基于星敏感器的无陀螺角速度测量新方法研究
|
摘要
近年深空自主探测和微小卫星技术发展迅速，采用成本相对较低的光学姿态敏感器实现角速度测量，具有很好的应用前景。针对深空自主导航和微小卫星姿态测量的需求，本文研究无陀螺条件下利用星敏感测量角速度的新方法，使得航天器减小对陀螺的依赖。
针对星敏感器角速度测量中的关键技术，从角速度估计方法、星点提取和内部参数的校准三个方面开展研究，主要工作包括：
⑴基于星敏感器测量的角速度估计方法研究
提出了利用星敏感器测量角速度的矢量差分法和恒星跟踪滤波法。矢量差分法采用同一恒星在星敏感器连续两帧图像中的测量矢量的一阶向后差分，构建角速度测量方程。恒星跟踪滤波法利用Singer模型的目标跟踪滤波，获得恒星投影位置和速度信息，构建角速度测量方程，实现角速度估计。与矢量差分法相比，恒星跟踪滤波法无需差分和上一时刻星敏感器的测量信息。
针对矢量差分法和恒星跟踪滤波法，设计了自适应卡尔曼滤波器，估计角速度。与现有的基于卡尔曼滤波估计角速度方法不同，该滤波器以当前时刻星图中导航星数目的增加作为时刻变化，更新状态量，获得角速度的最优估计值；不依赖于航天器动力学模型与转动惯量信息，以及星体参数向量或姿态的任何信息。对低轨卫星轨道仿真测试，以及对地球自转角速度测量的结果表明，在星敏感器采样频率10Hz条件下，该滤波器估计角速度的精度可以达到10-6rad/s量级。
⑵星点提取方法研究
提出了依赖姿态信息和不依赖姿态信息的两种卡尔曼滤波星点提取方法。具体步骤为：根据卡尔曼滤波的预测方程，预测星点位置；然后，在以预测位置为中心的m×m像元星图窗口，提取星体目标，采用质心法获得星点质心位置的测量值；最后，利用设计的卡尔曼滤波器，获得星点位置信息的最优估计。卡尔曼滤波的星点提取方法，可以在减小星点提取位置的随机噪声的同时，提高提取的速度、减小伪星出现的概率。
依赖于姿态信息的方法，根据星敏感器的姿态矩阵和姿态角速度，构建预测方程，预测星点位置。不依赖姿态信息的方法，采用Singer模型构建卡尔曼滤波的预测方程，具有不依赖于姿态矩阵和角速度信息的特点，能同时获得星点位置和速度，是恒星跟踪滤波法测量角速度的基础。
⑶内部参数的实验室校准
提出了一种星敏感器实验室校准的装置和方法。首先，利用激光自准直的方法测量光学中心位置；然后，采用单星模拟器结合二维可调平面反射镜，利用激光反射的方法监测平面反射镜转角，采集校准数据，估计星敏感器安装角、焦距和高阶畸变系数。该校准方法简单、无需高成本的精密转台；在采集星点数据时无需转动星敏感器，可以消除传统实验室校准方法中星敏感器安装误差对精度的限制。误差分析和实验结果表明，校准后的恒星测角误差小于4.0×105rad，通过增加激光反射距离的简单方法，校准的精度还有进一步提高的空间。
此外，还提出了一种新的量化的星敏感器调焦方法，该方法借助于上述装置，通过高斯曲面拟合法，测量不同视场、不同离焦位置的成像光斑的高斯半径，进而选择星敏感器“最佳”离焦位置。
⑷内部参数的在轨自主校准
研究基于姿态估计和基于角距的星敏感器内部参数在轨自主校准方法，并进行了地面观星测试实验。基于姿态估计的校准方法，在进行姿态估计的同时，估计光学中心、焦距以及高阶畸变系数。基于角距的校准方法，利用角距不变原理构建测量方程，设计结合最小二乘迭代法的卡尔曼滤波器，估计内部参数。当导航星数目较少时，基于姿态估计的校准方法内部参数和姿态存在耦合。与已有的扩展卡尔曼滤波校准方法相比，基于角距的校准方法估计结果不受初值的影响，且引入了高阶畸变模型，具有更高的校准精度。对观星数据处理结果显示，校准后的恒星角距误差为105rad量级
上述研究方法和结论可为无陀螺角条件下角速度测量提供参考。
With the development of autonomous navigation for deep space and smallspacecraft, there is often a desire to do away with gyros and use other means todetermine the angular rate. This dissertation focuses on proposing the novel approachfor gyroless angular rate measurement using a star tracker; and its key techniques, e.g.,angular rate estimation, star spot location and camera parameters calibration, have beendeveloped. The main contents and contribution of this dissertation are as follows:
1. Gyrosless angular rate determination from measurement of star tracker
Two approaches (i.e., the difference method and star tracking filter method,respectively) have been put forward to determine the angular rate, while the attitude andstar reference vectors are not required to be known. In the difference method, theangular rate is determined by the backward difference of the vector measurements,which are obtained directly from the star tracker. In the star tracking filter method, theangular rate is determined according to the star spot location and its velocity, which areachieved using the tracking filter of the Singer model. Therefore, the needs fordifference and previous vector measurements of star tracker are eliminated.
Adaptive Kalman filters are designed for the difference method and star trackingfilter method respectively. The Kalman filter states are updated on different guide starsin a same star image frame. Thus, the best estimates of angular rate can be achievedwithout the information of dynamic model. The simulations based on the orbit data ofnearly Earth-pointing satellite and experimental test with night sky observation areperformed. Both results indicate that the accuracies of the estimated angular rate are inthe order of10-6rad/s magnitude, when the refresh rate is10Hz.
2. Star spot location estimation
Two approaches for star spot location estimation with the Kalman filter (i.e.,attitude-dependent and attitude-independent, respectively) have been proposed, whichconsist of three steps. The approximate locations of the star spots in successive framesare predicted by the Kalman prediction equation firstly; then the measurement locationsare acquired by defining a series of small m×m pixels windows around each predictivelocation. Finally, the star spot location is updated using the designed Kalman filter. Theremarkable advantage of the Kalman filter over other methods for star spot location isthat it combines the predictive location to give more accurate estimates than that byusing the achieved centroids alone. Furthermore, as the threshold scan is only performedin small windows, it takes rather less time and can avoid false star spots effectively.
In the attitude-dependent approach, the prediction equation of the Kalman filter isconstructed according to the attitude matrix and angular rate. However, in theattitude-independent approach, the prediction equation is constructed according to the famous Singer model, which can estimate star spot location and velocity directly. It laysthe foundation of the star tracking filter method for angular rate determinion.
3. Laboratory calibration for star tracker camera
A simple and available calibration approach for star tracker camera has been putforward. The calibration procedure consists of two steps:(1) the principal point isestimated using autocollimation adjustment;(2) the focal length and distortions areestimated via least-squares iteration, taking into account the extrinsic parameters.Compared with traditional method, in which the calibration data are acquired viarotation of the star tracker installed on a two-axes rotating stage, the star data ofdifferent field angles are acquired via rotation of the adjustable plane mirror in theproposed approach. It could decrease the setting error during the rotation of the startracker and has the advantages of simplicity, low cost, and high accuracy. Thetheoretical analysis and experimental results both indicate that the uncertainties of themeasured star direction vectors are less than4.0×105rad after calibration, which can befurther improved.
Besides, an approach for defocus adjustment has been proposed for star tracker.This approach can measure the intensity distribution and spot size of pointsource imagebased on the calibration setup and Gaussian surface fitting method.
4. On-orbit autonomous calibration for star tracker camera
The calibration methods, i.e. attitude-dependent method and inter-star-anglemethod, are introduced to estimate parameters of on-orbit star tracker camera. And thenight sky observation is adopted to test their performance. In the attitude-dependentcalibration method, the camera internal parameters are combined with attitude matrices(or external parameters) determination. The error of attitude estimate will influence theerror of camera parameter estimate and vice-versa. Thus, the calibration accuracy isaffected by the number of stars identified as the control points. In the inter-star-anglecalibration method, a modified version of the least-squares iteration algorithmcombining Kalman filter is put forward on the assumption that the angle between twovectors is invariant. Compared with the traditional EKF (Extended Kalman Filter)method, the estimates are converged even for the poor initial guesses with nonlinearcamera distortions. The experimental results indicate that the deviation of the measuredinter-star angle is in the order of10-5rad magnitude after calibrated.
The research method and conclusion would have significance in improving theperformance of gyroless angular rate measurement using star tracker.
针对星敏感器角速度测量中的关键技术，从角速度估计方法、星点提取和内部参数的校准三个方面开展研究，主要工作包括：
⑴基于星敏感器测量的角速度估计方法研究
提出了利用星敏感器测量角速度的矢量差分法和恒星跟踪滤波法。矢量差分法采用同一恒星在星敏感器连续两帧图像中的测量矢量的一阶向后差分，构建角速度测量方程。恒星跟踪滤波法利用Singer模型的目标跟踪滤波，获得恒星投影位置和速度信息，构建角速度测量方程，实现角速度估计。与矢量差分法相比，恒星跟踪滤波法无需差分和上一时刻星敏感器的测量信息。
针对矢量差分法和恒星跟踪滤波法，设计了自适应卡尔曼滤波器，估计角速度。与现有的基于卡尔曼滤波估计角速度方法不同，该滤波器以当前时刻星图中导航星数目的增加作为时刻变化，更新状态量，获得角速度的最优估计值；不依赖于航天器动力学模型与转动惯量信息，以及星体参数向量或姿态的任何信息。对低轨卫星轨道仿真测试，以及对地球自转角速度测量的结果表明，在星敏感器采样频率10Hz条件下，该滤波器估计角速度的精度可以达到10-6rad/s量级。
⑵星点提取方法研究
提出了依赖姿态信息和不依赖姿态信息的两种卡尔曼滤波星点提取方法。具体步骤为：根据卡尔曼滤波的预测方程，预测星点位置；然后，在以预测位置为中心的m×m像元星图窗口，提取星体目标，采用质心法获得星点质心位置的测量值；最后，利用设计的卡尔曼滤波器，获得星点位置信息的最优估计。卡尔曼滤波的星点提取方法，可以在减小星点提取位置的随机噪声的同时，提高提取的速度、减小伪星出现的概率。
依赖于姿态信息的方法，根据星敏感器的姿态矩阵和姿态角速度，构建预测方程，预测星点位置。不依赖姿态信息的方法，采用Singer模型构建卡尔曼滤波的预测方程，具有不依赖于姿态矩阵和角速度信息的特点，能同时获得星点位置和速度，是恒星跟踪滤波法测量角速度的基础。
⑶内部参数的实验室校准
提出了一种星敏感器实验室校准的装置和方法。首先，利用激光自准直的方法测量光学中心位置；然后，采用单星模拟器结合二维可调平面反射镜，利用激光反射的方法监测平面反射镜转角，采集校准数据，估计星敏感器安装角、焦距和高阶畸变系数。该校准方法简单、无需高成本的精密转台；在采集星点数据时无需转动星敏感器，可以消除传统实验室校准方法中星敏感器安装误差对精度的限制。误差分析和实验结果表明，校准后的恒星测角误差小于4.0×105rad，通过增加激光反射距离的简单方法，校准的精度还有进一步提高的空间。
此外，还提出了一种新的量化的星敏感器调焦方法，该方法借助于上述装置，通过高斯曲面拟合法，测量不同视场、不同离焦位置的成像光斑的高斯半径，进而选择星敏感器“最佳”离焦位置。
⑷内部参数的在轨自主校准
研究基于姿态估计和基于角距的星敏感器内部参数在轨自主校准方法，并进行了地面观星测试实验。基于姿态估计的校准方法，在进行姿态估计的同时，估计光学中心、焦距以及高阶畸变系数。基于角距的校准方法，利用角距不变原理构建测量方程，设计结合最小二乘迭代法的卡尔曼滤波器，估计内部参数。当导航星数目较少时，基于姿态估计的校准方法内部参数和姿态存在耦合。与已有的扩展卡尔曼滤波校准方法相比，基于角距的校准方法估计结果不受初值的影响，且引入了高阶畸变模型，具有更高的校准精度。对观星数据处理结果显示，校准后的恒星角距误差为105rad量级
上述研究方法和结论可为无陀螺角条件下角速度测量提供参考。
With the development of autonomous navigation for deep space and smallspacecraft, there is often a desire to do away with gyros and use other means todetermine the angular rate. This dissertation focuses on proposing the novel approachfor gyroless angular rate measurement using a star tracker; and its key techniques, e.g.,angular rate estimation, star spot location and camera parameters calibration, have beendeveloped. The main contents and contribution of this dissertation are as follows:
1. Gyrosless angular rate determination from measurement of star tracker
Two approaches (i.e., the difference method and star tracking filter method,respectively) have been put forward to determine the angular rate, while the attitude andstar reference vectors are not required to be known. In the difference method, theangular rate is determined by the backward difference of the vector measurements,which are obtained directly from the star tracker. In the star tracking filter method, theangular rate is determined according to the star spot location and its velocity, which areachieved using the tracking filter of the Singer model. Therefore, the needs fordifference and previous vector measurements of star tracker are eliminated.
Adaptive Kalman filters are designed for the difference method and star trackingfilter method respectively. The Kalman filter states are updated on different guide starsin a same star image frame. Thus, the best estimates of angular rate can be achievedwithout the information of dynamic model. The simulations based on the orbit data ofnearly Earth-pointing satellite and experimental test with night sky observation areperformed. Both results indicate that the accuracies of the estimated angular rate are inthe order of10-6rad/s magnitude, when the refresh rate is10Hz.
2. Star spot location estimation
Two approaches for star spot location estimation with the Kalman filter (i.e.,attitude-dependent and attitude-independent, respectively) have been proposed, whichconsist of three steps. The approximate locations of the star spots in successive framesare predicted by the Kalman prediction equation firstly; then the measurement locationsare acquired by defining a series of small m×m pixels windows around each predictivelocation. Finally, the star spot location is updated using the designed Kalman filter. Theremarkable advantage of the Kalman filter over other methods for star spot location isthat it combines the predictive location to give more accurate estimates than that byusing the achieved centroids alone. Furthermore, as the threshold scan is only performedin small windows, it takes rather less time and can avoid false star spots effectively.
In the attitude-dependent approach, the prediction equation of the Kalman filter isconstructed according to the attitude matrix and angular rate. However, in theattitude-independent approach, the prediction equation is constructed according to the famous Singer model, which can estimate star spot location and velocity directly. It laysthe foundation of the star tracking filter method for angular rate determinion.
3. Laboratory calibration for star tracker camera
A simple and available calibration approach for star tracker camera has been putforward. The calibration procedure consists of two steps:(1) the principal point isestimated using autocollimation adjustment;(2) the focal length and distortions areestimated via least-squares iteration, taking into account the extrinsic parameters.Compared with traditional method, in which the calibration data are acquired viarotation of the star tracker installed on a two-axes rotating stage, the star data ofdifferent field angles are acquired via rotation of the adjustable plane mirror in theproposed approach. It could decrease the setting error during the rotation of the startracker and has the advantages of simplicity, low cost, and high accuracy. Thetheoretical analysis and experimental results both indicate that the uncertainties of themeasured star direction vectors are less than4.0×105rad after calibration, which can befurther improved.
Besides, an approach for defocus adjustment has been proposed for star tracker.This approach can measure the intensity distribution and spot size of pointsource imagebased on the calibration setup and Gaussian surface fitting method.
4. On-orbit autonomous calibration for star tracker camera
The calibration methods, i.e. attitude-dependent method and inter-star-anglemethod, are introduced to estimate parameters of on-orbit star tracker camera. And thenight sky observation is adopted to test their performance. In the attitude-dependentcalibration method, the camera internal parameters are combined with attitude matrices(or external parameters) determination. The error of attitude estimate will influence theerror of camera parameter estimate and vice-versa. Thus, the calibration accuracy isaffected by the number of stars identified as the control points. In the inter-star-anglecalibration method, a modified version of the least-squares iteration algorithmcombining Kalman filter is put forward on the assumption that the angle between twovectors is invariant. Compared with the traditional EKF (Extended Kalman Filter)method, the estimates are converged even for the poor initial guesses with nonlinearcamera distortions. The experimental results indicate that the deviation of the measuredinter-star angle is in the order of10-5rad magnitude after calibrated.
The research method and conclusion would have significance in improving theperformance of gyroless angular rate measurement using star tracker.
引文
[1]屠善澄,鲍百容.卫星姿态动力学与控制(3)[M].北京:中国科学出版社,2003.
[2]施少范.国外对地观测卫星高精度姿态控制系统研究[J].上海航天,2000,17(6):49~53.
[3] Liebe C C. Star Trackers for Attitude Determination[J]. Ieee Aerospace AndElectronic Systems Magazine,1995,10(6):10~16.
[4] Iwata T, Yoshizawa T. Precision Attitude and Orbit Control System for theAdvanced Land Observing Satellite (AlOS)[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit, Austin, Texas,2003,11~14.
[5] Schmidt U, Elstner C, Michel K. ASTRO15Star Tracker Flight Experienceand Further Improvements Towards the ASTRO APS Star Tracker [C]. AIAA Guidance,Navigation and Control Conference and Exhibit,2008, AIAA2008-6649.
[6] Liebe C C. Accuracy Performance of Star Trackers-A Tutorial[J]. IEEETransactions on Aerospace and Electronic Systems,2002,38(2):587~599.
[7]娇媛媛.基于星敏感器/陀螺组合测量的卫星姿态确定方法研究[D].国防科学技术大学,2007.
[8] Rao J S, Pullaiah D. Star Tracker Alignment Determination forResourcessat-I[C]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit,Providence, Rhode Island:2004.
[9] Iwata T, Hoshino H, Yoshizawa T, et al. Precision Attitude Determination forthe Advanced Land Observing Satellite (AlOS): Design, Verification and On-OrbitCalibration[C]. AIAA Guidance, Navigation and Control Conference and Exhibit,South Carolina,2007.
[10] Peter S J, John L J, Troelz D, et al. In-Flight Quality and Accuracy of AttitudeMeasurements From the Champ Advanced Stellar Compass[J]. Acta Astronuatica,2005,56:181~186.
[11] Leeghim H, Choi Y, Jaroux B A. Uncorrelated Unscented Filtering forSpacecraft Attitude Determination[J]. Acta Astronautica,2010,67(1-2):135~144.
[12]王晨,房建成.基于Unscented四元数粒子滤波的微小卫星姿态估计[J].北京航空航天大学学报,2007,35(5):553~556.
[13]段方,刘建业,李荣冰.一种改进的星敏感器/陀螺卫星定姿算法[J].系统工程与电子技术,2006,28(6):896~899.
[14] Brij N A, William J P. Angular Rate Estimation for Gyroless Satellite AttitudeControl[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit,5-8August2002, Monterey, California,2002, AIAA2002-4463.
[15]高云国.现代小卫星及其相关技术[J].光学精密工程,1999,7(5):16~21.
[16] Flatley T W, Forden J K, Henretty D A, et al. On-Board AttitudeDetermination and Control Algorithms for Sampex[R]. NASA CP3102, NASAGoddard Space Flight Center, Greenbelt, MD:1990.379~398.
[17] Liebe C C, Gromov K, Meller D M. Toward a Stellar Gyroscope forSpacecraft Attitude Determination[J]. Journal of Guidance, Control, and Dynamics,2004,27(1):91~99.
[18] Bar-Itzhack I Y, Harman R R. A Feedback Approach to Spacecraft AngularRate Estimation[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit,Keystone, Colorado,21-24August2006, AIAA2006-6807.
[19] Palermo W J. Angular Rate Estimation for Gyroless Satellite AttitudeControl[D]. Naval Postgraduate School,2001.
[20] Wahba G. A Least Squares Estimate of Spacecraft Attitude[J]. Problem65-1.SIAM Review,1965,7(3):409.
[21] Shuster M D. Maximum Likelihood Estimation of Spacecraft Attitude[J]. TheJournal of the Astronautical Sciences,1989,37(1):79~88.
[22] Barman I Y B R. Optimized Triad Algorithm for Attitude Determination[C].San Diego, CA: American Institute of Aeronautics and Astronautics, Inc.,1996.422~427.
[23] Vogt J. Attitude Determination of a Three-Axis Stabilized Spacecraft UsingStar Sensors[D]. Naval Postgraduate School,1999.
[24] Travis H D. Attitude Determination Using Star Tracker Data with KalmanFilters[D]. Naval Postgraduate School,2001.
[25]李春艳,谢华,李怀锋,等.高精度星敏感器星点光斑质心算法[J].光电工程,2006,33(2):41~44.
[26]王广君,房建成.一种星图识别的星体图像高精度内插算法[J].北京航空航天大学学报,2005,31(5):566~569.
[27] Rufino G, Accardo D. Enhancement of the Centroiding Algorithm for StarTracker Measure Refinement[J]. Acta Astronautica,2003,53(2):135~147.
[28] Lam Q, Woodruff C, Ashton S, et al. Noise Estimation for Star TrackerCalibration and Enhanced Precision Attitude Determination[C]. Proceedings of the FifthInternational Conference on Information Fusion,2002, I:235~242.
[29]张辉,钟建勇,袁家虎,等.电路噪声对星敏感器星点定位精度的影响[J].光学精密工程,2006,14(6):1052~1056.
[30]张辉,袁家虎,刘恩海. CCD噪声对星敏感器星点定位精度的影响[J].红外与激光工程,2006,35(5):629~633.
[31] Blarre L, Perrimon N, Majewski L, et al. Hydra Multiple Heads Star TrackerBased On Active Pixel Sensor and the Gyrometer Assistance Option[C]. AIAA57thInternational Astronautical Congress, IAC2006, October2,2006-October6,2006,4187~4195.
[32] Blarre L, Perrimon N, Airey S. New Multiple Head Star Sensor (HYDRA)Description and Development Status: a Highly Autonomous, Accurate and Very RobustSystem to Pave the Way for Gyroless Very Accurate AOCS Systems[C]. AIAAGuidance, Navigation, and Control Conference2005, San Francisco, CA, UnitedStates: American Institute of Aeronautics and Astronautics Inc.,2005,817~825.
[33] Liebe C C, Alkalai L, Domingo G, et al. Micro APS Based Star Tracker [C].IEEE,2002,5-2285~5-2300.
[34]李春艳.高精度轻小型星敏感器系统设计与技术研究[D].中国科学院国家天文台,2006.
[35]钟红军,杨孟飞,卢欣. APS图像传感器及其在星敏感器中的应用[J].光学技术,2009,35(2):204~208.
[36]袁彦红.星敏感器在轨标定算法研究[D].哈尔滨工业大学,2003.
[37] Paulsen T E, Maresi L. Calibration and Verification of the Terma Star Trackerfor the Nemo Satellite[C]. AIAA Space2000Conference and Exposition, Long Beach,CA, Sept.19-21,2000.
[38] Rufino G, Moccia A. Stellar Scene Simulation for Indoor Calibration ofModern Star Trackers[J]. Space Technology,2001,21(1-2):41~51.
[39]巩岩,胡宜宁.星模拟器星光颜色模拟的初步研究[J].光电工程,2010,37(2):65~68,73.
[40]李英才,冯广军,马臻.一种高星等标准星光模拟器的设计与性能分析[J].应用光学,2010,(01):39~42.
[41]潘平.单星模拟器数字光源研制技术[D].中国科学院西安光学精密机械研究所,2005.
[42]钟奉金,许世文,赵亮,等.星模拟器中积分球内光纤端面有效照度的计算[J].哈尔滨工业大学学报,1998,30(4):113~115.
[43] Griffith D T, Junkins J L. Recursive On-Orbit Calibration of Star Sensors[C].World Space Conference, Houston, Texas, October2002.
[44] Marschke J M, Crassidis J L, Lam Q M. Attitude Estimation without RateGyros Using Generalized Multiple Model Adaptive Estimation[C]. AIAA Guidance,Navigation, and Control Conference,10-13August2009.
[45] Bar-Itzhack I Y, Oshman Y. Attitude Determination From VectorObservations: Quaternion Estimation[J]. IEEE Transactions on Aerospace andElectronic Systems,1985, AES-21(1):128~136.
[46] Gai E, Daly K, Harrison J, et al. Star-Sensor-Based Satellite Attitude/AttitudeRate Estimater[J]. Journal of Guidance, Control and Dynamics,1982,8(5):565~650.
[47] Harman R R, Bar-Itzhack I Y. Angular-Rate Computation Using AttitudeDifferentiation[R]. Faculty of Aerospace Eng., Technion-Israel Institute of Technology,1997.
[48] Bar-Itzhack I Y. Classification of Algorithms for Angular VelocityEstimation[J]. Journal of Guidance, Control, and Dynamic,2001,24(2):214~218.
[49] Shuster M D. A Survey of Attitude Representations[J]. The Journal of theAstronautical Sciences,1993,41(4):439~517.
[50] Azor R, Bar-Itzhack I Y, Deutschmann J K, et al. Angular-Rate EstimationUsing Delayed Quaternion Measurements[J]. Journal of Guidance, Control, andDynamic,2001,24(3):436~443.
[51] Harman R R, Bar-Itzhack I Y. Pseudolinear and State-Dependent RiccatiEquation Filters for Angular Rate Estimation[J]. Journal Guidance,1999,22(5):723~725.
[52] Bar-Itzhack I Y, Harman R R, Choukroun D. State-Dependent Pseudo-LinearFilters for Spacecraft Attitude and Rate Estimation[C]. AIAA Guidance, Navigation,and Control Conference and Exhibit, Monterey, California: AIAA,2002.
[53] Carmi A, Oshman Y. Robust Spacecraft Angular-Rate Estimation FromVector Observations Using Fast Interlaced Particle Filtering[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit, San Francisco, California: AmericanInstitute of Aeronautics and Astronautics,2005.
[54] Nagendra G R, Alex T K. Incremental-Angle and Angular VelocityEstimation Using a Star Sensor[J]. Journal of Guidance, Control, and Dynamic,2002,25(3):433~441.
[55] Oshman Y, Landis Markley F. Sequential Attitude and Attitude-RateEstimation Using Integrated-Rate Parameters[J]. Journal of Guidance, Control, andDynamics,1999,22(3):385~394.
[56]杨亚非,李建国.基于UPF和修正Rodrigues参数的无陀螺姿态确定算法[J].中国惯性技术学报,2009,17(2):149~152.
[57] Shi Y, Zhang X D. Kalman-Filtering-Based Angular Velocity EstimationUsing Infrared Attitude Information of Spacecraft[J]. Optical Engineering,2000,39(2):551~557.
[58]林玉荣,邓正隆.基于星敏感器估计卫星姿态的预测Kalman滤波算法[J].中国科学（E辑）,2002,32(6):817~823.
[59]张惟,林宝军,张泽明,等.矢量观测确定卫星姿态的预测粒子滤波算法[J].宇航学报,2011,32(5):1077~1085.
[60]钱勇,周凤岐,周军.三轴稳定卫星无陀螺姿态确定算法研究[J].飞行力学,2001,19(4):45~48,53.
[61]杨小会.基于天文信息的卫星自主导航[D].西北工业大学,2006.
[62]孙兆伟,李晖,张世杰.仅用星敏感器的卫星姿态估计UKF算法研究[J].飞行力学,2006,24(3):56~60.
[63]程杨,杨涤,崔祜涛.利用Singer模型的无陀螺姿态和角速度估计[J].航空学报,2002,23(6):507~511.
[64]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[J].上海航天,2005,22(5):14~18.
[65]靳永强,刘向东,侯朝桢.基于UKF的无陀螺姿态确定[J].航天控制,2007,25(4):31~35.
[66] Crassidis J L. Angular Velocity Determination Directly From Star TrackerMeasurements[J]. Journal of Guidance, Control, and Dynamics,2002,25(6):1165~1168.
[67] Samaan M A, Mortari D, Junkins J L. Recursive Mode Star IdentificationAlgorithms[J]. IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1246~1254.
[68] Kolomenkin M, Pollak S, Shimshoni I, et al. Geometric Voting Algorithm forStar Trackers[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(2):441~456.
[69] Liu H B, Wang J Q, Tan J C, et al. Autonomous On-Orbit Calibration of aStar Tracker Camera[J]. Optical Engineering,2011,50(2):23604~23608.
[70] Sage A P, Husa G W. Adaptive Filtering with Unknown Prior Statistics[C].Joint Americam Control Conference,1969,769~774.
[71] Singer R A. Estimating Optimal Tracking Filter Performance for MannedManeuvering Targets[J]. IEEE Transactions on Aerospace and Electronic Systems,1970,6(4):473~483.
[72] Grossman S B, Emmons R B. Performance Analysis and Size Optimization ofFocal Planes for Point-Source Tracking Algorithm Applications[J]. Optical Engineering,1984,23(2):167~176.
[73] Abdou I E. Effect of Signal Truncation on Centroid Location ErrorEstimation[J]. Optical Engineering,1996,35(4):1221~1222.
[74] Salomon P M, Goss W C. A Microprocessor-Controlled CCD Star Tracker[C].AIAA1976, AIAA76-0116.
[75] Salomon P M, Glavich T A. Image Signal Processing in Sub-Pixel AccuracyStar Trackers[C]. Proc. SPIE,1980,252:64~74.
[76] Kraemar S, Downes R, Katsanis R, et al. STIS Target Acquisition[C]. inProceedings of Hubble Space Telescope Calibration Workshop,1997,39~46.
[77] Lee S. Pointing Accuracy Improvement Using Model-Based Noise ReductionMethod[C]. Proc. SPIE,2002,4635:65~71.
[78] Quine B M, Tarasyuk V, Mebrahtu H, et al. Determining Star-Image Location:A New Sub-Pixel Interpolation Technique to Process Image Centroids[J]. ComputerPhysics Communications,2007,177(9):700~706.
[79] Yang J, Zhang T, Song J Y, et al. A New Sub-Pixel Subdivision LocationAlgorithm for Star Image[C]. Tianjin, China: IEEE Computer Society,2009.
[80] Winick K A. Cramér-Rao Lower Bounds On the Performance ofCharge-Coupled-Device Optical Position Estimators[J]. Journal of the Optical Societyof America A: Optics and Image Science, and Vision,1986,3(11):1809~1815.
[81] Chen H L, and Rao C. Accuracy Analysis on Centroid Estimation AlgorithmLimited by Photon Noise for Point Object[J]. Optics Communications,2009,282(8):1526~1530.
[82] Jia H, Yang J K, Li X J, et al. Systematic Error Analysis and Compensationfor High Accuracy Star Centroid Estimation of Star Tracker[J]. Science ChinaTechnological Sciences,2010,53(11):3145~3152.
[83]王兆魁,张育林.一种CCD星图星点快速定位算法[J].空间科学学报,2006,26(3):209~214.
[84] Motari D, Romoli A, Difesa A. Starnav III: A Three Fields of View StarTracker[J]. IEEE on Aerospace Confence,2002,47~57.
[85] Samaan M A, Pollock T C, Junkins J L. Predictive Centroiding for StarTrackers with the Effect of Image Smear[J]. The Journal of the Astronautical Sciences,2002,50(1):113~123.
[86] Samaan M A, Mortari D, Pollock T C, et al. Predictive Centroiding for Singleand Multiple Fovs Star Trackers[C]. Spaceflight Mechanics2002, San Antonio, TX,United states: Univelt Inc.,2002,112I:59~71.
[87]江洁,张广军,李霄,等.一种快速的星敏感器星跟踪方法研究[J].航空学报,2006,27(5):913~916.
[88]江洁,张广军,李霄,等.星敏感器中快速星匹配跟踪算法研究[J].光电工程,2007,34(1):9~12.
[89]李葆华,马衍宇,刘睿,等.适用于星敏感器的预测未知恒星星像质心算法[J].光学精密工程,2009,17(1):191~195.
[90]王新升,李葆华,郑靖.应用有限冲击响应滤波器消除星敏感器星像噪声[J].光学精密工程,2010,18(06):1381~1386.
[91]刘海波,杨建坤,谭吉春,等.一种星敏感器恒星像点位置提取方法[P].中国专利:201010216643.1,2010-07-05.
[92] Welch G, Bishop G. An Introduction to the Kalman Filter[M]. SIGGRAPH2001, Los Angeles, CA, August12-17,2001.
[93] Zheng S, Tian Y L, Tian J W, et al. Facet-Based Star Acquisition Method[J].Optical Engineering,2004,43(11):2796~2805.
[94]刘海波,宿德志,谭吉春,等.考虑卫星轨道和像移影响的星敏感器星图模拟方法[J].宇航学报,2011,32(5):1190~1194.
[95]何友,修建娟,张晶炜,等.雷达数据处理及应用（第二版）[M].北京:电子工业出版社,2009.
[96] Castro G J, Nieto J, Gallego L M, et al. An Effective Camera CalibrationMethod[C]. Advanced Motion Control,1998,171~174.
[97] Wang J, Lu N G, Dong M L, et al. A New Method for Linear CameraCalibration and Nonlinear Distortion Correction [C]. Proc. SPIE,2006,6280:62802O-1~62802O-6.
[98] Penna M A. Camera Calibration: A Quick and Easy Way to Determine theScale Factor[J]. IEEE Transactions on Paitern Analysis and Machine Intelligence,1991,13(12):1240~1245.
[99] Faig W. Calibration of Close-Range Photogrammetric Systems:Mathematical Formulation[J]. Photogrammetric Eng. Remote Sensing,1975,41(12):1479~1486.
[100] Ganapathy S. Decomposition of Transformation Matrices for RobotVision[J]. IEEE Conference on Robotics Automat,1984,130~139.
[101] Tsai R T. A Versatile Camera Calibration Technique for High-Accuracy3DMachine Vision Metrology Using off the Shelf TV Camera and Lenses[J]. IEEE Journalof Robotics and Automation,1987, RA-3(4):323~344.
[102] Bacakoglu H, Kamel M S. A Three-Step Camera Calibration Method[J].IEEE Transactions on Instrumentation and Measurement,1997,46(5):1165~1172.
[103] Weng J, Cohen P, Herniou M. Camera Calibration with Distortion Modelsand Accuracy Evaluation[J]. IEEE Transactions on Pattern Analysis and MachineIntelligence,1992,14(10):965~980.
[104]于起峰,陆宏伟,刘肖琳.基于图像的精密测量与运动测量[M].北京:科学出版社,2002.
[105] Klaus A, Bauer J, Karner K, et al. Camera Calibration from a Single NightSky Image[C]. Proceedings of the2004IEEE Computer Society Conference onComputer Vision and Pattern Recognition, Washington, DC: Institute of Electricaland Electronics Computer Society, Palo Alto,2004,151~157.
[106]李春艳,李怀锋,孙才红.高精度星敏感器天文标定方法及观测分析[J].光学精密工程,2006,14(4):558~563.
[107]田宏,袁家虎,李展,等.星敏感器在地面观星实验的结果分析[J].光电工程,2001,28(5):1~4.
[108]李学夔,李杰.一种非设备方式对星敏感器进行精度标定的新方法[J].电子器件,2009,32(1):204~207.
[109]张广军,郝雪涛,江洁.一种基于无偏差带的星敏感器地面校准方法[P].中国专利:200610065233.5,2007-8-8.
[110] Rufino G, Moccia A. Laboratory Test System for Performance Evaluation ofAdvanced Star Sensors[J]. Journal of Guidance Control and Dynamics,2002,25(2):200~208.
[111] Quan W, Fang J C, Zhang W N, A Method of Optimization for the DistortedModel of Star Map Based On Improved Genetic Algorithm[J]. Aerospace Science andTechnology,2011,15(2):103~107.
[112] Xing F, Dong Y, You Z. Laboratory Calibration of Star Tracker withBrightness Independent Star Identification Strategy[J]. Optical Engineering,2006,45(6):63601~63604.
[113]史英海,王志峰,黄欣,等.面向星敏感器测试的数字星模系统设计[J].空间控制技术与应用,2009,35(3):39~43.
[114]巩岩,胡宜宁,赵阳.基于数字光处理技术的小型星模拟器设计[J].光学精密工程,2007,15(11):1698~1703.
[115]孙高飞,张国玉,姜会林,等.甚高精度星模拟器设计[J].光学精密工程,2011,19(8):1730~1735.
[116]塬陈,张文明.面向星模拟器的可调标准色温光源[J].光电工程,2010,37(8):24~28.
[117]张文明,王效才,马屹,等.星敏感器单星模拟光源系统[J].光电工程,1998,25(A12):74~78.
[118]张建伟.动态星图形成及星空模拟器研究[D].哈尔滨工业大学,2003.
[119]赵晨光,谭久彬,刘俭,等.用于天文导航设备检测的星模拟装置[J].光学精密工程,2010,18(6):1326~1332.
[120]张伟,潘海斌,鲍文卓,等.星空背景数字图像的生成[J].光学精密工程,2009,17(3):676~682.
[121]陈吉.基于液晶光阀的星模拟器研究[D].长春理工大学,2008.
[122]郝允慧,张国玉.小型静态星模拟器光学系统设计[J].长春理工大学学报(自然科学版),2009,32(4):545~546,549.
[123]马士宝.动态星模拟器星图仿真技术研究[D].长春理工大学,2009.
[124]张文明.小型星模拟器的研制方法和研制技术[D].电子科技大学,2003.
[125]邢飞,武延鹏,董瑛,等.微型星敏感器实验室测试系统研究[J].光学技术,2004,30(6):703~709.
[126]君杨,涛张,宋靖雁,等.全天球地面动态星模拟器算法研究[J].系统仿真学报,2010,22(Sl1):202~206.
[127]魏晓蓉.精密双轴位置转台设计[D].电子科技大学,2008.
[128] Liu H B, Tan Y C, Sheng D Y, et al. Distortion Model for Star Tracker[C].Proc. SPIE,2010,75445:75445T~75446T.
[129]闫亚东.用Zemax模拟五棱镜误差对平行度检测的影响[J].应用光学,2007,28(5):649~653.
[130] Hancock B R, Stirbl R C, Cunningham T J, et al. CMOS Active Pixel SensorSpecific Performance Effects on Star Tracker/Imager Position Accuracy[C]. Proc. SPIE,2001,4284:43~53.
[131] Liu X P, Cai X Y, Chang S D, et al. Bifocal Optical System for DistantObject Tracking[J]. Optics Express,2005,13(1):136~141.
[132] Kawano H, Shimoj H, Yoshikawa S, et al. Optical Testing of Star Sensor(I):Defocus Spot Measuring Technique for Ground-Based Test[J]. Optical Review,2008,15(2):110~117.
[133]蔻生,余建军,郭旭红,等.新型敏感器有限元动力学分析[J].光学技术,2010,36(4):505~508.
[134]刘海波,谭吉春,沈本剑.星敏感器光学系统的热/结构/光分析[J].宇航学报,2010,31(3):875~879.
[135]刘海波,谭吉春,郝云彩,等.环境温度对星敏感器测量精度的影响[J].光电工程,2008,35(12):40~44.
[136]牛晓明.空间光学遥感器的热响应分析及热控[J].光学精密工程,1998,6(6):74~78.
[137]卢欣,周建涛,蔡伟,等.星敏感器空间辐射效应研究[J].宇航学报,2010,31(1):24~30.
[138] Singla P, Griffith D T, Crassidis J L, et al. Attitude Determination andAutonomous On-orbit Calibration of Star Tracker for the Gifts Mission[J]. Advances inthe Astronautical Sciences,2002,112I:19~38.
[139] Shuster M D, OHS D. Three-Axis Attitude Determination From VectorObservation[J]. Journal of Guidance and Control,1981,1(4):70~77.
[140] Snow F, Krack K, Sheu Y, et al. Accuracy Study of the Upper AtmosphereResearch Satellite （UARS） Definitive Attitude Determination[J]. FlightMechanics/Estimation Theory Symposium,1988,10(11):26~41.
[141] Shuster M D, Pitone D S, Bierman G J. Batch Estimation of SpacecraftSensor Alignments I-Relative Alignment Estimation[J]. The Journal of theAstronautical Sciences,1991,4(39):519~545.
[142] Shuster M D, Pitone D S. Batch Estimation of Spacecraft Sensor AlignmentsIi-Absoulte Alignment Estimation[J]. The Journal of the Astronautical Sciences,1991,4(39):547~571.
[143] Pal M, Bhat M S. Star Camera Calibration Combined with IndependentSpacecraft Attitude Determination[C].2009American Control Conference, HyattRegency Riverfront, St. Louis, MO, USA, June10-12,2009,4836-4841.
[144]袁彦红,耿云海,陈雪芹.基于陆标敏感器对星敏感器在轨标定算法研究[J].哈尔滨商业大学学报（自然科学版）,2008,24(4):448~453.
[145] Griffith D T, Singla P, Junkins J L. Autonomous On-Orbit CalibrationApproaches for Star Tracker Cameras[C]. Spaceflight Mechanics2002, San Antonio,TX, United states: Univelt Inc.,2002,39~57.
[146] Samaan M A, Griffith T, Junkins J L. Autonomous On-Orbit Calibration ofStar Trackers[C].2001Core Technologies for Space Systems Conference, ColoradoSprings, CO, Nov28-30,2001.
[147]刘一武.惯性敏感器与星敏感器之间在轨自主标定比较研究[J].航天控制,2005,23(2):59~63.
[148]袁彦红.利用高精度陀螺对星敏感器在轨标定算法研究[J].系统工程与电子技术,2008,30(1):120~123.
[149]袁彦红,耿云海,陈雪芹.星敏感器自主在轨标定算法[J].上海航天,2008,25(3):3~10.
[150]魏新国,张广军,樊巧云,等.基于RAC约束的星敏感器在轨校准方法[J].光学精密工程,2008,16(10):2009~2013.
[151]钟红军,杨孟飞,卢欣.星敏感器标定方法研究[J].光学学报,2010,30(5):1343~1348.
[152]申娟,张广军,魏新国.基于卡尔曼滤波的星敏感器在轨校准方法[J].航空学报,2010,31(6):1220~1224.
[153] Smith N H. Localized Distortion Estimation and Correction for the ICESatStar Trackers[D]. The University of Texas at Austin,2006.
[154] Meeus J. Astronomical Algorithms[M]. United States: Willmann-Bell, Inc,1991.
[155] Padgett C, Kreutz-Delgado K. A Grid Algorithm for Autonomous StarIdentification[J]. IEEE Transactions on Aerospace and Electronic Systems,1997,33(1):202~212.
[2]施少范.国外对地观测卫星高精度姿态控制系统研究[J].上海航天,2000,17(6):49~53.
[3] Liebe C C. Star Trackers for Attitude Determination[J]. Ieee Aerospace AndElectronic Systems Magazine,1995,10(6):10~16.
[4] Iwata T, Yoshizawa T. Precision Attitude and Orbit Control System for theAdvanced Land Observing Satellite (AlOS)[C]. AIAA Guidance, Navigation, andControl Conference and Exhibit, Austin, Texas,2003,11~14.
[5] Schmidt U, Elstner C, Michel K. ASTRO15Star Tracker Flight Experienceand Further Improvements Towards the ASTRO APS Star Tracker [C]. AIAA Guidance,Navigation and Control Conference and Exhibit,2008, AIAA2008-6649.
[6] Liebe C C. Accuracy Performance of Star Trackers-A Tutorial[J]. IEEETransactions on Aerospace and Electronic Systems,2002,38(2):587~599.
[7]娇媛媛.基于星敏感器/陀螺组合测量的卫星姿态确定方法研究[D].国防科学技术大学,2007.
[8] Rao J S, Pullaiah D. Star Tracker Alignment Determination forResourcessat-I[C]. AIAA/AAS Astrodynamics Specialist Conference and Exhibit,Providence, Rhode Island:2004.
[9] Iwata T, Hoshino H, Yoshizawa T, et al. Precision Attitude Determination forthe Advanced Land Observing Satellite (AlOS): Design, Verification and On-OrbitCalibration[C]. AIAA Guidance, Navigation and Control Conference and Exhibit,South Carolina,2007.
[10] Peter S J, John L J, Troelz D, et al. In-Flight Quality and Accuracy of AttitudeMeasurements From the Champ Advanced Stellar Compass[J]. Acta Astronuatica,2005,56:181~186.
[11] Leeghim H, Choi Y, Jaroux B A. Uncorrelated Unscented Filtering forSpacecraft Attitude Determination[J]. Acta Astronautica,2010,67(1-2):135~144.
[12]王晨,房建成.基于Unscented四元数粒子滤波的微小卫星姿态估计[J].北京航空航天大学学报,2007,35(5):553~556.
[13]段方,刘建业,李荣冰.一种改进的星敏感器/陀螺卫星定姿算法[J].系统工程与电子技术,2006,28(6):896~899.
[14] Brij N A, William J P. Angular Rate Estimation for Gyroless Satellite AttitudeControl[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit,5-8August2002, Monterey, California,2002, AIAA2002-4463.
[15]高云国.现代小卫星及其相关技术[J].光学精密工程,1999,7(5):16~21.
[16] Flatley T W, Forden J K, Henretty D A, et al. On-Board AttitudeDetermination and Control Algorithms for Sampex[R]. NASA CP3102, NASAGoddard Space Flight Center, Greenbelt, MD:1990.379~398.
[17] Liebe C C, Gromov K, Meller D M. Toward a Stellar Gyroscope forSpacecraft Attitude Determination[J]. Journal of Guidance, Control, and Dynamics,2004,27(1):91~99.
[18] Bar-Itzhack I Y, Harman R R. A Feedback Approach to Spacecraft AngularRate Estimation[C]. AIAA Guidance, Navigation, and Control Conference and Exhibit,Keystone, Colorado,21-24August2006, AIAA2006-6807.
[19] Palermo W J. Angular Rate Estimation for Gyroless Satellite AttitudeControl[D]. Naval Postgraduate School,2001.
[20] Wahba G. A Least Squares Estimate of Spacecraft Attitude[J]. Problem65-1.SIAM Review,1965,7(3):409.
[21] Shuster M D. Maximum Likelihood Estimation of Spacecraft Attitude[J]. TheJournal of the Astronautical Sciences,1989,37(1):79~88.
[22] Barman I Y B R. Optimized Triad Algorithm for Attitude Determination[C].San Diego, CA: American Institute of Aeronautics and Astronautics, Inc.,1996.422~427.
[23] Vogt J. Attitude Determination of a Three-Axis Stabilized Spacecraft UsingStar Sensors[D]. Naval Postgraduate School,1999.
[24] Travis H D. Attitude Determination Using Star Tracker Data with KalmanFilters[D]. Naval Postgraduate School,2001.
[25]李春艳,谢华,李怀锋,等.高精度星敏感器星点光斑质心算法[J].光电工程,2006,33(2):41~44.
[26]王广君,房建成.一种星图识别的星体图像高精度内插算法[J].北京航空航天大学学报,2005,31(5):566~569.
[27] Rufino G, Accardo D. Enhancement of the Centroiding Algorithm for StarTracker Measure Refinement[J]. Acta Astronautica,2003,53(2):135~147.
[28] Lam Q, Woodruff C, Ashton S, et al. Noise Estimation for Star TrackerCalibration and Enhanced Precision Attitude Determination[C]. Proceedings of the FifthInternational Conference on Information Fusion,2002, I:235~242.
[29]张辉,钟建勇,袁家虎,等.电路噪声对星敏感器星点定位精度的影响[J].光学精密工程,2006,14(6):1052~1056.
[30]张辉,袁家虎,刘恩海. CCD噪声对星敏感器星点定位精度的影响[J].红外与激光工程,2006,35(5):629~633.
[31] Blarre L, Perrimon N, Majewski L, et al. Hydra Multiple Heads Star TrackerBased On Active Pixel Sensor and the Gyrometer Assistance Option[C]. AIAA57thInternational Astronautical Congress, IAC2006, October2,2006-October6,2006,4187~4195.
[32] Blarre L, Perrimon N, Airey S. New Multiple Head Star Sensor (HYDRA)Description and Development Status: a Highly Autonomous, Accurate and Very RobustSystem to Pave the Way for Gyroless Very Accurate AOCS Systems[C]. AIAAGuidance, Navigation, and Control Conference2005, San Francisco, CA, UnitedStates: American Institute of Aeronautics and Astronautics Inc.,2005,817~825.
[33] Liebe C C, Alkalai L, Domingo G, et al. Micro APS Based Star Tracker [C].IEEE,2002,5-2285~5-2300.
[34]李春艳.高精度轻小型星敏感器系统设计与技术研究[D].中国科学院国家天文台,2006.
[35]钟红军,杨孟飞,卢欣. APS图像传感器及其在星敏感器中的应用[J].光学技术,2009,35(2):204~208.
[36]袁彦红.星敏感器在轨标定算法研究[D].哈尔滨工业大学,2003.
[37] Paulsen T E, Maresi L. Calibration and Verification of the Terma Star Trackerfor the Nemo Satellite[C]. AIAA Space2000Conference and Exposition, Long Beach,CA, Sept.19-21,2000.
[38] Rufino G, Moccia A. Stellar Scene Simulation for Indoor Calibration ofModern Star Trackers[J]. Space Technology,2001,21(1-2):41~51.
[39]巩岩,胡宜宁.星模拟器星光颜色模拟的初步研究[J].光电工程,2010,37(2):65~68,73.
[40]李英才,冯广军,马臻.一种高星等标准星光模拟器的设计与性能分析[J].应用光学,2010,(01):39~42.
[41]潘平.单星模拟器数字光源研制技术[D].中国科学院西安光学精密机械研究所,2005.
[42]钟奉金,许世文,赵亮,等.星模拟器中积分球内光纤端面有效照度的计算[J].哈尔滨工业大学学报,1998,30(4):113~115.
[43] Griffith D T, Junkins J L. Recursive On-Orbit Calibration of Star Sensors[C].World Space Conference, Houston, Texas, October2002.
[44] Marschke J M, Crassidis J L, Lam Q M. Attitude Estimation without RateGyros Using Generalized Multiple Model Adaptive Estimation[C]. AIAA Guidance,Navigation, and Control Conference,10-13August2009.
[45] Bar-Itzhack I Y, Oshman Y. Attitude Determination From VectorObservations: Quaternion Estimation[J]. IEEE Transactions on Aerospace andElectronic Systems,1985, AES-21(1):128~136.
[46] Gai E, Daly K, Harrison J, et al. Star-Sensor-Based Satellite Attitude/AttitudeRate Estimater[J]. Journal of Guidance, Control and Dynamics,1982,8(5):565~650.
[47] Harman R R, Bar-Itzhack I Y. Angular-Rate Computation Using AttitudeDifferentiation[R]. Faculty of Aerospace Eng., Technion-Israel Institute of Technology,1997.
[48] Bar-Itzhack I Y. Classification of Algorithms for Angular VelocityEstimation[J]. Journal of Guidance, Control, and Dynamic,2001,24(2):214~218.
[49] Shuster M D. A Survey of Attitude Representations[J]. The Journal of theAstronautical Sciences,1993,41(4):439~517.
[50] Azor R, Bar-Itzhack I Y, Deutschmann J K, et al. Angular-Rate EstimationUsing Delayed Quaternion Measurements[J]. Journal of Guidance, Control, andDynamic,2001,24(3):436~443.
[51] Harman R R, Bar-Itzhack I Y. Pseudolinear and State-Dependent RiccatiEquation Filters for Angular Rate Estimation[J]. Journal Guidance,1999,22(5):723~725.
[52] Bar-Itzhack I Y, Harman R R, Choukroun D. State-Dependent Pseudo-LinearFilters for Spacecraft Attitude and Rate Estimation[C]. AIAA Guidance, Navigation,and Control Conference and Exhibit, Monterey, California: AIAA,2002.
[53] Carmi A, Oshman Y. Robust Spacecraft Angular-Rate Estimation FromVector Observations Using Fast Interlaced Particle Filtering[C]. AIAA Guidance,Navigation, and Control Conference and Exhibit, San Francisco, California: AmericanInstitute of Aeronautics and Astronautics,2005.
[54] Nagendra G R, Alex T K. Incremental-Angle and Angular VelocityEstimation Using a Star Sensor[J]. Journal of Guidance, Control, and Dynamic,2002,25(3):433~441.
[55] Oshman Y, Landis Markley F. Sequential Attitude and Attitude-RateEstimation Using Integrated-Rate Parameters[J]. Journal of Guidance, Control, andDynamics,1999,22(3):385~394.
[56]杨亚非,李建国.基于UPF和修正Rodrigues参数的无陀螺姿态确定算法[J].中国惯性技术学报,2009,17(2):149~152.
[57] Shi Y, Zhang X D. Kalman-Filtering-Based Angular Velocity EstimationUsing Infrared Attitude Information of Spacecraft[J]. Optical Engineering,2000,39(2):551~557.
[58]林玉荣,邓正隆.基于星敏感器估计卫星姿态的预测Kalman滤波算法[J].中国科学（E辑）,2002,32(6):817~823.
[59]张惟,林宝军,张泽明,等.矢量观测确定卫星姿态的预测粒子滤波算法[J].宇航学报,2011,32(5):1077~1085.
[60]钱勇,周凤岐,周军.三轴稳定卫星无陀螺姿态确定算法研究[J].飞行力学,2001,19(4):45~48,53.
[61]杨小会.基于天文信息的卫星自主导航[D].西北工业大学,2006.
[62]孙兆伟,李晖,张世杰.仅用星敏感器的卫星姿态估计UKF算法研究[J].飞行力学,2006,24(3):56~60.
[63]程杨,杨涤,崔祜涛.利用Singer模型的无陀螺姿态和角速度估计[J].航空学报,2002,23(6):507~511.
[64]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[J].上海航天,2005,22(5):14~18.
[65]靳永强,刘向东,侯朝桢.基于UKF的无陀螺姿态确定[J].航天控制,2007,25(4):31~35.
[66] Crassidis J L. Angular Velocity Determination Directly From Star TrackerMeasurements[J]. Journal of Guidance, Control, and Dynamics,2002,25(6):1165~1168.
[67] Samaan M A, Mortari D, Junkins J L. Recursive Mode Star IdentificationAlgorithms[J]. IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1246~1254.
[68] Kolomenkin M, Pollak S, Shimshoni I, et al. Geometric Voting Algorithm forStar Trackers[J]. IEEE Transactions on Aerospace and Electronic Systems,2008,44(2):441~456.
[69] Liu H B, Wang J Q, Tan J C, et al. Autonomous On-Orbit Calibration of aStar Tracker Camera[J]. Optical Engineering,2011,50(2):23604~23608.
[70] Sage A P, Husa G W. Adaptive Filtering with Unknown Prior Statistics[C].Joint Americam Control Conference,1969,769~774.
[71] Singer R A. Estimating Optimal Tracking Filter Performance for MannedManeuvering Targets[J]. IEEE Transactions on Aerospace and Electronic Systems,1970,6(4):473~483.
[72] Grossman S B, Emmons R B. Performance Analysis and Size Optimization ofFocal Planes for Point-Source Tracking Algorithm Applications[J]. Optical Engineering,1984,23(2):167~176.
[73] Abdou I E. Effect of Signal Truncation on Centroid Location ErrorEstimation[J]. Optical Engineering,1996,35(4):1221~1222.
[74] Salomon P M, Goss W C. A Microprocessor-Controlled CCD Star Tracker[C].AIAA1976, AIAA76-0116.
[75] Salomon P M, Glavich T A. Image Signal Processing in Sub-Pixel AccuracyStar Trackers[C]. Proc. SPIE,1980,252:64~74.
[76] Kraemar S, Downes R, Katsanis R, et al. STIS Target Acquisition[C]. inProceedings of Hubble Space Telescope Calibration Workshop,1997,39~46.
[77] Lee S. Pointing Accuracy Improvement Using Model-Based Noise ReductionMethod[C]. Proc. SPIE,2002,4635:65~71.
[78] Quine B M, Tarasyuk V, Mebrahtu H, et al. Determining Star-Image Location:A New Sub-Pixel Interpolation Technique to Process Image Centroids[J]. ComputerPhysics Communications,2007,177(9):700~706.
[79] Yang J, Zhang T, Song J Y, et al. A New Sub-Pixel Subdivision LocationAlgorithm for Star Image[C]. Tianjin, China: IEEE Computer Society,2009.
[80] Winick K A. Cramér-Rao Lower Bounds On the Performance ofCharge-Coupled-Device Optical Position Estimators[J]. Journal of the Optical Societyof America A: Optics and Image Science, and Vision,1986,3(11):1809~1815.
[81] Chen H L, and Rao C. Accuracy Analysis on Centroid Estimation AlgorithmLimited by Photon Noise for Point Object[J]. Optics Communications,2009,282(8):1526~1530.
[82] Jia H, Yang J K, Li X J, et al. Systematic Error Analysis and Compensationfor High Accuracy Star Centroid Estimation of Star Tracker[J]. Science ChinaTechnological Sciences,2010,53(11):3145~3152.
[83]王兆魁,张育林.一种CCD星图星点快速定位算法[J].空间科学学报,2006,26(3):209~214.
[84] Motari D, Romoli A, Difesa A. Starnav III: A Three Fields of View StarTracker[J]. IEEE on Aerospace Confence,2002,47~57.
[85] Samaan M A, Pollock T C, Junkins J L. Predictive Centroiding for StarTrackers with the Effect of Image Smear[J]. The Journal of the Astronautical Sciences,2002,50(1):113~123.
[86] Samaan M A, Mortari D, Pollock T C, et al. Predictive Centroiding for Singleand Multiple Fovs Star Trackers[C]. Spaceflight Mechanics2002, San Antonio, TX,United states: Univelt Inc.,2002,112I:59~71.
[87]江洁,张广军,李霄,等.一种快速的星敏感器星跟踪方法研究[J].航空学报,2006,27(5):913~916.
[88]江洁,张广军,李霄,等.星敏感器中快速星匹配跟踪算法研究[J].光电工程,2007,34(1):9~12.
[89]李葆华,马衍宇,刘睿,等.适用于星敏感器的预测未知恒星星像质心算法[J].光学精密工程,2009,17(1):191~195.
[90]王新升,李葆华,郑靖.应用有限冲击响应滤波器消除星敏感器星像噪声[J].光学精密工程,2010,18(06):1381~1386.
[91]刘海波,杨建坤,谭吉春,等.一种星敏感器恒星像点位置提取方法[P].中国专利:201010216643.1,2010-07-05.
[92] Welch G, Bishop G. An Introduction to the Kalman Filter[M]. SIGGRAPH2001, Los Angeles, CA, August12-17,2001.
[93] Zheng S, Tian Y L, Tian J W, et al. Facet-Based Star Acquisition Method[J].Optical Engineering,2004,43(11):2796~2805.
[94]刘海波,宿德志,谭吉春,等.考虑卫星轨道和像移影响的星敏感器星图模拟方法[J].宇航学报,2011,32(5):1190~1194.
[95]何友,修建娟,张晶炜,等.雷达数据处理及应用（第二版）[M].北京:电子工业出版社,2009.
[96] Castro G J, Nieto J, Gallego L M, et al. An Effective Camera CalibrationMethod[C]. Advanced Motion Control,1998,171~174.
[97] Wang J, Lu N G, Dong M L, et al. A New Method for Linear CameraCalibration and Nonlinear Distortion Correction [C]. Proc. SPIE,2006,6280:62802O-1~62802O-6.
[98] Penna M A. Camera Calibration: A Quick and Easy Way to Determine theScale Factor[J]. IEEE Transactions on Paitern Analysis and Machine Intelligence,1991,13(12):1240~1245.
[99] Faig W. Calibration of Close-Range Photogrammetric Systems:Mathematical Formulation[J]. Photogrammetric Eng. Remote Sensing,1975,41(12):1479~1486.
[100] Ganapathy S. Decomposition of Transformation Matrices for RobotVision[J]. IEEE Conference on Robotics Automat,1984,130~139.
[101] Tsai R T. A Versatile Camera Calibration Technique for High-Accuracy3DMachine Vision Metrology Using off the Shelf TV Camera and Lenses[J]. IEEE Journalof Robotics and Automation,1987, RA-3(4):323~344.
[102] Bacakoglu H, Kamel M S. A Three-Step Camera Calibration Method[J].IEEE Transactions on Instrumentation and Measurement,1997,46(5):1165~1172.
[103] Weng J, Cohen P, Herniou M. Camera Calibration with Distortion Modelsand Accuracy Evaluation[J]. IEEE Transactions on Pattern Analysis and MachineIntelligence,1992,14(10):965~980.
[104]于起峰,陆宏伟,刘肖琳.基于图像的精密测量与运动测量[M].北京:科学出版社,2002.
[105] Klaus A, Bauer J, Karner K, et al. Camera Calibration from a Single NightSky Image[C]. Proceedings of the2004IEEE Computer Society Conference onComputer Vision and Pattern Recognition, Washington, DC: Institute of Electricaland Electronics Computer Society, Palo Alto,2004,151~157.
[106]李春艳,李怀锋,孙才红.高精度星敏感器天文标定方法及观测分析[J].光学精密工程,2006,14(4):558~563.
[107]田宏,袁家虎,李展,等.星敏感器在地面观星实验的结果分析[J].光电工程,2001,28(5):1~4.
[108]李学夔,李杰.一种非设备方式对星敏感器进行精度标定的新方法[J].电子器件,2009,32(1):204~207.
[109]张广军,郝雪涛,江洁.一种基于无偏差带的星敏感器地面校准方法[P].中国专利:200610065233.5,2007-8-8.
[110] Rufino G, Moccia A. Laboratory Test System for Performance Evaluation ofAdvanced Star Sensors[J]. Journal of Guidance Control and Dynamics,2002,25(2):200~208.
[111] Quan W, Fang J C, Zhang W N, A Method of Optimization for the DistortedModel of Star Map Based On Improved Genetic Algorithm[J]. Aerospace Science andTechnology,2011,15(2):103~107.
[112] Xing F, Dong Y, You Z. Laboratory Calibration of Star Tracker withBrightness Independent Star Identification Strategy[J]. Optical Engineering,2006,45(6):63601~63604.
[113]史英海,王志峰,黄欣,等.面向星敏感器测试的数字星模系统设计[J].空间控制技术与应用,2009,35(3):39~43.
[114]巩岩,胡宜宁,赵阳.基于数字光处理技术的小型星模拟器设计[J].光学精密工程,2007,15(11):1698~1703.
[115]孙高飞,张国玉,姜会林,等.甚高精度星模拟器设计[J].光学精密工程,2011,19(8):1730~1735.
[116]塬陈,张文明.面向星模拟器的可调标准色温光源[J].光电工程,2010,37(8):24~28.
[117]张文明,王效才,马屹,等.星敏感器单星模拟光源系统[J].光电工程,1998,25(A12):74~78.
[118]张建伟.动态星图形成及星空模拟器研究[D].哈尔滨工业大学,2003.
[119]赵晨光,谭久彬,刘俭,等.用于天文导航设备检测的星模拟装置[J].光学精密工程,2010,18(6):1326~1332.
[120]张伟,潘海斌,鲍文卓,等.星空背景数字图像的生成[J].光学精密工程,2009,17(3):676~682.
[121]陈吉.基于液晶光阀的星模拟器研究[D].长春理工大学,2008.
[122]郝允慧,张国玉.小型静态星模拟器光学系统设计[J].长春理工大学学报(自然科学版),2009,32(4):545~546,549.
[123]马士宝.动态星模拟器星图仿真技术研究[D].长春理工大学,2009.
[124]张文明.小型星模拟器的研制方法和研制技术[D].电子科技大学,2003.
[125]邢飞,武延鹏,董瑛,等.微型星敏感器实验室测试系统研究[J].光学技术,2004,30(6):703~709.
[126]君杨,涛张,宋靖雁,等.全天球地面动态星模拟器算法研究[J].系统仿真学报,2010,22(Sl1):202~206.
[127]魏晓蓉.精密双轴位置转台设计[D].电子科技大学,2008.
[128] Liu H B, Tan Y C, Sheng D Y, et al. Distortion Model for Star Tracker[C].Proc. SPIE,2010,75445:75445T~75446T.
[129]闫亚东.用Zemax模拟五棱镜误差对平行度检测的影响[J].应用光学,2007,28(5):649~653.
[130] Hancock B R, Stirbl R C, Cunningham T J, et al. CMOS Active Pixel SensorSpecific Performance Effects on Star Tracker/Imager Position Accuracy[C]. Proc. SPIE,2001,4284:43~53.
[131] Liu X P, Cai X Y, Chang S D, et al. Bifocal Optical System for DistantObject Tracking[J]. Optics Express,2005,13(1):136~141.
[132] Kawano H, Shimoj H, Yoshikawa S, et al. Optical Testing of Star Sensor(I):Defocus Spot Measuring Technique for Ground-Based Test[J]. Optical Review,2008,15(2):110~117.
[133]蔻生,余建军,郭旭红,等.新型敏感器有限元动力学分析[J].光学技术,2010,36(4):505~508.
[134]刘海波,谭吉春,沈本剑.星敏感器光学系统的热/结构/光分析[J].宇航学报,2010,31(3):875~879.
[135]刘海波,谭吉春,郝云彩,等.环境温度对星敏感器测量精度的影响[J].光电工程,2008,35(12):40~44.
[136]牛晓明.空间光学遥感器的热响应分析及热控[J].光学精密工程,1998,6(6):74~78.
[137]卢欣,周建涛,蔡伟,等.星敏感器空间辐射效应研究[J].宇航学报,2010,31(1):24~30.
[138] Singla P, Griffith D T, Crassidis J L, et al. Attitude Determination andAutonomous On-orbit Calibration of Star Tracker for the Gifts Mission[J]. Advances inthe Astronautical Sciences,2002,112I:19~38.
[139] Shuster M D, OHS D. Three-Axis Attitude Determination From VectorObservation[J]. Journal of Guidance and Control,1981,1(4):70~77.
[140] Snow F, Krack K, Sheu Y, et al. Accuracy Study of the Upper AtmosphereResearch Satellite （UARS） Definitive Attitude Determination[J]. FlightMechanics/Estimation Theory Symposium,1988,10(11):26~41.
[141] Shuster M D, Pitone D S, Bierman G J. Batch Estimation of SpacecraftSensor Alignments I-Relative Alignment Estimation[J]. The Journal of theAstronautical Sciences,1991,4(39):519~545.
[142] Shuster M D, Pitone D S. Batch Estimation of Spacecraft Sensor AlignmentsIi-Absoulte Alignment Estimation[J]. The Journal of the Astronautical Sciences,1991,4(39):547~571.
[143] Pal M, Bhat M S. Star Camera Calibration Combined with IndependentSpacecraft Attitude Determination[C].2009American Control Conference, HyattRegency Riverfront, St. Louis, MO, USA, June10-12,2009,4836-4841.
[144]袁彦红,耿云海,陈雪芹.基于陆标敏感器对星敏感器在轨标定算法研究[J].哈尔滨商业大学学报（自然科学版）,2008,24(4):448~453.
[145] Griffith D T, Singla P, Junkins J L. Autonomous On-Orbit CalibrationApproaches for Star Tracker Cameras[C]. Spaceflight Mechanics2002, San Antonio,TX, United states: Univelt Inc.,2002,39~57.
[146] Samaan M A, Griffith T, Junkins J L. Autonomous On-Orbit Calibration ofStar Trackers[C].2001Core Technologies for Space Systems Conference, ColoradoSprings, CO, Nov28-30,2001.
[147]刘一武.惯性敏感器与星敏感器之间在轨自主标定比较研究[J].航天控制,2005,23(2):59~63.
[148]袁彦红.利用高精度陀螺对星敏感器在轨标定算法研究[J].系统工程与电子技术,2008,30(1):120~123.
[149]袁彦红,耿云海,陈雪芹.星敏感器自主在轨标定算法[J].上海航天,2008,25(3):3~10.
[150]魏新国,张广军,樊巧云,等.基于RAC约束的星敏感器在轨校准方法[J].光学精密工程,2008,16(10):2009~2013.
[151]钟红军,杨孟飞,卢欣.星敏感器标定方法研究[J].光学学报,2010,30(5):1343~1348.
[152]申娟,张广军,魏新国.基于卡尔曼滤波的星敏感器在轨校准方法[J].航空学报,2010,31(6):1220~1224.
[153] Smith N H. Localized Distortion Estimation and Correction for the ICESatStar Trackers[D]. The University of Texas at Austin,2006.
[154] Meeus J. Astronomical Algorithms[M]. United States: Willmann-Bell, Inc,1991.
[155] Padgett C, Kreutz-Delgado K. A Grid Algorithm for Autonomous StarIdentification[J]. IEEE Transactions on Aerospace and Electronic Systems,1997,33(1):202~212.