基于数字高程模型高程快速迭代的航拍图像目标定位方法

李梓豪; 匡海鹏; 张泓; 庄楚恒

doi:10.37188/CO.2022-0215

基于数字高程模型高程快速迭代的航拍图像目标定位方法

doi: 10.37188/CO.2022-0215

李梓豪^{1, 2,},
匡海鹏^1, ,,
张泓^3,,
庄楚恒^{1, 2,}

1.
中国科学院长春光学精密机械与物理研究所航空光学成像与测量重点实验室,吉林长春 130033
2.
中国科学院大学, 北京 100049
3.
空军装备部驻长春地区军事代表室, 吉林长春 130033

基金项目: 高分辨率对地观测系统重大专项（No. 80-H30G03-9001-20/22）

详细信息

作者简介:
李梓豪（1998—），男，山西大同人，硕士研究生，2020年于哈尔滨工业大学获得学士学位，目前主要从事航空目标定位方面的研究。E-mail：17863107753@163.com

匡海鹏（1971—），男，吉林长春人，博士，研究员，硕士生导师，1994年于吉林工业大学获得学士学位，2008年于中国科学院研究生院获得博士学位。主要从事航空相机电子学方面的研究。E-mail：kuanghp@163.com

中图分类号: V443.5
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出版历程
- 收稿日期: 2022-11-11
- 修回日期: 2022-12-12
- 网络出版日期: 2023-04-14

A target location method for aerial images through fast iteration of elevation based on DEM

LI Zi-hao^{1, 2
,},
KUANG Hai-peng^{1
, ,},
ZHANG Hong^3
,,
ZHUANG Chu-heng^{1, 2
,}

1.
Key Laboratory of Airborne Optical Image and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
Representative Office of Air Force Department in Changchun, Changchun 130033, China

Funds: Supported by Key Project of High Resolution Earth Observation System (No. 80-H30G03-9001-20/22)

More Information

Corresponding author: kuanghp@163.com

摘要

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。
- 航空相机 /
- 对地目标定位 /
- 数字高程模型 /
- 快速迭代法 /
- 误差分析
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.
- aerial camera /
- ground target localization /
- digital elevation model /
- fast iteration method /
- the error analysis

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图 1 航空相机原理示意图

Figure 1. Schematic diagram of the principle of the aerial camera

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图 2 航空相机成像示意图

Figure 2. Schematic diagram of airborne camera imaging

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图 3 图像平面坐标系示意图

Figure 3. Schematic diagram of the image plane coordinate system

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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

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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

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图 6 迭代摄影测量法计算过程

Figure 6. Calculation process of the iterative photogrammetry method

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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

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图 8 文献[9]的改进迭代方法。（a）可收敛情形；（b）不收敛情形

Figure 8. Improved iterative calculation method in Ref. [9]. (a) Convergent situation; (b) non-convergent situation

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图 9 视向量分段迭代基本原理

Figure 9. Basic principle of visual vector segmentation iterative calculation

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图 10 快速迭代法基本原理

Figure 10. Basic principle of the fast iterative method

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图 11 快速迭代法示意图

Figure 11. Schematic diagram of fast iterative method

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图 12 视轴指向误差概率分布图

Figure 12. Probability distribution of the LOS pointing error

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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

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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°
相机框架角测量误差	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°
相机框架安装误差	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°

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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

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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

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