. AIAA 78-1249, AIAA Guidance and Control Conference, Palo Alto, CA, 1978
19 M. D. Shuster, S. D. Oh. Three-Axis Attitude Determination from Vector Observations. Journal of Guidance and Control, 1981, 4(1): 70~77
20 F. L. Markley. Attitude Determination Using Vector Observations: A Fast Optimal Matrix Algorithm. The Journal of the Astronautical Sciences, 1993, 41(2): 261~280
21 F. L. Markley. Attitude Determination Using Vector Observations and the Singular Value Decomposition. The journal of the Astronautical Sciences, 1988,36(3):245~258
22 I. Y. Bar-Itzhack, P. Y. Montgomery, J. C. Garrick. Algorithms for Attitude Determination Using the Global Positioning Systerm. Journal of Guidance, Control, and Dynamics, 1998, 21(6): 846~852
23 J. L. Crassidis, F. L. Markley. New Algorithm for Attitude Determination Using Global Positioning System Signals. Journal of Guidance, Control, and Dynamics, 1997, 20(5): 891~896
24 F. C. Park, J. Kim, C. Kee. Geometric Descent Algorithms for Attitude Determination Using the Global Positioning System. Journal of Guidance, Control, and Dynamics, 2000, 23(1): 26~33
25 A. Nadler, I. Y. Bar-Itzhack, H. Weiss. Iterative Algorihms for Attitude Estimation Using Global Positioning System Phase Measurements. Journal of Guidance, Control, and Dynamics, 2001, 24(5): 983~990
26刘良栋等.卫星控制系统仿真技术.宇航出版社, 2003:34~45
27 A. H. Jazwinski. Stochastic Processes and Filtering Theory. New York: Academic Press, 1970: 142~360
28 R. E. Kalman. A New Approach to Linear Filtering and Prediction Problem. Journal of Basic Eng. (ASME). 1960, 82: 35~46
29 S. M. Joshi. On Attitude Estimation Schemes for Fine-Pointing Control. IEEETrans. on Aerospace and Electronic. 1978, 14(2): 258~265
30 T. W. Flatley, J. K. Forden, et al. On-board Attitude Determination and Control Algorithms for SAMPEX. Proc. of Flight Mechanics/Estimation Theory Symposium. NASA CP 3102, NASA Goddard Space Flight Center, Greenbelt, MD, 1990: 379~398
31 Y. J. Yoon, J. W. Choi, et al. An Attitude Determination Algorithm for a Spacecraft Using Nonlinear Filter. KSME International Journal. 1999, 13(2): 130~143
32 I. Y. Bar-itzhack, J. Oshman. Attitude Determination from Vector Observations: Quaternion Estimation. IEEE Trans. on AES. 1985, 21(1): 128~135
33 Thompson, I. C. and Quasuis, G. R.,”Attitude Determination for the P80-1 Satellite”AIAA Paper No.80-001, AAS Guidance and Control Conference, Keystone, CO,1980:17~21,
34 Lefferts, E. J., Markleyy, F. L., and Shuster, M. D.,”Kalman Filtering for Spacecraft Attitude Estimation”Journal of Guidance and Control, 1982, 5(5):417~429
35 Glenn Creamer, Spacecraft Attitude Determination Using Gyros and Quaternion Measurements. The Journal of the Astronautical Sciences, 1996, 44(3):357~371
36西蒙.赫金.自适应滤波器原理.第四版.郑宝玉等译.电子工业出版社, 2003: 613~617
37武廷鹏,尤政,任大海.采样Kalman滤波器在天文卫星定姿滤波中的应用.清华大学学报(自然科学版). 2003,43(8): 1013~1016
38 Ping Lu. Optimal predictive control of continuous nonlinear systems. International Journal of Control, 1995,62(3): 633~649
39 John L. Crassidis, F. Landis Markley. Predictie Filtering for Nonlinear System. Journal of Guidance, Control, and Dynamics, 1997,20(3): 566~572
40廖晖,周凤岐等.利用预测滤波法估计小卫星姿态角速度.西北工业大学学报. 2001, 19(1): 84~87
41屠善澄.卫星姿态动力学与控制.北京:宇航出版社,1998: 22~45
42 Joshua Cemenska. Sensor Modeling and Kalman Filtering Applied to Satellite Attetude Determination. Master’s thesis, The University of California at Berkeley, 2004:11~16
43 J. L. Crassidis. Sigma-Point Kalman Filtering for Integrated GPS and InertialNavigation. AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, 2005, AIAA-2005-6052
44何炬.国外天文导航技术发展综述.舰船科学技术. 2005,27(5):91~96
45李勇,魏春岭.卫星自主导航技术发展综述.航天控制. 2002,(2):70~74
46朱庆华,李英波.基于陀螺和四元数的EKF卫星姿态确定算法.上海航天[J]. 2005,(4): 1~5
47 Henry D. Travis. Attitude Determination Using Star Tracker Data with Kalman Filters. Master’s thesis, Naval Postgraduate School,2001:9~11
48林玉荣,邓正隆.基于模型误差确定卫星姿态的预测滤波算法.宇航学报. 2001, 22(1): 79~83
49林玉荣,邓正隆.基于MME准则估计卫星姿态的非线性滤波算法.哈尔滨工业大学学报. 2002,34(1): 14~18
50朱庆华,李英波.基于星敏感器四元数的卫星角速度预测滤波算法.上海航天. 2005,5: 14~18
51孙兆伟,耿云海,何平.小卫星大角度姿态机动研究及半实物仿真验证.航天控制. 2000, 2: 28~33
52王宁强,刘向东,陈振等.基于MATLAB的卫星姿态控制半物理实时仿真平台.系统仿真学报. 2005, 17(7): 1617~1620
53 Zhou Yijun. RT-LAB Training for 812. PowerPoint presentation, Dec. 2006. www.opal-rt.com