基于室内GPS的弹头形心轴线测量方法的研究
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摘要
导弹弹头是导弹的最重要的部件之一,而形心轴线作为其重要几何特征量,影响着导弹的命中精度,因此对于形心轴线测量方法的研究具有实际意义和应用价值。中远程导弹弹头具有外形特殊,尺寸和重量都很大等特点,其形心轴线的测量属于大尺寸几何测量。而室内GPS测量系统是大尺寸三维坐标测量中的一种新型技术,具有测量效率高,测量时不需要转站,而且能够满足多用户同时使用等特点。因此研究基于室内GPS的导弹弹头形心轴线测量方法对于提高导弹生产和研制效率具有重要的意义。
本文首先论述了室内GPS测量系统的工作原理,对其结构组成以及应用特点等进行了分析;然后对导弹弹头形心轴线和型面点坐标的测量过程中的关键问题进行了详细分析,结合室内GPS测量系统,研究了最佳测量配置方案,重点研究了仪器坐标系与产品坐标系的建立过程和相互转换关系。其次,论文建立了常见空间几何元素的数学模型,并通过对数学模型的线性化,推导了线性最小二乘拟合模型;对于圆的拟合,提出了以非线性最小二乘法拟合来提高拟合精度的方法;根据测点和空间元素的相对位置关系,研究了测点投影、测头半径补偿等关键问题。
然后,本文分析了影响测量系统精度的关键因素,并对各关键因素作了定量分析,并给出了测量系统的单点测量不确定度的估计公式。论文最后结合某实际弹头的尺寸大小、根据室内GPS测量系统的精度条件对本文所提出的测量方法进行了仿真实验。处理结果表明,本文所提出的弹头形心轴线测量方法具有较高的测量精度,其测量不确定度满足弹头形心轴的实际测量需求。
The warhead is one of the most important parts of a missile. Symmetry axis is an important geometric specificity of it which affects the hit precision of a missile; therefore it is significant to study measuring techniques of symmetry axis. The warheads of medium-long range missiles have some features such as special contour, large size and heavy weight, etc., thus, the measurement of symmetry axis is a kind of large-scale measurement. Indoor GPS is a new technique in large scale three-dimensional coordinate measurement, which has some specialties such as high measuring efficiency, no need to move stations, and it also can satisfy multi-user to work simultaneously. Because of these merits, it is meaningful to study on the measuring techniques of the symmetry axes of warheads based on Indoor GPS in improving the producing and developing efficiency of missiles.
First in this thesis, the work principle of Indoor GPS measuring system is studied; its structure as well as the application characteristic is analyzed. Then the measuring principles of the symmetry axis and point coordinate are introduced in detail. According to Indoor GPS system, not only the best measuring disposition plan is given in the thesis, but also the establishment process, the conversion relations of the instrument coordinate and the product coordinate are researched.
Second, the mathematical model of geometry element is established and a linear least-square fitting model is deduced; Nonlinear least-square fitting method is developed to improve precision in fitting circles; also some key questions about point project, compensation of probe’s radius and so on are studied.
And then, the critical factors that affect measuring accuracy of the system were listed in the thesis, the quantitative analysis of them and an estimated formula of the single-axes uncertainty was given. At last, the simulation tests of the measuring technique and the measurement precision of the system described in the thesis were taken based on one real warhead’s dimensions. The simulation results indicated that the measuring technique mentioned in this paper had high precision, and its measuring uncertainty could satisfy the requirements of the symmetry axes.
本文首先论述了室内GPS测量系统的工作原理,对其结构组成以及应用特点等进行了分析;然后对导弹弹头形心轴线和型面点坐标的测量过程中的关键问题进行了详细分析,结合室内GPS测量系统,研究了最佳测量配置方案,重点研究了仪器坐标系与产品坐标系的建立过程和相互转换关系。其次,论文建立了常见空间几何元素的数学模型,并通过对数学模型的线性化,推导了线性最小二乘拟合模型;对于圆的拟合,提出了以非线性最小二乘法拟合来提高拟合精度的方法;根据测点和空间元素的相对位置关系,研究了测点投影、测头半径补偿等关键问题。
然后,本文分析了影响测量系统精度的关键因素,并对各关键因素作了定量分析,并给出了测量系统的单点测量不确定度的估计公式。论文最后结合某实际弹头的尺寸大小、根据室内GPS测量系统的精度条件对本文所提出的测量方法进行了仿真实验。处理结果表明,本文所提出的弹头形心轴线测量方法具有较高的测量精度,其测量不确定度满足弹头形心轴的实际测量需求。
The warhead is one of the most important parts of a missile. Symmetry axis is an important geometric specificity of it which affects the hit precision of a missile; therefore it is significant to study measuring techniques of symmetry axis. The warheads of medium-long range missiles have some features such as special contour, large size and heavy weight, etc., thus, the measurement of symmetry axis is a kind of large-scale measurement. Indoor GPS is a new technique in large scale three-dimensional coordinate measurement, which has some specialties such as high measuring efficiency, no need to move stations, and it also can satisfy multi-user to work simultaneously. Because of these merits, it is meaningful to study on the measuring techniques of the symmetry axes of warheads based on Indoor GPS in improving the producing and developing efficiency of missiles.
First in this thesis, the work principle of Indoor GPS measuring system is studied; its structure as well as the application characteristic is analyzed. Then the measuring principles of the symmetry axis and point coordinate are introduced in detail. According to Indoor GPS system, not only the best measuring disposition plan is given in the thesis, but also the establishment process, the conversion relations of the instrument coordinate and the product coordinate are researched.
Second, the mathematical model of geometry element is established and a linear least-square fitting model is deduced; Nonlinear least-square fitting method is developed to improve precision in fitting circles; also some key questions about point project, compensation of probe’s radius and so on are studied.
And then, the critical factors that affect measuring accuracy of the system were listed in the thesis, the quantitative analysis of them and an estimated formula of the single-axes uncertainty was given. At last, the simulation tests of the measuring technique and the measurement precision of the system described in the thesis were taken based on one real warhead’s dimensions. The simulation results indicated that the measuring technique mentioned in this paper had high precision, and its measuring uncertainty could satisfy the requirements of the symmetry axes.
引文
1孙家栋.导弹武器与航天器装备.原子能出版社,2003:2~4
2 B. Douglas. Missile Guidance. Aviation Week and Space Technology. 2005,163(10): 32~34
3 M. Montoya. Standard Missile: A Cornerstone of Navy Theater Air Missile Defense. Johns Hopkins APL Technical Digest (Applied Physics Laboratory). 2001,22(3): 234~247
4 W. Robert. Missile Shield. Aviation Week and Space Technology. 2005,162(15): 35
5 Anon. Misguided Missile Shield. Scientific American. 2003,288(5):8
6胡林.大尺寸测量.中国计量出版社, 1994:2
7刘庆伟.航天飞行器总装精测方法及技术研究.哈尔滨工业大学博士论文. 1998:2~12
8廖念钊.大轴几何精度在位检测系统.仪器仪表学报. 1998,19(1): 109~112
9李广云.工业三维坐标测量系统的最新进展.测绘通报. 1998,10:2~5
10 Arcsecond Inc. : Indoor GPS Technology for Metrology, 2003
11 R. M. Toms. An Improved Algorithm for Geocentric Coordinate Conversion. Proceedings on Standards for the Interoperability of Distributed Simulation, Vol 2, Institute for Simulation and Training. 1996
12冯文灏.近景摄影测量.武汉大学出版社, 2002:47~51
13 Shi Sheng Wen. Accurate Linear Technique for Camera Calibration Considering Lens Distortion by Solving an Eigenvalue Problem. Optical Engineer. 1993,32(1):138~149
14贾盛举,于晶涛.数字近景摄影测量在工业检测中的应用.测绘学报. 2002,31(5):61~65
15黄桂平,李广云.电子经纬仪工业测量系统定向及坐标解算算法研究.测绘学报. 2003,32(3):256~260
16周维虎,李百源,兰一兵,丁叔丹,费业泰.经纬仪坐标测量系统检测方法的研究.航空计测技术. 2000,20(1):6~9:
17杜俊峰.光电经纬仪测量精度指标的确定.应用光学. 2006, 27(6):507~508
18林永兵.四路激光干涉柔性坐标测量系统的优化设计.天津大学博士学位文. 2002:56
19 Bob Bridges, Kevin Hagan. Laser Tracker Maps Three Dimensional Features.American Institute of Physics.2001,8:28~32
20刘永东,王佳等.运动目标空间位置坐标激光跟踪测量的数学模型.光学技术. 1997,11(6):30~33
21高才栋.导弹弹头形心轴线测量方法及数据处理的研究.哈尔滨工业大学硕士论文. 2003:20~26
22李慧鹏.弹头形心轴线及主惯性轴线测量关键技术研究.哈尔滨工业大学硕士论文.2006:25,26
23张国雄.三坐标测量机.天津大学出版社, 1999:149~164
24 J. Dold, A. Markendorf.Expression of Measurement Uncertainty for Laser Tracker based on Distance Measurements.Coordinate Measuring Systems Conference 1998
25李达.导弹弹头形心轴线测量及数据处理技术的研究.哈尔滨工业大学硕士学位论文. 2002:8~15
26 Partial Metrix Corporation. SMX Insight 4.0 User’s Guide. 1999:8-1~8-31
27 Hofmann W. B. Global Positioning System Theory and Practice. Berlin Springer Verlag.2001:66~78
28 Arcsecond Inc. WorkSpace Advanced Metrology Edition User’s Guide.2003
29 Arcsecond Inc. X-Station Manual Vulcan Version 2.6. 2003:13~16
30宋明顺,顾龙芳,陈意华.最小二乘测量结果不确定度的评定及案例. 2000,1:43~45
31 Indoor GPS competitive benefits files: http://www.arcsecond.com
32 Indoor GPS configurations files: http://www.arcsecond.com
33张国雄.三坐标测量机.天津大学出版社,1998:149~164
34周维虎,兰一兵等.空间坐标转换技术的分析与研究.航空计测技术. 1999,19(4):10~12
35 Grafarend E. W., Awange L. J.. Nonlinear analysis of the three dimensional datum transformation. Journal of Geodesy. 2003,77:66~76
36邓红,陈昊明,刘光斌.基于星敏感的导弹姿态矩阵线性化解算方法.战术导弹控制技术. 2006,4:83~86
37 Yang Y. X.. Robust estimation of Geodetic Datum Transformation. Journal of Geodesy. 1999,73:268~274
38 Y. H. Chen, C. Y. Liu. Quadric Surface extraction Genetic Algorithms. CAD Computer Aided Design. 1999,31(2): 101~110
39张宗达等.工科数学分析.哈尔滨工业大学出版社, 2000:147~157
40葛照强.矩阵理论及其在工程技术中的应用.陕西科学技术出版社, 1991:111~122
41段虎荣,郭新成,丁宁.最小二乘预估法在GPS高程转换中的应用.西安电子科技大学学报.2006:72~73
42刑书珍,刑天奇.非线性最小二乘拟合的计算方法.中国铁道科学. 1995,16(3):64~71
43王解先.工业测量中一种二次曲面拟合方法.武汉大学学报信息科学版. 2007,32(1):47~50
44翟家波,李海奎.非线性最小二乘数值求解中Hesse矩阵的快速计算方法.微电子学与计算机. 2004,21(12):64~66
45 G. Roth, M. Levine. Geometric Primitive Extraction Using a Genetic Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1994,16(9): 901~905
46 Error Budget and Specifications. http://www.arcsecond.com
47 Indoor GPS Metrology System with 3D Probe for Precision Applications. http://www.arcsecond.com
48 James M. Cobb. Infrared GPS: Technology Application by Manufacturing Research & Development. Coordinate Measuring Systems Conference 2002
49丁振良.误差理论与数据处理.哈尔滨工业大学出版社, 2002:138
50郑芳,邬钧霆,马德宝.基于轨道误差的基线估计及其对高程精度的影响.信息工程大学学报. 2005,6(1):77~79
2 B. Douglas. Missile Guidance. Aviation Week and Space Technology. 2005,163(10): 32~34
3 M. Montoya. Standard Missile: A Cornerstone of Navy Theater Air Missile Defense. Johns Hopkins APL Technical Digest (Applied Physics Laboratory). 2001,22(3): 234~247
4 W. Robert. Missile Shield. Aviation Week and Space Technology. 2005,162(15): 35
5 Anon. Misguided Missile Shield. Scientific American. 2003,288(5):8
6胡林.大尺寸测量.中国计量出版社, 1994:2
7刘庆伟.航天飞行器总装精测方法及技术研究.哈尔滨工业大学博士论文. 1998:2~12
8廖念钊.大轴几何精度在位检测系统.仪器仪表学报. 1998,19(1): 109~112
9李广云.工业三维坐标测量系统的最新进展.测绘通报. 1998,10:2~5
10 Arcsecond Inc. : Indoor GPS Technology for Metrology, 2003
11 R. M. Toms. An Improved Algorithm for Geocentric Coordinate Conversion. Proceedings on Standards for the Interoperability of Distributed Simulation, Vol 2, Institute for Simulation and Training. 1996
12冯文灏.近景摄影测量.武汉大学出版社, 2002:47~51
13 Shi Sheng Wen. Accurate Linear Technique for Camera Calibration Considering Lens Distortion by Solving an Eigenvalue Problem. Optical Engineer. 1993,32(1):138~149
14贾盛举,于晶涛.数字近景摄影测量在工业检测中的应用.测绘学报. 2002,31(5):61~65
15黄桂平,李广云.电子经纬仪工业测量系统定向及坐标解算算法研究.测绘学报. 2003,32(3):256~260
16周维虎,李百源,兰一兵,丁叔丹,费业泰.经纬仪坐标测量系统检测方法的研究.航空计测技术. 2000,20(1):6~9:
17杜俊峰.光电经纬仪测量精度指标的确定.应用光学. 2006, 27(6):507~508
18林永兵.四路激光干涉柔性坐标测量系统的优化设计.天津大学博士学位文. 2002:56
19 Bob Bridges, Kevin Hagan. Laser Tracker Maps Three Dimensional Features.American Institute of Physics.2001,8:28~32
20刘永东,王佳等.运动目标空间位置坐标激光跟踪测量的数学模型.光学技术. 1997,11(6):30~33
21高才栋.导弹弹头形心轴线测量方法及数据处理的研究.哈尔滨工业大学硕士论文. 2003:20~26
22李慧鹏.弹头形心轴线及主惯性轴线测量关键技术研究.哈尔滨工业大学硕士论文.2006:25,26
23张国雄.三坐标测量机.天津大学出版社, 1999:149~164
24 J. Dold, A. Markendorf.Expression of Measurement Uncertainty for Laser Tracker based on Distance Measurements.Coordinate Measuring Systems Conference 1998
25李达.导弹弹头形心轴线测量及数据处理技术的研究.哈尔滨工业大学硕士学位论文. 2002:8~15
26 Partial Metrix Corporation. SMX Insight 4.0 User’s Guide. 1999:8-1~8-31
27 Hofmann W. B. Global Positioning System Theory and Practice. Berlin Springer Verlag.2001:66~78
28 Arcsecond Inc. WorkSpace Advanced Metrology Edition User’s Guide.2003
29 Arcsecond Inc. X-Station Manual Vulcan Version 2.6. 2003:13~16
30宋明顺,顾龙芳,陈意华.最小二乘测量结果不确定度的评定及案例. 2000,1:43~45
31 Indoor GPS competitive benefits files: http://www.arcsecond.com
32 Indoor GPS configurations files: http://www.arcsecond.com
33张国雄.三坐标测量机.天津大学出版社,1998:149~164
34周维虎,兰一兵等.空间坐标转换技术的分析与研究.航空计测技术. 1999,19(4):10~12
35 Grafarend E. W., Awange L. J.. Nonlinear analysis of the three dimensional datum transformation. Journal of Geodesy. 2003,77:66~76
36邓红,陈昊明,刘光斌.基于星敏感的导弹姿态矩阵线性化解算方法.战术导弹控制技术. 2006,4:83~86
37 Yang Y. X.. Robust estimation of Geodetic Datum Transformation. Journal of Geodesy. 1999,73:268~274
38 Y. H. Chen, C. Y. Liu. Quadric Surface extraction Genetic Algorithms. CAD Computer Aided Design. 1999,31(2): 101~110
39张宗达等.工科数学分析.哈尔滨工业大学出版社, 2000:147~157
40葛照强.矩阵理论及其在工程技术中的应用.陕西科学技术出版社, 1991:111~122
41段虎荣,郭新成,丁宁.最小二乘预估法在GPS高程转换中的应用.西安电子科技大学学报.2006:72~73
42刑书珍,刑天奇.非线性最小二乘拟合的计算方法.中国铁道科学. 1995,16(3):64~71
43王解先.工业测量中一种二次曲面拟合方法.武汉大学学报信息科学版. 2007,32(1):47~50
44翟家波,李海奎.非线性最小二乘数值求解中Hesse矩阵的快速计算方法.微电子学与计算机. 2004,21(12):64~66
45 G. Roth, M. Levine. Geometric Primitive Extraction Using a Genetic Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1994,16(9): 901~905
46 Error Budget and Specifications. http://www.arcsecond.com
47 Indoor GPS Metrology System with 3D Probe for Precision Applications. http://www.arcsecond.com
48 James M. Cobb. Infrared GPS: Technology Application by Manufacturing Research & Development. Coordinate Measuring Systems Conference 2002
49丁振良.误差理论与数据处理.哈尔滨工业大学出版社, 2002:138
50郑芳,邬钧霆,马德宝.基于轨道误差的基线估计及其对高程精度的影响.信息工程大学学报. 2005,6(1):77~79