基于光学测量的相对导航方法及在星际着陆中的应用研究
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摘要
探测器在行星表面实现自主的精确着陆(Pin-point landing)是一项富于挑战性的任务,探测器必须具备精确相对导航的能力。传统的基于航位推算的星际着陆导航方式无法满足未来星际精确着陆任务对着陆精度的要求,因此有必要发展新一代基于光学测量的星际着陆相对导航方法。
本学位论文结合“十五”863计划项目——“深空探测自主技术与仿真演示系统”,从光学测量相对导航方法和软着陆小行星自主导航半物理仿真两方面出发,对基于光学测量的相对导航方法及其在星际精确着陆任务中的应用进行了深入系统的研究。论文的主要研究内容包括:
首先,基于探测器和目标天体表面特征点之间的矢量观测,提出了一种基于矢量测量的自主相对导航方法。通过光学导航相机和激光测距仪组合测量输出构建探测器到三个非共线的特征点之间矢量,进而构建特征点固连坐标系和定义于着陆点固连坐标系下探测器的相对位置和姿态。为了解决导航过程中可能发生的由于特征点逸出相机视场导致导航失败的难题,发展了基于特征点跟踪、继承的自主光学相对导航算法。
其次,基于探测器和目标天体表面特征点之间的视线(方向矢量)观测,提出了一种基于视线测量的自主相对导航方法。通过对四个或者四个以上的视线的观测,借助非线性估计理论的批处理算法和导航滤波算法,唯一地确定了探测器的六自由度运动状态—相对位置和姿态。为了克服高斯最小二乘微分修正算法存在的由于初值偏离真实值较大而导致收敛困难的问题,发展了视线测量相对导航的龙贝格-马尔塔算法。
接着,对视线测量相对导航系统的可观性问题进行了深入的分析研究。以共线方程作为观测模型,利用极大似然估计得到了相对导航系统满足克拉马-罗下边界的最优误差方差阵和费歇尔信息阵。通过对费歇尔信息阵的秩、特征值和特征向量的分析,深入研究了不同视线测量数目条件下的相对导航系统的可观性和可观度,并借助于Matlab Symbolic Toolbox提供的符号计算功能验证了理论分析的正确性。
然后,为了克服光学导航和惯性导航在实际应用中各自存在的缺点和不足,发展了光学测量辅助的星际软着陆惯性导航方法。利用光学导航相机识别、跟踪目标天体表面的自然特征点,通过导航滤波融合惯性测量单元输出和光学导航量测,有效地修正惯性测量单元的常值偏差和避免光学导航中存在的由于跟踪目标丢失导致导航中断现象的发生。
最后,结合“十五”863计划项目——“深空探测自主技术与仿真演示系统”,在上述研究成果基础上,建立了基于光学导航相机/小行星地貌模拟器和Matlab/Simulink/dSPACE集成仿真环境的软着陆小行星自主导航半物理仿真分析系统,通过半物理仿真分析对所提出的光学测量相对导航算法的可行性进行了验证。
Autonomous landing probe on planetary surface and achieving pinpoint planetary landing is a rather challenging task. Probe must possess the ability of accurate relative navigation. Traditional dead-reckoning based navigation mode can’t meet the accuracy requirement of future planetary pin-point landing mission. So it’s necessary to develop the new generation optical measurement based planetary landing relative navigation algorithms.
With the supports of the Tenth Five-Year 863 Program‘Autonomy Technology of Deep Space Exploration and its Simulation and Demonstration System’, this dissertation deeply and systemically studies the optical measurement based relative navigation algorithm and its application in planetary pin-point landing from the following two aspects: optical measurement relative navigation algorithm and soft landing asteroids autonomous navigation semi-physical simulation. The main contents of this dissertation are as follows.
Firstly, vector measurement based autonomous relative navigation algorithm is proposed, which is based on vector measurement between the probe and the feature points on the surface of target celestial body. The position vectors from the probe to three non-collinear feature points can be constructed form the measurements of optical navigation camera and laser range finder, and then, the feature point fixed coordinate system and the probe relative position and attitude, defined in the landing site coordinate system, can be directly constructed. Feature points tracking and inheritance based autonomous optical measurement relative navigation algorithm is developed to overcome the problem of navigation failure due to feature points outflow from camera field of view.
Secondly, line-of-sight (LOS) measurement based autonomous relative navigation algorithm is presented, which is based on LOS measurement between the probe and the feature points on the surface of target celestial body. The six degree-of-freedom motion parameters of the probe, relative position and attitude, can be uniquely determined using nonlinear estimation algorithm (batch method or kalman filter) processing four or more than four LOS observations. In order to overcome Gaussian Least Square Differential Correction algorithm convergence difficulty when an accurate initial estimate is not given, LOS measurement relative navigation Levenberg-Marquardt algorithm is developed.
Next, observability analysis of LOS measurement relative navigation system is deeply analyzed. Navigation observation model is constructed based on collinearity equations, optimal error variance matrix and Fisher information matrix, satisfying Cramer-Rao lower bound, are obtained using maximum likelihood estimation. Observability and observable degree of LOS measurement relative navigation system are studied by analyzing the rank, eigenvalue and eigenvector of Fisher information matrix. Theory analysis above-mentioned is confirmed by Matlab symbolic operation.
Then, optical measurement aided inertial navigation algorithm is developed to overcome the shortcoming of optical navigation and inertial naviagiton alone. Natural feature points are identified and tracked by use of optical navigation camera and onboard software; and then, the landmark image information derived from navigation camera and the spacecraft state information sensed by IMU (Inertial Measurement Unit) are integrated in extended kalman filter algorithm to effectively correct the constant biases of IMU and avoid the navigation interregnum due to tracked landmark drop-out.
Lastly, combining with the Tenth Five-Year 863 Program‘Autonomy Technology of Deep Space Exploration and its Simulation and Demonstration System’, semi-physical simulation system of asteroid soft landing autonomous navigation is built up based on optical navigation camera, asteroid geomorphy simulator and Matlab/Simulink/dSPACE integration simulation flatform. The feasibility of the proposed optical measurement based relative navigation algorithm is confirmed by semi-physical simulation and analysis.
本学位论文结合“十五”863计划项目——“深空探测自主技术与仿真演示系统”,从光学测量相对导航方法和软着陆小行星自主导航半物理仿真两方面出发,对基于光学测量的相对导航方法及其在星际精确着陆任务中的应用进行了深入系统的研究。论文的主要研究内容包括:
首先,基于探测器和目标天体表面特征点之间的矢量观测,提出了一种基于矢量测量的自主相对导航方法。通过光学导航相机和激光测距仪组合测量输出构建探测器到三个非共线的特征点之间矢量,进而构建特征点固连坐标系和定义于着陆点固连坐标系下探测器的相对位置和姿态。为了解决导航过程中可能发生的由于特征点逸出相机视场导致导航失败的难题,发展了基于特征点跟踪、继承的自主光学相对导航算法。
其次,基于探测器和目标天体表面特征点之间的视线(方向矢量)观测,提出了一种基于视线测量的自主相对导航方法。通过对四个或者四个以上的视线的观测,借助非线性估计理论的批处理算法和导航滤波算法,唯一地确定了探测器的六自由度运动状态—相对位置和姿态。为了克服高斯最小二乘微分修正算法存在的由于初值偏离真实值较大而导致收敛困难的问题,发展了视线测量相对导航的龙贝格-马尔塔算法。
接着,对视线测量相对导航系统的可观性问题进行了深入的分析研究。以共线方程作为观测模型,利用极大似然估计得到了相对导航系统满足克拉马-罗下边界的最优误差方差阵和费歇尔信息阵。通过对费歇尔信息阵的秩、特征值和特征向量的分析,深入研究了不同视线测量数目条件下的相对导航系统的可观性和可观度,并借助于Matlab Symbolic Toolbox提供的符号计算功能验证了理论分析的正确性。
然后,为了克服光学导航和惯性导航在实际应用中各自存在的缺点和不足,发展了光学测量辅助的星际软着陆惯性导航方法。利用光学导航相机识别、跟踪目标天体表面的自然特征点,通过导航滤波融合惯性测量单元输出和光学导航量测,有效地修正惯性测量单元的常值偏差和避免光学导航中存在的由于跟踪目标丢失导致导航中断现象的发生。
最后,结合“十五”863计划项目——“深空探测自主技术与仿真演示系统”,在上述研究成果基础上,建立了基于光学导航相机/小行星地貌模拟器和Matlab/Simulink/dSPACE集成仿真环境的软着陆小行星自主导航半物理仿真分析系统,通过半物理仿真分析对所提出的光学测量相对导航算法的可行性进行了验证。
Autonomous landing probe on planetary surface and achieving pinpoint planetary landing is a rather challenging task. Probe must possess the ability of accurate relative navigation. Traditional dead-reckoning based navigation mode can’t meet the accuracy requirement of future planetary pin-point landing mission. So it’s necessary to develop the new generation optical measurement based planetary landing relative navigation algorithms.
With the supports of the Tenth Five-Year 863 Program‘Autonomy Technology of Deep Space Exploration and its Simulation and Demonstration System’, this dissertation deeply and systemically studies the optical measurement based relative navigation algorithm and its application in planetary pin-point landing from the following two aspects: optical measurement relative navigation algorithm and soft landing asteroids autonomous navigation semi-physical simulation. The main contents of this dissertation are as follows.
Firstly, vector measurement based autonomous relative navigation algorithm is proposed, which is based on vector measurement between the probe and the feature points on the surface of target celestial body. The position vectors from the probe to three non-collinear feature points can be constructed form the measurements of optical navigation camera and laser range finder, and then, the feature point fixed coordinate system and the probe relative position and attitude, defined in the landing site coordinate system, can be directly constructed. Feature points tracking and inheritance based autonomous optical measurement relative navigation algorithm is developed to overcome the problem of navigation failure due to feature points outflow from camera field of view.
Secondly, line-of-sight (LOS) measurement based autonomous relative navigation algorithm is presented, which is based on LOS measurement between the probe and the feature points on the surface of target celestial body. The six degree-of-freedom motion parameters of the probe, relative position and attitude, can be uniquely determined using nonlinear estimation algorithm (batch method or kalman filter) processing four or more than four LOS observations. In order to overcome Gaussian Least Square Differential Correction algorithm convergence difficulty when an accurate initial estimate is not given, LOS measurement relative navigation Levenberg-Marquardt algorithm is developed.
Next, observability analysis of LOS measurement relative navigation system is deeply analyzed. Navigation observation model is constructed based on collinearity equations, optimal error variance matrix and Fisher information matrix, satisfying Cramer-Rao lower bound, are obtained using maximum likelihood estimation. Observability and observable degree of LOS measurement relative navigation system are studied by analyzing the rank, eigenvalue and eigenvector of Fisher information matrix. Theory analysis above-mentioned is confirmed by Matlab symbolic operation.
Then, optical measurement aided inertial navigation algorithm is developed to overcome the shortcoming of optical navigation and inertial naviagiton alone. Natural feature points are identified and tracked by use of optical navigation camera and onboard software; and then, the landmark image information derived from navigation camera and the spacecraft state information sensed by IMU (Inertial Measurement Unit) are integrated in extended kalman filter algorithm to effectively correct the constant biases of IMU and avoid the navigation interregnum due to tracked landmark drop-out.
Lastly, combining with the Tenth Five-Year 863 Program‘Autonomy Technology of Deep Space Exploration and its Simulation and Demonstration System’, semi-physical simulation system of asteroid soft landing autonomous navigation is built up based on optical navigation camera, asteroid geomorphy simulator and Matlab/Simulink/dSPACE integration simulation flatform. The feasibility of the proposed optical measurement based relative navigation algorithm is confirmed by semi-physical simulation and analysis.
引文
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77 黄翔宇, 崔祜涛, 崔平远. 探测器着陆小天体的自主光学导航研究. 电子学报. 2003,31(5):659~661
78 X.Y. Huang, H.T. Cui and P.Y. Cui. An Autonomous Optical Navigation and Guidance for Soft Landing on Asteroids. Acta Astronautica. 2004, 54(10):763~771
79 R. Flatscher, A. Ullrich and G.J. Ulbrich. Laser Radar for Scientific Space Applications. ESA bulletin 101, 2000
80 I. Kawano, et al. Study on Laser Rangerfinder for Non-cooperative Rendezvous. Proceeding of the 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space, NARA, Japan, 2003
81 F. J. Pelletier. Lidar-based Autonomous Rendezvous in Mars Orbit. Proceeding of the 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space, NARA, Japan, May 19-23, 2003
82 K. Gleichman, et al. Application of Laser Radar to Autonomous Spacecraft Landing. SPIE, 1991, 1416(6):286~294
83 M. F Reiley, D. C Carmer and W. F Pont. 3-D Laser Radar Simulation for Autonomous Spacecraft Landing. SPIE, 1991, 1416(6):295~303
84 S. I. Roumeliotis, A. E. Johnson, and J. F. Montgomery. Augmenting Inertial Navigation with Image-Based Motion Estimation. IEEE International Conference on Robotics and Automation, Washington D.C.,2002:4326~4333
85 A.D. Wu, E.N. Johnson and A.A. Proctor. Vision-Aided Inertial Navigation for Flight Control. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, 2005. AIAA 2005-5998
86 I. Kaminer, A. Pascoal and W. Kang. Integrated vision/Inertial navigation system design using nonlinear. Proceedings of the America control conference, San Diego, California, Jun 1999
87 H. H. Brita. Integrated Camera-Based Navigation. Journal of Navigation. 2000, 53:237~245
88 V. Silva and S. Parkes. Integration of Vision and Navigation Information for Autonomous Planetary Landers. Proceeding of 6th Dynamics and Control of Systems and Structures in Space Conference, Riomaggiore, Italy, 2004
89 J.L. Crassidis and F.L. Markley. Predictive Filtering for Nonlinear Systems. Journal of Guidance, Control, and Dynamics. 1997, 20(3):566~572
90 J. L. Crassidis and F. L. Markley. Minimum Model Error Aproach for Attitude Estimation. Journal of Guidance, Control, and Dynamics. 1997, 20(6):1241~1247
91 D. J. Mook and J. L. Junkins. Minimum Model Error Estimation for Poorly Medeled Dynamics Systems. Journal of Guidance, Control, and Dynamics. 1988, 11(3):256~261
92 柴霖 , 袁建平等 . 非线性估计理论的最新进展 . 宇航学报 . 2005, 26(3):380~384
93 张友民等. 卡尔曼滤波计算方法研究进展.控制理论与应用. 1995, 12(5): 529~538
94 S. J. Julier and J. K. Uhlmann. A Consistent, Debiased Method for Converting between Polar and Cartesian Coordinate Systems. Proceedings of AeroSense: Acquisition, Tracking and Pointing. 1997, 3086:110~121
95 S. J. Julier and J. K. Uhlmann. A General Method for Approximating Nonlinear Transformations of Probability Distributions. Technical Report, University of Oxford. 1996
96 S. J. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Approach for Filtering Nonliear Systems. Proceedings of the American Control Conference, Seattle, WA. 1995:1628~1632
97 S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando, FL. 1997:182~193
98 S. J. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Transactions on Automatic Control. 2000, 45(3):477~482
99 S. J. Julier. The Scaled Unscented Transformation. Proceedings of the American Control Conference, Anchorage, AK. 2002:4555~4559
100 E. A. Wan and V. D. M Rudolph. The Unscented Kalman Filter for Nonlinear Estimation. IEEE Proceedings of the Symposium 2000 on Adaptive Systems for Signal Processing, Communication and Control. Lake Louise, Alberta, Canada, 2000:153~158
101 M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing. 2002, 50(2):174~185
102 N. J. Gordon, D. J. Salmond, and A. F. M. Smith. A Novel Approach to Non-Linear/Non-Gaussian Bayesian State Estimation. IEE Proceedings, Part F: Radar and Signal Processing, 1993, 140(2):107~113
103 J. Shi and C. Tomasi. Good Features to Track. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994:593~600
104 A. Benedetti and P. Perona. Real-time 2-D Feature Detection on a Reconfigurable Computer. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1998:586~593
105 D. German and A. L. Friedlander. A Simulation of Orbits around Asteoids Using Potential Field Modelling. Advances in the Astronautical Sciences, Spaceflight Mechanics, 1991, 75:1183~1201. AAS 91-182
106 G. Wahba. Problem 65-1: A Least Square Estimate of Satellite Attitude. SIAM Review. 1965, 7(3):409
107 J. L. Farrell, et al. Solution 65-1: A Least Square Estimate of Satellite Attitude. SIAM Review. 1965, 7(3):383~386
108 H. Schaub and J. L. Junkins. Analytical Mechanics of Space Systems. AIAAEducation Series, 2003:107~115
109 J. L. Crassidis and J. L. Junkins. Optimal Estimation of Dynamic Systems. Chapman & Hall/CRC. 2004:48~49
110 S. Haykin. Kalman Filtering and Neural Networks. John Wiley & Sons, Inc. 2001:123~174
111 S. Dan. Optimal State Estimation: Kalman, Hinf and Nonlinear Approaches. John Wiley & Sons, Inc. 2006:433~458
112 P. T. Liu, H. Fang, F. Li and H. Xiao. State Decouple in Estimation Theory. Proceedings-ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing, May 9-12, 1995:2024~2027
113 R. Hermann, J.K. Arthur. Nonlinear Controllability and Observability. IEEE Transactions on Automatic Control, 1977, 22(5):728~740.
114 F. M. HAM and R. G. Brown. Observability, Eigenvalues and Kalman filtering. IEEE Transaction on Aerospace and Electronic Systems. 1983, 19(2):269~273
115 J. R. YIM. Autonomous spacecraft orbit navigation. Ph.D Thesis of Texas A&M University. 2002:33~45
116 黄翔宇. 探测器自主导航方法及在小天体探测中的应用研究. 哈尔滨工业大学博士学位论文. 2005:31~52
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46 J. C. Weeks, J. Lynch and A. Girardi. Autonomous Navigation with Laser Altimetry. Advances in the Astronautical Sciences, Astrodynamics 1997. AAS 97-629
47 W. G. Robert. Automated Landmark Identification for Spacecraft Navigation. AIAA/AAS Astrodynamics Conference, Quebec City, Canada, August 2001. AAS 01-422
48 W.G. Robert. Small Body Simulations for Navigation Approach and Landing. AIAA Space 2005, Long Beach, CA, United States, 2005
49 W. Owen, T. C Wang, et al. NEAR Optical Navigation at Eros. AAS/AIAA Astrodynamics Specialist Conference Quebec, Canada, 2001
50 W. G. Robert. Landmark Navigation and Target Characterization in a Simulated Itokawa Encounter. AAS/AIAA Astrodynamics Specialists Conference, Lake Tahoe, CA, United States, 2005
51 Y. Cheng, et al. Optical Landmark Detection for Spacecraft Navigation. AAS/AIAA Astrodynamics Specialist Conference, Ponce, Puerto Rico, 2003
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54 Y. Cheng and A. Ansar. Landmark based Position Estimation for Pinpoint Landing on Mars. Proceedings of the 2005 IEEE international conference on robotics and automation, Barcelona, Spain, 2005:4470~4475
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64 T. Misu, T. Hashimto and K. Ninomiya. Autonomy in Guidance using Image-based Terrain Recognition and Optical Navigation. J. of the Braz. Soc. Mechanical Sciences. 1999, 21:227~236
65 T. Nakamura, et al. Image based Relative Motion Estimation around a Celestial Body. Advances in the Astronautical Sciences, Astrodynamics 1997. AAS 97-630
66 T. Nakamura, et al. Image based Relative Motion Estimatin with respect to an Unknown Body. Technical Papers of Workshop on Astrodynamics and Flight Mechanics, 1997:342~347
67 T. Hashimoto, et al. Autonomous Descent and Touch-down via Optical Sensors. Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Santa Barbara, California, 2001, AAS 01-134
68 T. Hashimoto, et al. Image-based Guidance, Navigation and Control for MUSES-C Sample and Return Spacecraft. Advances in the Astronautical Sciences. 2002, 111:181~192. AAS 02-023
69 M. Uo, et al. HAYABUSA’s Touching Down to ITOKAWA – Autonomous Guidance and Navigation. Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Tampa, Florida, 2006. AAS 06-214
70 K. Shirakawa, et al. Accurate Landmark Tracking for Navigating HAYABUSA prior to Final Descent. Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, Tampa, Florida, 2006. AAS 06-215
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75 S. Mancuso. Vision based GNC Systems for Planetary Exploration. Proceedings of 6th Dynamics and Control of Systems and Structures in Space Conference. Riomaggiore, Italy, 2004
76 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. 2006:250~275
77 黄翔宇, 崔祜涛, 崔平远. 探测器着陆小天体的自主光学导航研究. 电子学报. 2003,31(5):659~661
78 X.Y. Huang, H.T. Cui and P.Y. Cui. An Autonomous Optical Navigation and Guidance for Soft Landing on Asteroids. Acta Astronautica. 2004, 54(10):763~771
79 R. Flatscher, A. Ullrich and G.J. Ulbrich. Laser Radar for Scientific Space Applications. ESA bulletin 101, 2000
80 I. Kawano, et al. Study on Laser Rangerfinder for Non-cooperative Rendezvous. Proceeding of the 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space, NARA, Japan, 2003
81 F. J. Pelletier. Lidar-based Autonomous Rendezvous in Mars Orbit. Proceeding of the 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space, NARA, Japan, May 19-23, 2003
82 K. Gleichman, et al. Application of Laser Radar to Autonomous Spacecraft Landing. SPIE, 1991, 1416(6):286~294
83 M. F Reiley, D. C Carmer and W. F Pont. 3-D Laser Radar Simulation for Autonomous Spacecraft Landing. SPIE, 1991, 1416(6):295~303
84 S. I. Roumeliotis, A. E. Johnson, and J. F. Montgomery. Augmenting Inertial Navigation with Image-Based Motion Estimation. IEEE International Conference on Robotics and Automation, Washington D.C.,2002:4326~4333
85 A.D. Wu, E.N. Johnson and A.A. Proctor. Vision-Aided Inertial Navigation for Flight Control. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, 2005. AIAA 2005-5998
86 I. Kaminer, A. Pascoal and W. Kang. Integrated vision/Inertial navigation system design using nonlinear. Proceedings of the America control conference, San Diego, California, Jun 1999
87 H. H. Brita. Integrated Camera-Based Navigation. Journal of Navigation. 2000, 53:237~245
88 V. Silva and S. Parkes. Integration of Vision and Navigation Information for Autonomous Planetary Landers. Proceeding of 6th Dynamics and Control of Systems and Structures in Space Conference, Riomaggiore, Italy, 2004
89 J.L. Crassidis and F.L. Markley. Predictive Filtering for Nonlinear Systems. Journal of Guidance, Control, and Dynamics. 1997, 20(3):566~572
90 J. L. Crassidis and F. L. Markley. Minimum Model Error Aproach for Attitude Estimation. Journal of Guidance, Control, and Dynamics. 1997, 20(6):1241~1247
91 D. J. Mook and J. L. Junkins. Minimum Model Error Estimation for Poorly Medeled Dynamics Systems. Journal of Guidance, Control, and Dynamics. 1988, 11(3):256~261
92 柴霖 , 袁建平等 . 非线性估计理论的最新进展 . 宇航学报 . 2005, 26(3):380~384
93 张友民等. 卡尔曼滤波计算方法研究进展.控制理论与应用. 1995, 12(5): 529~538
94 S. J. Julier and J. K. Uhlmann. A Consistent, Debiased Method for Converting between Polar and Cartesian Coordinate Systems. Proceedings of AeroSense: Acquisition, Tracking and Pointing. 1997, 3086:110~121
95 S. J. Julier and J. K. Uhlmann. A General Method for Approximating Nonlinear Transformations of Probability Distributions. Technical Report, University of Oxford. 1996
96 S. J. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Approach for Filtering Nonliear Systems. Proceedings of the American Control Conference, Seattle, WA. 1995:1628~1632
97 S. J. Julier and J. K. Uhlmann. A New Extension of the Kalman Filter to Nonlinear Systems. Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Orlando, FL. 1997:182~193
98 S. J. Julier, J. K. Uhlmann and H. F. Durrant-Whyte. A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators. IEEE Transactions on Automatic Control. 2000, 45(3):477~482
99 S. J. Julier. The Scaled Unscented Transformation. Proceedings of the American Control Conference, Anchorage, AK. 2002:4555~4559
100 E. A. Wan and V. D. M Rudolph. The Unscented Kalman Filter for Nonlinear Estimation. IEEE Proceedings of the Symposium 2000 on Adaptive Systems for Signal Processing, Communication and Control. Lake Louise, Alberta, Canada, 2000:153~158
101 M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp. A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing. 2002, 50(2):174~185
102 N. J. Gordon, D. J. Salmond, and A. F. M. Smith. A Novel Approach to Non-Linear/Non-Gaussian Bayesian State Estimation. IEE Proceedings, Part F: Radar and Signal Processing, 1993, 140(2):107~113
103 J. Shi and C. Tomasi. Good Features to Track. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994:593~600
104 A. Benedetti and P. Perona. Real-time 2-D Feature Detection on a Reconfigurable Computer. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1998:586~593
105 D. German and A. L. Friedlander. A Simulation of Orbits around Asteoids Using Potential Field Modelling. Advances in the Astronautical Sciences, Spaceflight Mechanics, 1991, 75:1183~1201. AAS 91-182
106 G. Wahba. Problem 65-1: A Least Square Estimate of Satellite Attitude. SIAM Review. 1965, 7(3):409
107 J. L. Farrell, et al. Solution 65-1: A Least Square Estimate of Satellite Attitude. SIAM Review. 1965, 7(3):383~386
108 H. Schaub and J. L. Junkins. Analytical Mechanics of Space Systems. AIAAEducation Series, 2003:107~115
109 J. L. Crassidis and J. L. Junkins. Optimal Estimation of Dynamic Systems. Chapman & Hall/CRC. 2004:48~49
110 S. Haykin. Kalman Filtering and Neural Networks. John Wiley & Sons, Inc. 2001:123~174
111 S. Dan. Optimal State Estimation: Kalman, Hinf and Nonlinear Approaches. John Wiley & Sons, Inc. 2006:433~458
112 P. T. Liu, H. Fang, F. Li and H. Xiao. State Decouple in Estimation Theory. Proceedings-ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing, May 9-12, 1995:2024~2027
113 R. Hermann, J.K. Arthur. Nonlinear Controllability and Observability. IEEE Transactions on Automatic Control, 1977, 22(5):728~740.
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