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iGPS测量不确定度空间分布分析方法

1. 北京航空航天大学 机械工程及自动化学院, 北京 100191;
12. 上海飞机制造有限公司, 上海 200436

Analysis method of iGPS measurement uncertainty spatial distribution
SUN Fulong1, ZHAO Gang1 , WANG Wei1, CHEN Lei2
1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Shanghai Aircraft Manufacturing Co. Ltd, Shanghai 200436, China
Abstract:The spatial distribution of iGPS measurement uncertainty was studied to help rapid assessment and layout optimization of iGPS measurement. According to the measurement model of iGPS, a typical two-station model of measurement uncertainty was established. Furthermore, a universal analysis method of iGPS measurement uncertainty distribution was proposed and modified in accordance with transmitter coverage. This method is applicable to diverse iGPS measurement environment with an arbitrary number of the transmitters in different layouts, and can be used to calculate the measurement uncertainty at any spatial point. Real measurement environment with two stations and four stations were established respectively. The distribution of actual measured deviations corresponded to the numerical simulation results. This analysis method was proved effective to describe the measurement uncertainty distribution pattern of iGPS.
Key words: iGPS     measurement model     measurement uncertainty     two-station model     spatial distribution

iGPS是一种新型数字化大尺寸空间测量设备,相较于其他数字化测量设备,它凭借其大尺寸测量精度高、测量实时性好、可同时多点测量、无光路遮挡失效问题、扩展方便等优势[1, 2],已逐渐在航空航天制造领域得以应用,如美国波音公司将iGPS应用于747,777与787等型号飞机的总装对接中[2, 3],加拿大庞巴迪公司将其用于C系列飞机的装配对接过程等,目前我国的航空航天企业也开始引进iGPS,并对其应用进行了初步探索.

1 iGPS测量原理

iGPS测量的基本原理为前方交会原理.接收器接收到空间中任意两台发射器的信号,即可解算出测点的空间位置.考虑到发射器空间布局的任意性,建立通用两站测量模型如下.

 图 1 通用两站测量模型 Fig. 1 Universal two-station measurement model

2 iGPS测量不确定度分析方法 2.1 iGPS测量不确定度

2.2 不确定度通用两站分析模型

2.3 基于两站模型变换的测量不确定度空间分布分析方法

 图 2 两站模型变换示意图 Fig. 2 Two-station model transformation

y′T的符号进行判断,根据上述两站模型的对称性可知,由于不确定度u关于xOz平面对称分布,于是可取y′T=y′T.x′T的符号进行判断,由于在两站模型中,两发射器的x坐标值互为相反数,因此根据TA与TBxOy平面上的投影即可判断x′T的符号,即:若TAxOyxOy,则x′T=-x′T;反之x′T=x′T.

2.4 考虑发射器覆盖范围的影响

3 数值仿真与实验分析 3.1 方案设计 3.1.1 实验环境

3.1.2实验设备

Nikon iGPS 4Tx全空间跟踪定位测量系统,Leica AT901-B激光跟踪仪.其不确度变如表 1所示.

 实验设备 测量不确定度 Nikon iGPS 4Tx 0.25mm/(30m×30m) Leica AT901-B (7.5μm+3μm)/m

3.1.3 实验方案

3.2两站系统 3.2.1 实验方法与过程

 发射器 位置坐标/mm A (-2042.73,0,-64.75) B (2042.73,0,64.75)

3.2.2 结果与分析

 图 3 两站系统测量不确定度分布数值仿真 Fig. 3 Numerical simulation of two stations measurement uncertainty distribution

 图 4 两站系统实际测量偏差分布 Fig. 4 Actual deviations distribution of two stations measurement

 图 5 两站系统方位方向与俯仰方向测量 不确定度分布数值仿真 Fig. 5 Numerical simulation of two stations measurement uncertainty distribution in azimuth and elevation direction

 发射器 位置坐标/mm A (-11393.95,-1668.69,-29.37) B (-10906.01,3111.19,147.70) C (-1809.09,6957.79,23.94) D (-87.68,3708.70,43.96)

3.3.2 结果与分析

 图 6 四站系统测量不确定度分布数值仿真 不确定度分布数值仿真 Fig. 6 Numerical simulation of four stations measurement uncertainty distribution

 图 7 四站系统测量不确定度分布数值仿真(俯视图) Fig. 7 Numerical simulation of four stations measurement uncertainty distribution (top view)

 图 8 四站系统实际测量偏差分布(俯视图) Fig. 8 Actual deviations distribution of four stations measurement (top view)

4 结 论

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#### 文章信息

SUN Fulong, ZHAO Gang, WANG Wei, CHEN Lei
iGPS测量不确定度空间分布分析方法
Analysis method of iGPS measurement uncertainty spatial distribution

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 174-180.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0044