轨道机动航天器的SINS/GPS组合导航系统算法研究
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摘要
近年来,交会对接、空间攻防、星际探测成为航天研究的热点,长时间、大范围的轨道机动成为必然。因此,实现空间机动目标的自主导航,并要求其自主性强、抗干扰、可靠性高,成本低是面向我国航天控制发展的实际提出的挑战性新课题。
SINS导航系统和GPS导航系统各有优缺点,但在误差传播特性上正好是互补的,前者长期稳定性差,但短期稳定性好。所以采用组合导航技术将这两个子导航系统有机地组合起来,克服各自的缺点,互相取长补短,能够实现轨道机动航天器的实时、高精度的导航定位。
对于轨道机动航天器而言,以地理坐标系或地固坐标系为导航坐标系的SINS系统模型并不适用,其导航参数应该是在地心惯性坐标系下的。针对这种情况,本文采用基于地心惯性坐标系的SINS系统,并建立了系统在地心惯性坐标系下的位置、速度、姿态误差传播方程。
将误差传播方程与C/A码GPS接收机的误差方程组合,建立起轨道机动航天器的SINS/GPS组合导航系统模型,利用集中式卡尔曼滤波进行优化处理,并通过数学仿真验证该组合导航算法的可行性。
建立的组合导航模型的状态变量为48维,计算速度慢。利用奇异值分解法进行可观测性/可观测度分析,降维,并对降维后的组合导航系统进行数学仿真,与降维前的仿真结果相比较来验证可观测性/可观测度结果的正确性以及降维后的组合导航系统方案的可行性。
Recent years, Rendezvous and Docking, space attack and defense, space detection is the focus of astronautics research. It results in space vehicle doing long-time and extensive orbit transfer. Autonomous navigation of orbital transfer vehicle which has the characters of independence, high reliability and low cost is an attractive and challenged subject of Chinese astronautics.
The SINS navigation system and GPS system each has its own advantage and disadvantage. But the error propagation property is complementary. Long time stability of fist is bad, but its short time stability is good. So the combined navigation system which can compensate each other can realize real-time and high accuracy of position fixing for orbit transfer vehicle.
For orbit transfer vehicle, it’s not suitable that using geographic coordinate system or terrestrial coordinate system as navigation coordinate system. Its navigation parameters should be in geometric inertial coordinate system. In this study, geometric inertial coordinate system is navigation coordinate system. And the position, velocity and attitude error propagation equation is established in geometric inertial coordinate system.
SINS/GPS navigation system of orbit transfer vehicle is established by making the equation combination with error equation of C/A code GPS receiver. To validate the feasibility of this algorithm through arithmetic simulation by using centralized Kalman filter.
The dimension of state equation is 48. It could cause the lowering of calculated speed. So it’s adopted that using singular value decomposition method to analyze the observability and degree and descend the dimensions of combined navigation system. And make the arithmetic simulation of combined navigation system which the dimensions is descended. Then contrast with undescended navigation system to test and verify the validity of observability and its degree results and the feasibility of combined navigation system which is descended.
SINS导航系统和GPS导航系统各有优缺点,但在误差传播特性上正好是互补的,前者长期稳定性差,但短期稳定性好。所以采用组合导航技术将这两个子导航系统有机地组合起来,克服各自的缺点,互相取长补短,能够实现轨道机动航天器的实时、高精度的导航定位。
对于轨道机动航天器而言,以地理坐标系或地固坐标系为导航坐标系的SINS系统模型并不适用,其导航参数应该是在地心惯性坐标系下的。针对这种情况,本文采用基于地心惯性坐标系的SINS系统,并建立了系统在地心惯性坐标系下的位置、速度、姿态误差传播方程。
将误差传播方程与C/A码GPS接收机的误差方程组合,建立起轨道机动航天器的SINS/GPS组合导航系统模型,利用集中式卡尔曼滤波进行优化处理,并通过数学仿真验证该组合导航算法的可行性。
建立的组合导航模型的状态变量为48维,计算速度慢。利用奇异值分解法进行可观测性/可观测度分析,降维,并对降维后的组合导航系统进行数学仿真,与降维前的仿真结果相比较来验证可观测性/可观测度结果的正确性以及降维后的组合导航系统方案的可行性。
Recent years, Rendezvous and Docking, space attack and defense, space detection is the focus of astronautics research. It results in space vehicle doing long-time and extensive orbit transfer. Autonomous navigation of orbital transfer vehicle which has the characters of independence, high reliability and low cost is an attractive and challenged subject of Chinese astronautics.
The SINS navigation system and GPS system each has its own advantage and disadvantage. But the error propagation property is complementary. Long time stability of fist is bad, but its short time stability is good. So the combined navigation system which can compensate each other can realize real-time and high accuracy of position fixing for orbit transfer vehicle.
For orbit transfer vehicle, it’s not suitable that using geographic coordinate system or terrestrial coordinate system as navigation coordinate system. Its navigation parameters should be in geometric inertial coordinate system. In this study, geometric inertial coordinate system is navigation coordinate system. And the position, velocity and attitude error propagation equation is established in geometric inertial coordinate system.
SINS/GPS navigation system of orbit transfer vehicle is established by making the equation combination with error equation of C/A code GPS receiver. To validate the feasibility of this algorithm through arithmetic simulation by using centralized Kalman filter.
The dimension of state equation is 48. It could cause the lowering of calculated speed. So it’s adopted that using singular value decomposition method to analyze the observability and degree and descend the dimensions of combined navigation system. And make the arithmetic simulation of combined navigation system which the dimensions is descended. Then contrast with undescended navigation system to test and verify the validity of observability and its degree results and the feasibility of combined navigation system which is descended.
引文
1王炯琦,周海银,赵德勇等.基于双星系统的卫星几何学精密定规方法研究.飞行器测控学报. 2005,24(5):27~32
2宋福香,左文辑.近地卫星的GPS自主定轨算法研究.空间科学学报. 2000,20(1):40~46
3杨泗智.卫星组合导航与相对定位方法研究.哈尔滨工业大学硕士学位论文. 2005:1~6
4 L. Shuang, C. Pingyuan, C. Hutao. Autonomous navigation and guidance for landing on asteroids. Aerospace Science and Technology 2006, 10(3):239~247
5王旭东,李果,谢斌.卫星交会的自主导航技术.航天控制. 2002,20(3): 32~38
6李恒年,祝转民,李济生.空间机动目标的跟踪和定位.中国空间科学技术. 2003,23(3):13~17
7周雪梅.低成本SINS/GPS组合导航系统研究.哈尔滨工程大学硕士学位论文. 2003:1~13
8孟焱,孙增. INS/GPS组合导航中实时模糊自适应滤波技术的研究.计算机工程与应用. 2002,38(8):63~65
9张男,王莹,张尔杨. GPS/INS组合导航系统设计及实现方案.遥感技术与应用. 2002,17(2):70~73
10 Peter, Nicolas. Economical aspects of global satellite navigation systems. Comparison between GPS and Galileo. 54th International Astronautical Congress of the International Astronautical Federation. Bremen, Germany, 2003:3061~3070
11 Dave. Gaylor, E. Glenn Lightsey. GPS/INS Kalman Filter Design for Spacecraft Operating in the Proximity of the international Space Station. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, 2003: 88~95
12 X. H. Zhang. Intergration of GPS with a Medium Accuracy IMU for Metre-Level Position. University of Calgary Submitted to the Faculty Graduate Studies in Partial fulfillment of the Requirements for the degree of Master of Science in Engineering. 2003: 25~32
13 FA. Faruqi. Non-linear Mathematical Model for Integrated Global Positioning/Inertial Navigation Systems. Applied Mathematics and Computation.2000 , 115(2): 191~212
14王鹏,张迎春,强文义等.捷联惯导/星敏感器组合导航控制研究.航天控制. 2005,23(5): 31~36
15赵黎平.近地卫星自主轨道确定和控制系统研究.西北工业大学博士学位论文.2002年:1~2
16林来兴.美国“轨道快车”计划中的自主空间交会对接技术.国际太空.2005, (2):23~27
17 Roux, D. A. Paul. The GNC Measurement system for the automated transfer vehicle. 18th International Symposium on Space Flight Dynamics. Munich, Germany. 2004:111~116
18王华.交会对接仿真系统.国防科学技术大学硕士学位论文.2002年:11~13
19 S. Dussy, P. Delaux and P. Simon. Navigation sensors architecture for the Automated Transfer Vehicle. 15th IFAC Symposium on Automatic Control in Aerospace. Bologna, Italy, 2001:32~38
20陈允宗,才满瑞.欧洲自动转移飞行器.导弹与航天运载技术.2006, (1):32~37
21 D. Berthelier. Automated Transfer Vehicle (ATV) critical software GNC validation. First IAASS Conference - Space Safety. Nice, France, 2006:465~476
22 D. Berthelier. Automated Transfer Vehicle proximity flight safety overview. First IAASS Conference - Space Safety. Nice, France, 2005: 89-95
23曹锡生.日本后勤支援飞行器与国际空间站的交会策略.控制工程.1998, (1):47~52
24 Y. Ohkami, I. Kawano. Autonomous rendezvous and docking by engineering testsatellite VII: a challenge of Japan in guidance, navigation and control—Breakwell memorial lecture. the 51st International Astronautical Congress. Rio de Janeiro, Brazil. 2000:1~8
25陈洪,张尔扬.基于紧耦合的GPS/INS全组合导航系统在载人航天中的应用.载人航天. 2005, (4): 21~35
26杨艳娟,卞鸿巍等.一种新的INS/GPS组合导航技术.中国惯性技术学报. 2004,12 (4): 23~26
27张玉堂. SINS/GPS系统组合滤波设计与分析.哈尔滨工业大学硕士学位论文.2003年:2~4
28张国良,李呈良等.弹道导弹INS/GNSS/CNS组合导航系统研究.导弹与航天运载技术. 2004, (2):11~15
29 D. Gaylor. Simulation of an Unaided INS in Orbit. Center for Space Research Ph. D. dissertation, the University of Texas at Austin. 2002: 1~23
30 J. Ali, F. jiancheng. SINS/ANS/GPS Integration using Federated Kalman Filter Based on Optimized Information-Sharing Coefficients. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, AIAA2005-6452. 2005:1~13
31 U. Jaeyong. Relative Navigation and Attitude Determination Using a GPS/INS Integrated System Near the International Space Station. Ph. D. dissertation, University of Texas at Austin. 2001:65~71
32 K. Braden, C. Browning. Integrated Inertial Navigation System/Global Position System (INS/GPS) for automatic space return vehicle. Digital Avionics Systems Conference. Virginia, 1990:409~414
33 L. Qin, L. Li. Error Analysis and Compensation of Strapdown Inertial Navigation System. Journal of Beijing Institute of Technology. 2002, 11(2):117~120
34 H. Xiufeng. Analysis of Lever Arm Effects in GPS/IMU Integration System. Transaction of Nanjing University of Aeronautics & Astronautics. 2002, 19(1): 59~63
35何秀凤,袁信.平台惯导系统中杆臂效应误差的研究和分析.航天控制. 1995,13 (2):22~30
36 B. Friedland. Analysis Strapdown Navigation Using Quaternions. IEEE Transactions on Aerospace and electronic system. 1978, (14)5:764~768
37 T. N. Upadhyay, S. Cotterill, A. W. Deaton. Autonomous GPS/INS Navigation Experiments for Space Transfer Vehicle. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(3):772~784
38 E. Mooij, Q. Chu. IMU/GPS Integrated Navigation System for a Winged Re-entry Vehicle. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada, AIAA 2001-4169. 2001:1~11
39 E. Mooij, Q. Chu. Tightly-coupled IMU/GPS Re-entry Navigation System.AIAA Guidance, Navigation, and Control Conference and Exhibit. Monterey, California, AIAA 2002-5005. 2002:1~11
40 J. Vasconcelos, P. Oliveira, Carlos Silvestre. Inertial Navigation System Aided by GPS and Selective Frequency Contents of Vector Measurements. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, AIAA 2005-6057. 2005:1~15
41 Y. Xiaokui, Y. Jianping. Study on Low-cost GPS/DMU Integrated Navigation System. AIAA Guidance, Navigation, and Control Conference and Exhibit. Monterey, California, AIAA 2002-4827. 2002:1~4
42秦永元,张洪钺,汪淑华.卡尔曼滤波与组合导航原理.西北工业大学出版社,1998:243~314
43房建成,宁晓琳,田玉龙.航天器自主天文导航原理与方法.国防工业出版社,2006:182~185
44 D. G. Meskin, B. Itzhack, Observability analysis of piece-wise constant systems. Application to inertial navigation in-flight alignment IEEE Transactions on Aerospace and Electronic Systems. 1992, 28(4):1068-1075
45 T. Zhang, B. Wang. Observability of Inertial Navigation System. Journal of Beijing Institute of Technology. 2005, 14 (3):269~272
46 H. Rotstein, J. Reiner, A. Ben-Ishai. Kalman Filter Mechanization in INS/Seeker Fusion and Observability Analysis. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada, AIAA 2001-4402. 2001:1~14
2宋福香,左文辑.近地卫星的GPS自主定轨算法研究.空间科学学报. 2000,20(1):40~46
3杨泗智.卫星组合导航与相对定位方法研究.哈尔滨工业大学硕士学位论文. 2005:1~6
4 L. Shuang, C. Pingyuan, C. Hutao. Autonomous navigation and guidance for landing on asteroids. Aerospace Science and Technology 2006, 10(3):239~247
5王旭东,李果,谢斌.卫星交会的自主导航技术.航天控制. 2002,20(3): 32~38
6李恒年,祝转民,李济生.空间机动目标的跟踪和定位.中国空间科学技术. 2003,23(3):13~17
7周雪梅.低成本SINS/GPS组合导航系统研究.哈尔滨工程大学硕士学位论文. 2003:1~13
8孟焱,孙增. INS/GPS组合导航中实时模糊自适应滤波技术的研究.计算机工程与应用. 2002,38(8):63~65
9张男,王莹,张尔杨. GPS/INS组合导航系统设计及实现方案.遥感技术与应用. 2002,17(2):70~73
10 Peter, Nicolas. Economical aspects of global satellite navigation systems. Comparison between GPS and Galileo. 54th International Astronautical Congress of the International Astronautical Federation. Bremen, Germany, 2003:3061~3070
11 Dave. Gaylor, E. Glenn Lightsey. GPS/INS Kalman Filter Design for Spacecraft Operating in the Proximity of the international Space Station. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, 2003: 88~95
12 X. H. Zhang. Intergration of GPS with a Medium Accuracy IMU for Metre-Level Position. University of Calgary Submitted to the Faculty Graduate Studies in Partial fulfillment of the Requirements for the degree of Master of Science in Engineering. 2003: 25~32
13 FA. Faruqi. Non-linear Mathematical Model for Integrated Global Positioning/Inertial Navigation Systems. Applied Mathematics and Computation.2000 , 115(2): 191~212
14王鹏,张迎春,强文义等.捷联惯导/星敏感器组合导航控制研究.航天控制. 2005,23(5): 31~36
15赵黎平.近地卫星自主轨道确定和控制系统研究.西北工业大学博士学位论文.2002年:1~2
16林来兴.美国“轨道快车”计划中的自主空间交会对接技术.国际太空.2005, (2):23~27
17 Roux, D. A. Paul. The GNC Measurement system for the automated transfer vehicle. 18th International Symposium on Space Flight Dynamics. Munich, Germany. 2004:111~116
18王华.交会对接仿真系统.国防科学技术大学硕士学位论文.2002年:11~13
19 S. Dussy, P. Delaux and P. Simon. Navigation sensors architecture for the Automated Transfer Vehicle. 15th IFAC Symposium on Automatic Control in Aerospace. Bologna, Italy, 2001:32~38
20陈允宗,才满瑞.欧洲自动转移飞行器.导弹与航天运载技术.2006, (1):32~37
21 D. Berthelier. Automated Transfer Vehicle (ATV) critical software GNC validation. First IAASS Conference - Space Safety. Nice, France, 2006:465~476
22 D. Berthelier. Automated Transfer Vehicle proximity flight safety overview. First IAASS Conference - Space Safety. Nice, France, 2005: 89-95
23曹锡生.日本后勤支援飞行器与国际空间站的交会策略.控制工程.1998, (1):47~52
24 Y. Ohkami, I. Kawano. Autonomous rendezvous and docking by engineering testsatellite VII: a challenge of Japan in guidance, navigation and control—Breakwell memorial lecture. the 51st International Astronautical Congress. Rio de Janeiro, Brazil. 2000:1~8
25陈洪,张尔扬.基于紧耦合的GPS/INS全组合导航系统在载人航天中的应用.载人航天. 2005, (4): 21~35
26杨艳娟,卞鸿巍等.一种新的INS/GPS组合导航技术.中国惯性技术学报. 2004,12 (4): 23~26
27张玉堂. SINS/GPS系统组合滤波设计与分析.哈尔滨工业大学硕士学位论文.2003年:2~4
28张国良,李呈良等.弹道导弹INS/GNSS/CNS组合导航系统研究.导弹与航天运载技术. 2004, (2):11~15
29 D. Gaylor. Simulation of an Unaided INS in Orbit. Center for Space Research Ph. D. dissertation, the University of Texas at Austin. 2002: 1~23
30 J. Ali, F. jiancheng. SINS/ANS/GPS Integration using Federated Kalman Filter Based on Optimized Information-Sharing Coefficients. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, AIAA2005-6452. 2005:1~13
31 U. Jaeyong. Relative Navigation and Attitude Determination Using a GPS/INS Integrated System Near the International Space Station. Ph. D. dissertation, University of Texas at Austin. 2001:65~71
32 K. Braden, C. Browning. Integrated Inertial Navigation System/Global Position System (INS/GPS) for automatic space return vehicle. Digital Avionics Systems Conference. Virginia, 1990:409~414
33 L. Qin, L. Li. Error Analysis and Compensation of Strapdown Inertial Navigation System. Journal of Beijing Institute of Technology. 2002, 11(2):117~120
34 H. Xiufeng. Analysis of Lever Arm Effects in GPS/IMU Integration System. Transaction of Nanjing University of Aeronautics & Astronautics. 2002, 19(1): 59~63
35何秀凤,袁信.平台惯导系统中杆臂效应误差的研究和分析.航天控制. 1995,13 (2):22~30
36 B. Friedland. Analysis Strapdown Navigation Using Quaternions. IEEE Transactions on Aerospace and electronic system. 1978, (14)5:764~768
37 T. N. Upadhyay, S. Cotterill, A. W. Deaton. Autonomous GPS/INS Navigation Experiments for Space Transfer Vehicle. IEEE Transactions on Aerospace and Electronic Systems. 1993, 29(3):772~784
38 E. Mooij, Q. Chu. IMU/GPS Integrated Navigation System for a Winged Re-entry Vehicle. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada, AIAA 2001-4169. 2001:1~11
39 E. Mooij, Q. Chu. Tightly-coupled IMU/GPS Re-entry Navigation System.AIAA Guidance, Navigation, and Control Conference and Exhibit. Monterey, California, AIAA 2002-5005. 2002:1~11
40 J. Vasconcelos, P. Oliveira, Carlos Silvestre. Inertial Navigation System Aided by GPS and Selective Frequency Contents of Vector Measurements. AIAA Guidance, Navigation, and Control Conference and Exhibit. San Francisco, California, AIAA 2005-6057. 2005:1~15
41 Y. Xiaokui, Y. Jianping. Study on Low-cost GPS/DMU Integrated Navigation System. AIAA Guidance, Navigation, and Control Conference and Exhibit. Monterey, California, AIAA 2002-4827. 2002:1~4
42秦永元,张洪钺,汪淑华.卡尔曼滤波与组合导航原理.西北工业大学出版社,1998:243~314
43房建成,宁晓琳,田玉龙.航天器自主天文导航原理与方法.国防工业出版社,2006:182~185
44 D. G. Meskin, B. Itzhack, Observability analysis of piece-wise constant systems. Application to inertial navigation in-flight alignment IEEE Transactions on Aerospace and Electronic Systems. 1992, 28(4):1068-1075
45 T. Zhang, B. Wang. Observability of Inertial Navigation System. Journal of Beijing Institute of Technology. 2005, 14 (3):269~272
46 H. Rotstein, J. Reiner, A. Ben-Ishai. Kalman Filter Mechanization in INS/Seeker Fusion and Observability Analysis. AIAA Guidance, Navigation, and Control Conference and Exhibit. Montreal, Canada, AIAA 2001-4402. 2001:1~14
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