标志点定向系统几何精度因子的计算方法
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摘要
为了满足在准备发射导弹时估计精度以及在建立发射阵地时优化标志点布局的需求,借鉴卫星导航定位系统的几何精度因子(GDOP)的定义,提出了适用发射车的标志点定向系统的GDOP的计算方法。根据多变量函数协方差合成公式,建立了定向误差的数学模型,以此为基础结合车体基本水平的特点,设计了该系统定向误差GDOP简化公式。计算结果显示GDOP值在以标志点为顶点的三角形附近区域的分布特点为:三角形内部的值比外部小;正三角形比其他形状的三角形能在更大范围内取得较小的值。数值仿真和外场实验证明了该方法的正确性。
In order to meet the requirements for the user to estimate the accuracy of orientation and to optimize the layout of landmarks, the GDOP( geometric dilution of precision) formulas for landmark-based orientation method is proposed by referencing to the definition of GDOP of GPS. Based on the formula for the propagation of error, the mathematical model of orientation errors was established. For leveling body, the simplified GDOP formulas were obtained. The distribution characteristics of the GDOP near the triangle formed by the landmarks are that their values are smaller inside the triangle than that on the outside, and the equilateral triangle achieves larger area with small values than other triangles. Simulation and experiment results verify the proposed GDOP formulas.
In order to meet the requirements for the user to estimate the accuracy of orientation and to optimize the layout of landmarks, the GDOP( geometric dilution of precision) formulas for landmark-based orientation method is proposed by referencing to the definition of GDOP of GPS. Based on the formula for the propagation of error, the mathematical model of orientation errors was established. For leveling body, the simplified GDOP formulas were obtained. The distribution characteristics of the GDOP near the triangle formed by the landmarks are that their values are smaller inside the triangle than that on the outside, and the equilateral triangle achieves larger area with small values than other triangles. Simulation and experiment results verify the proposed GDOP formulas.
引文
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[2]Teng Y L,Wang J L. A closed-form formula to calculate geometric dilution of precision(GDOP)for multi-GNSS constellations[J].GPSSolutions, 2016,20(3):331-339.
[3]何颖,李岁劳,郭强,基于地标观测的导弹发射车定位定向算法[J].仪器仪表学报,2016,37(4):751-756.
[4]王玮,王丹,冯培德.基于光电探测系统的地面车精确定位定向技术[J].北京航空航天大学学报,2007.33(8).
[5]He Y,Li s L,Guo Q.Landmark based position and orientation method with tilt compensation for missile launcher[c]//201635th Chinese Control Conference. 2016:5585-5589.
[6]云超,张晓明,吕妍红,等,一种发射车快速精确定位定向技术的研究[J].测绘科学,2009,34(2):81-84.
[7]郭强,李岁劳,王玮.光电探测系统辅助SINS的动态对准方法[J].仪器仪表学报,2015,36(11):2435-2442.
[8]胡超,王潜心,王中元,等,一种基于观测方程GDOP值的优化选站模型[J].武汉大学学报(信息科学版),2017,42(6):838-844.
[9]孙淑光,贾昌磊,王天游,夏冬.基于CKF的GPS定位误差估计及故障检测[J].测控技术,2015,34(8):126-129.
[10]Gong F X,Ma Y Q.Positioning performance analysis of the timesum of arrival algorithm with error features[J].OptoelectronicsLetters, 2018, 14(2):133-137.
[11]赵连军,刘恩海,张文明,等.单目三点置测量精度分析[J].光学精密工程,2014,22(5):1190-1197.
[12]Acuna R, Willert V.Robustness of control point configurations for homography and planar pose estimation[J].Computer Vision and Pattem Recognition,2018:22-28.
[13]周慧.靶场光电经纬仪最优布站方法研究[J].测控技术,2018,37(3):142-144.
[14] FomasiniP.The Uncertainty in Physical Measurements[M]. NewYork:Springer-Verlag, 2008:155-168.
[15]王波,胡浩,张彩霞,等.P3P问题多解现象的普遍性[J].中国科学:信息科学,2017,44(4):482-491.