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热漂移标定位置误差检测模型通过分别测量各个平台基准棱镜的坐标偏移量,获取其相邻垂直面即平台中心位置的姿态信息。误差检测模型计算时所用的3种坐标系如图 2所示。多星敏感器在真空罐内部安装平台上的中心坐标为m0(xm0, ym0, zm0),n0(xn0, yn0, zn0),p0(xp0, yp0, zp0)。系统开始运行前,通过误差检测模型得到的3个基准方棱镜在棱镜坐标系中的坐标位移偏差为m1(xm1, ym1, zm1),n1(xn1, yn1, zn1),p1(xp1, yp1, zp1);系统稳定时再次测量得到的坐标位移偏差为m2(xm2, ym2, zm2),n2(xn2, yn2, zn2),p2(xp2, yp2, zp2)。系统由开始到稳定运行时,测得基准棱镜沿各轴方向产生的误差矩阵C为:
$ \begin{array}{*{20}{l}} {{\bm{C}} = \left[ {\begin{array}{*{20}{l}} {\Delta {x_1}\;\;\;\;\Delta {x_2}\;\;\;\;\Delta {x_3}}\\ {\Delta {y_1}\;\;\;\;\Delta {y_2}\;\;\;\;\Delta {y_3}}\\ {\Delta {z_1}\;\;\;\;\Delta {z_2}\;\;\;\;\Delta {z_3}} \end{array}} \right] = }\\ {\left[ {\begin{array}{*{20}{l}} {{x_{{m_2}}} - {x_{{m_1}}}\;\left[ {\left( {{x_{{n_2}}} - {x_{{n_1}}}} \right) - \sqrt 3 \left( {{z_{{n_2}}} - {z_{{n_1}}}} \right)} \right]/2\left[ {\left( {{x_{{p_2}}} - {x_{{p_1}}}} \right) + \sqrt 3 \left( {{z_{{p_2}}} - {z_{{p_1}}}} \right)} \right]/2}\\ {{y_{{m_2}}} - {y_{{m_1}}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{y_{{n_2}}} - {y_{{n_1}}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{y_{{p_2}}} - {y_{{p_1}}}}\\ {{z_{{m_2}}} - {z_{{m_1}}}\;\;\left[ {\sqrt 3 \left( {{x_{{n_2}}} - {x_{{n_1}}}} \right) + \left( {{z_{{n_2}}}{ - _{{n_1}}}} \right)} \right]/2\left[ {\sqrt 3 \left( {{x_{{p_2}}} - {x_{{p_1}}}} \right) - \left( {{z_{{p_2}}} - {z_{{p_1}}}} \right)} \right]/2} \end{array}} \right]} \end{array} $
(1) 则基准棱镜坐标矩阵M的计算公式为:
$ \;\mathit{\boldsymbol{M}} = \left[ \begin{array}{l} {x_{{m_0}}} + \Delta {x_1}\;\;\;\;\;{x_{{n_0}}} + \Delta {x_2}\;\;\;\;\;{x_{{p_0}}} + \Delta {x_3}\\ {y_{{m_0}}} + \Delta {y_1}\;\;\;\;\;{y_{{n_0}}} + \Delta {y_2}\;\;\;\;\;\;{y_{{p_0}}} + \Delta {y_3}\\ {z_{{m_0}}} + \Delta {z_1}\;\;\;\;\;{z_{{n_0}}} + \Delta {z_2}\;\;\;\;\;\;{z_{{p_0}}} + \Delta {z_3} \end{array} \right] $
(2) 设变化坐标矩阵M与初始坐标矩阵M0之间的变化矩阵为A,根据MA=M0,可以得到变换矩阵A的计算公式如下:
$ \begin{array}{l} \mathit{\boldsymbol{A}} = \left[ \begin{array}{l} {a_{11}}\;\;\;\;\;{a_{12}}\;\;\;\;\;{a_{13}}\\ {a_{21}}\;\;\;\;\;{a_{22}}\;\;\;\;\;{a_{23}}\\ {a_{31}}\;\;\;\;\;{a_{32}}\;\;\;\;\;{a_{33}} \end{array} \right] = \\ {\left[ \begin{array}{l} {x_{{m_0}}} + \Delta {x_1}\;\;\;{x_{{n_0}}} + \Delta {x_2}\;\;\;{x_{{p_0}}} + \Delta {x_3}\\ {y_{{m_0}}} + \Delta {y_1}\;\;\;\;{y_{{n_0}}} + \Delta {y_2}\;\;\;{y_{{p_0}}} + \Delta {y_3}\\ {z_{{m_0}}} + \Delta {z_1}\;\;\;\;{z_{{n_0}}} + \Delta {z_2}\;\;\;{z_{{p_0}}} + \Delta {z_3} \end{array} \right]^{ - 1}}\left[ \begin{array}{l} {x_{{m_0}}}\;\;\;{x_{{n_0}}}\;\;\;{x_{{p_0}}}\\ {y_{{m_0}}}\;\;\;{y_{{n_0}}}\;\;\;{y_{{p_0}}}\\ {z_{{m_0}}}\;\;\;{z_{{n_0}}}\;\;\;{z_{{p_0}}}\; \end{array} \right] \end{array} $
(3) 根据星敏感器标定系统测量结果,由3个星敏感分别测得的星图姿态四元数分别为:
$ \left\{ \begin{array}{l} {\mathit{\boldsymbol{q}}_m} = {\left[ {{q_{{m_0}}}\;\;\;{q_{{m_1}}}\;\;\;{q_{{m_2}}}\;\;\;{q_{{m_3}}}} \right]^{\rm{T}}} = {\left[ {{q_{{m_0}}}\;\;\;{{\mathit{\boldsymbol{\hat q}}}_m}} \right]^{\rm{T}}}\\ {\mathit{\boldsymbol{q}}_n} = {\left[ {{q_{{n_0}}}\;\;\;{q_{{n_1}}}\;\;\;{q_{{n_2}}}\;\;\;{q_{{n_3}}}} \right]^{\rm{T}}} = {\left[ {{q_{{n_0}}}\;\;\;{{\mathit{\boldsymbol{\hat q}}}_n}} \right]^{\rm{T}}}\\ {\mathit{\boldsymbol{q}}_p} = {[{q_{{p_0}}}\;\;\;\;{q_{{p_1}}}\;\;\;{q_{{p_2}}}\;\;\;{q_{{p_3}}}]^{\rm{T}}} = {[{q_{{p_0}}}\;\;\;{{\mathit{\boldsymbol{\hat q}}}_p}]^{\rm{T}}} \end{array} \right. $
(4) 式中, q为四元数标部,$ {\mathit{\boldsymbol{\hat q}}} $为四元数矢部。根根据角距测量原理,将星敏感器姿态偏移角等效为坐标偏移变化,则变化后的姿态四元数矢部矩阵为:
$ {\left[ \begin{array}{l} {{\mathit{\boldsymbol{\hat q}}}_{{m_1}}}\\ {{\mathit{\boldsymbol{\hat q}}}_{{n_1}}}\\ {{\mathit{\boldsymbol{\hat q}}}_{{p_1}}} \end{array} \right]^{\rm{T}}} = \mathit{\boldsymbol{A}}{\left[ \begin{array}{l} {{\mathit{\boldsymbol{\hat q}}}_m}\\ {{\mathit{\boldsymbol{\hat q}}}_n}\\ {{\mathit{\boldsymbol{\hat q}}}_p} \end{array} \right]^{^{\rm{T}}}} = \left[ \begin{array}{l} {a_{11}}\;\;\;\;{a_{12}}\;\;\;\;{a_{13}}\\ {a_{21}}\;\;\;\;{a_{22}}\;\;\;\;{a_{23}}\\ {a_{31}}\;\;\;\;{a_{32}}\;\;\;\;{a_{33}} \end{array} \right]\cdot{\left[ \begin{array}{l} {{\mathit{\boldsymbol{\hat q}}}_m}\\ {{\mathit{\boldsymbol{\hat q}}}_n}\\ {{\mathit{\boldsymbol{\hat q}}}_p} \end{array} \right]^{^{\rm{T}}}} $
(5) 由此得到剔除星敏感器相互间位置误差的姿态四元数矩阵结果如下:
$ {\left[ {{\mathit{\boldsymbol{q}}_{{m_1}}}\;\;\;\;{\mathit{\boldsymbol{q}}_{{n_1}}}\;\;\;\;{\mathit{\boldsymbol{q}}_{{p_1}}}} \right]^{\rm{T}}} = {\left[ \begin{array}{l} {\mathit{q}_{{m_0}}}\;\;\;\;\mathit{\boldsymbol{A}}{{\mathit{\boldsymbol{\hat q}}}_m}\\ {\mathit{q}_{{n_0}}}\;\;\;\;\mathit{\boldsymbol{A}}{{\mathit{\boldsymbol{\hat q}}}_n}\\ {\mathit{q}_{{p_0}}}\;\;\;\;\mathit{\boldsymbol{A}}{{\mathit{\boldsymbol{\hat q}}}_p} \end{array} \right]^{\rm{T}}} $
(6) -
为了验证多星敏感器热漂移标定位置误差检测模型的有效性,设置了试验对其检测精度进行计算。用于试验的星敏感器参量设置如表 1所示。
Table 1. Design parameters for the star sensors
parameters index field of view 12°×12° focal length 1121.54mm equipment length ≤1000mm angular accuracy ≤10″ temperature range -25℃~60℃ 为了减小初始安装位差以及平台自身制造误差带来的影响,试验初设3个星敏感平台位于同一平面上,且不存在倾斜等可能导致误差的情形。根据标定系统要求设置工作环境为真空,星敏感器固定安装面为平台底面,其温度变化范围为-25℃~60℃,且各星敏感器之间温度差值设置为±1℃,在温度变化范围内每隔1℃获取一次数据;平台安装面温度设置为恒温20℃。试验装置图如图 3所示。
Figure 3. Test device arrangement a—internal three-dimensional layout diagram b—experimental actual device layout
试验获得的各个基准棱镜变形偏移量结果见图 4。将上述结果所示的258组数据代入位置误差模型的(1)式~(5)式进行计算,得到多星敏感器热漂移标定时产生的姿态四元数极限偏差如列表 2所示。
Table 2. Deformation angle results of different temperature
temperature/℃ prism offset around the x axis/(″·℃-1) offset around the y axis/(″·℃-1) Offset around the z axis/(″·℃-1) -25 m -31.2349134 -0.0235792 0.3789641 n -39.3412561 -0.0155460 -24.1372848 p -38. 5584741 0.0609176 -23.4569765 60 m -24.6603975 0.0150 403 0.0159451 n -34.7124605 -0.0492412 -23.5409127 p -35.6208196 0.0143522 -23.7295659 计算结果显示,多星敏感器标定系统在-25℃和60℃时分别达到单位温度内的姿态极限偏移,多星敏感器由于位置误差造成的绕x, y, z轴的最小变化量分别为-24.660″/℃, 0.015″/℃, 0.159″/℃,而最大变化量分别为-39.341 ″/℃, -0.060″/℃, -24.137″/℃。根据数据可知,星敏感器平台位置误差在x向和z向更为敏感,会对星敏感器最终姿态偏移测量结果产生较大影响。当星敏感器热漂移标定精度要求控制在0.05°/℃时,经过误差检测模型的计算结果可比未检测前的精度提高至少11%,证实了该误差检测模型有效提高了系统标定精度。
多星敏感器地面热漂移标定位置误差检测研究
Method research of multiple star sensors ground thermal drift calibration position error detection
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摘要: 为了减少多个星敏感器地面热漂移标定时受到不同安装平台的位置误差影响, 采取一种多星敏感器地面热漂移标定位置误差检测方法,进行了理论分析和实验验证,取得了-25℃~60℃真空状态下系统中基准方棱镜变形的位置偏移量数据,并进行了标定位置误差精度分析。结果表明,多星敏感器位置绕各轴产生的最大偏移量分别为-39.341″/℃, -0.060″/℃, -24.137″/℃,通过建立误差检测模型对位置误差进行计算,将其从姿态测量结果的偏移量中剔除后获得更准确的星敏感器姿态测量四元数,剔除位置误差后的系统精度至少提高了11%。该研究在提高星敏感器热漂移标定精度方面具有很好的应用前景。Abstract: In order to reduce the affect of the deformation offset of different installation platforms on the ground thermal drift calibration of multiple star sensors, a multiple star sensor ground thermal drift calibration position error detection method was proposed. Theoretical analysis and experimental verification were carried out. The position deviation data of the reference square prism deformation in the system under the vacuum of -25℃~60℃ was obtained. And the accuracy analysis of calibration position error was carried out.The results show that, the maximum offsets of the multi-star sensor positions around each axis are -39.341″/℃, -0.060″/℃, and -24.137″/℃, repectively. By establishing the error detection model which was established according to the method of measuring position error, the position error was removed from the offset of the attitude measurement result to obtain a more accurate star sensor attitude measurement quaternion. And the system accuracy after removing the position error was improved by at least 11%, which means it has a good application prospect in improving the accuracy of star sensor thermal drift calibration.
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Table 1. Design parameters for the star sensors
parameters index field of view 12°×12° focal length 1121.54mm equipment length ≤1000mm angular accuracy ≤10″ temperature range -25℃~60℃ Table 2. Deformation angle results of different temperature
temperature/℃ prism offset around the x axis/(″·℃-1) offset around the y axis/(″·℃-1) Offset around the z axis/(″·℃-1) -25 m -31.2349134 -0.0235792 0.3789641 n -39.3412561 -0.0155460 -24.1372848 p -38. 5584741 0.0609176 -23.4569765 60 m -24.6603975 0.0150 403 0.0159451 n -34.7124605 -0.0492412 -23.5409127 p -35.6208196 0.0143522 -23.7295659 -
[1] LIANG B, ZHU H L, ZHANG T, et al. Research status and development tendency of star tracker technique[J]. Chinese Optics, 2016, 9(1):16-29(in Chinese). [2] LI X P, SUN Sh Y, ZHENG X J, et al. On-orbit real time installation matrix calibration method for high accuracy star trackers [J]. Infrared and Laser Engineering, 2018, 47(12): 205-211(in Chinese). [3] CHEN W X, WANG L, ZHENG T, et al. An automatic measurement method for installation error of star sensor [J].China Measurement, 2019, 45(2): 111-115(in Chinese). [4] GAO Q, REN Zh B, SUN A M, et al. Research on satellite attitude estimation based on star sensor[J].Navigation Positioning and Timing, 2018, 5(1):42-47(in Chinese). [5] XIONG Y Zh, WU Y P, CHENG H Y. Attitude determination accuracy of multi-head star tracker based on star-image fusion [J].Journal of Chinese Inertial Technology, 2016, 24(5):612-618(in Chinese). [6] SONG L L, ZHANG T, LIANG B, et al. Attitude determination method based on star sensor [J]. Journal of System Simulation, 2010, 22(s1):1-6(in Chinese). [7] XIE J F. The critical technology of data processing of satellite attitude determination based on star sensor[D]. Wuhan: Wuhan University, 2010: 80-84(in Chinese). [8] DUAN Y H, GUAN L. High precision attitude measurement and Calibration method of spacecraft based on precision star sensor [J]. Computer Measurement and Control, 2019, 27(11):1-5(in Chinese). [9] LONG L, LI Z F. 3-D position measurement algorithm based on laser displacement sensors[J].Laser Technology, 2017, 41(4):531-536(in Chinese). [10] JIANG X D, YU J Y, ZHU L K. Research of combined navigation technology based on position sensitive detectors[J] Laser Technology, 2019, 43(3):335-340(in Chinese). [11] JIN H, ZHAI Zh Y, DU W F, et al. Experimental analysis of star sensor thermostability [J]. Chinese Journal of Lasers, 2020, 47(2):0204001(in Chinese). [12] XU Y X, CHEN Q. Analysis and compensation of the star sensor's HFE in the satellite attitude determination [J].Pattern Recognition and Simulation, 2016, 35(10):109-113(in Chinese). [13] WANG H L, HE Y Y, LU J H, et al. Ground calibration method of installation error for star sensor based on three positions method[J]. Infrared and Laser Engineering, 2016, 45(11): 327-332(in Chinese). [14] LIAN Y Y, ZHANG Ch, ZHAN Y H, et al. Star apparent position calculation and updating method of attitude determination [J]. Science of Surveying and Mapping, 2015, 40(12): 134-139(in Chinese). [15] WANG X, CAI Sh J, WU L H, et al. Research on calibration technology of star sensor installation error angle[J]. Navigation Position-ing and Timing, 2019, 6(3): 125-130(in Chinese). [16] YE T, YANG F. Autonomous calibration of star sensors based on nonlinear optimization algorithm[J]. Optics and Precision Engineering, 2017, 25(9): 2483-2489(in Chinese). doi: 10.3788/OPE.20172509.2483 [17] ZHANG X, WANG H L, LU J H, et al. Calibration method of optical errors for star sensor based onparticle swarm optimization algorithm[J].Infrared and Laser Engineering, 2017, 46(10): 172-179(in Chinese).