A target location method for aerial images through fast iteration of elevation based on DEM
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摘要:
在大倾角航空相机对地面目标定位过程中，借助数字高程模型（DEM）可有效解决地球椭球模型定位存在的大地高误差影响。为获取地面坐标的准确信息特别是高程信息，首先，根据载机的位置姿态信息以及航空相机的框架角等信息利用齐次坐标变换求解出成像系统视轴在地理坐标系下的指向，再利用数字高程模型确定目标点的坐标。针对成像过程中目标点高程计算繁琐、容易不迭代等问题，提出了一种对目标高程值进行快速迭代的方法。通过对目标区域高程进行折半查找处理，计算该处视轴光线高程与地面高程差值。继续计算该高程差中值并继续迭代，直到小于一定阈值。最后使用蒙特卡洛分析法对整个成像过程存在的误差项进行分析。实验结果表明：采用快速迭代法进行计算，当收敛阈值为十分之一DEM网格精度时，迭代效率提升45.5%，收敛速度大大提高；且通过数字高程模型计算，在飞行高度为15409 m，相机框架角大于74°时，对于山地区域目标的圆概率误差小于200 m，可以满足实际工程需要。
Abstract:In the positioning process of aerial cameras with large inclination angles, the influence of height error in the earth ellipsoid model can be effectively solved with the help of a digital elevation model (DEM). This is very important for obtaining accurate ground coordinates, especially elevation. Firstly, the orientation of the line-of-sight angle in the geographic coordinate system is solved by transforming homogeneous coordinates according to the position and attitude information of the carrier aircraft and the frame angle information of the aerial camera, and then the longitude and latitude of the target point are determined by a digital elevation model. To overcome the tedious nature of calculating target elevation and the non-convergence in the imaging process, a fast iterative method is proposed to iterate over the target elevation’s value. The difference between the light elevation of the visual axis and the ground elevation is calculated by halving the target elevation. The median elevation difference is calculated iteratively until it is less than a certain threshold. Finally, Monte Carlo analysis was used to analyze the error terms in the whole imaging process. When the convergence threshold is 1/10 DEM in grid accuracy, the iteration efficiency increases by 45.5% and the convergence speed is greatly improved. Through the calculation of the digital elevation model, when the flight height is 15,409 meters and the camera frame’s angle is greater than 74°, a mountainous area’s target circular error probability is less than 200 m which meets the real engineering needs.
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图 4地球坐标系与地球椭球模型示意图
Figure 4.Schematic diagram of the ECEF coordinate frame and the Earth ellipsoid model
图 5不同大地高标准差下成像倾角对目标定位精度的影响
Figure 5.Effects of imaging inclinations on target positioning accuracy under different ground height standard deviations
图 7常规迭代方法不收敛的情形。（a）情形1；（b）情形2
Figure 7.Situations of the iterative non-convergence of the regular iterative method. (a) Situation 1; (b) situation 2
图 9视向量分段迭代基本原理
Figure 9.Basic principle of visual vector segmentation iterative calculation
图 13不同地区航空影像及定位结果。（a）~（b）平原；（c）~（d）丘陵；（e）~（f）山脉
Figure 13.Aerial images of different regions and positioning results. (a)−(b) plain; (c)−(d) hill; (e)−(f) mountain
表 1视轴指向误差计算中的仿真数据
Table 1.The simulation data for the line-of-sight (LOS) direction error calculation
误差来源 误差σ 载机姿态测量误差 航向方向 0.05° 俯仰方向 0.02° 横滚方向 0.02° 相机框架角测量误差 外框架 0.02° 内框架 0.02° 组合导航系统校准误差 航向方向 0.03° 俯仰方向 0.01° 横滚方向 0.01° 相机框架安装误差 外框架 0.01° 内框架 0.01° 
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表 2测量变量的名义值
Table 2.Nominal values of the measurement variable
误差变量 平原 丘陵 山地 载机纬度 28.9702° 28.9703° 28.9705° 载机经度 89.0043° 89.0045° 89.0056° 载机大地高 15409 m 15409 m 15409 m 载机航向角 −102.4800° −102.4800° −102.4800° 载机俯仰角 2.8679° 2.8679° 2.8679° 载机横滚角 −0.3876° −0.3876° −0.3876° 外框架 74.6747° 75.3977° 78.7673° 内框架 0.2304° −0.7532° −0.7064° 下载:
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表 3快速迭代法坐标定位误差结果
Table 3.Error results of coordinate positioning by the fast iterative method
地形 平原 丘陵 山地 纬度均方根误差 0.001131° 0.000903° 0.001923° 经度均方根误差 0.000546° 0.000496° 0.000499° 大地高均方根误差 20.3096 m 26.7596 m 36.2531 m 定位均方根误差 137.7469 m 114.3994 m 221.8547 m 圆概率误差 114.7890 m 95.3328 m 184.8812 m 下载:
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表 4不同方法迭代时间统计
Table 4.Iteration times of different methods (ms)
局部穷举法 改进迭代法 视向量迭代法 快速迭代法 平原 4156 3843 3540 3648 丘陵 18610 5269 4712 4530 山地 1249840 86312 36879 20106 下载:
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