﻿ 一种航空重力测线交叉点搜索新方法
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 大地测量与地球动力学  2018, Vol. 38 Issue (12): 1302-1305  DOI: 10.14075/j.jgg.2018.12.017

### 引用本文

WEI Jiancheng, XIAO Yun, WANG Li, et al. A New Method for Searching Intersection of Airborne Gravity Survey[J]. Journal of Geodesy and Geodynamics, 2018, 38(12): 1302-1305.

### Foundation support

National Natural Science Foundation of China, No. 41374083, 61427817; Fundamental Research Fund for the Central Universities, No.310826172006, 310826172202, 310826173101.

### 第一作者简介

WEI Jiancheng, postgraduate, majors in the data processing of airborne gravity, E-mail: 1205834766@qq.com.

### 文章历史

1. 长安大学地质工程与测绘学院，西安市雁塔路126号，710054;
2. 地理信息工程国家重点实验室，西安市雁塔路中段1号，710054;
3. 地理国情监测国家测绘地理信息局工程技术研究中心，西安市雁塔路中段1号，710054;
4. 西安测绘研究所，西安市雁塔路中段1号，710054

1 滑动窗口交叉点搜索方法

1.1 测线交叉点计算

 图 1 交叉点示意图 Fig. 1 Line intersection schematic

p1p2p3p4连接起来，组成线段p1p2p3p4，它们所在直线的参数方程分别为：

 $\left\{ \begin{array}{l} x = {x_1} + \lambda ({x_2} - {x_1})\\ y = {y_1} + \lambda ({y_2} - {y_1}) \end{array} \right.\left\{ \begin{array}{l} x = {x_3} + \mu ({x_4} - {x_3})\\ y = {y_3} + \mu ({y_4} - {y_3}) \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} {x_0} = {x_1} + \lambda ({x_2} - {x_1}) = {x_3} + \mu ({x_4} - {x_3})\\ {y_0} = {y_1} + \lambda ({y_2} - {y_1}) = {y_3} + \mu ({y_4} - {y_3}) \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} ({x_2} - {x_1})\lambda - ({x_4} - {x_3})\mu = {x_3} - {x_1}\\ ({y_2} - {y_1})\lambda - ({y_4} - {y_3})\mu = {y_3} - {y_1} \end{array} \right.$ (3)

 $\Delta = \left| \begin{array}{l} {x_2} - {x_1}\;\;\;\; - ({x_4} - {x_3})\\ {y_2} - {y_1}\;\;\; - ({y_4} - {y_3}) \end{array} \right| = 0$ (4)

 $\left\{ \begin{array}{l} \lambda = \frac{1}{\Delta }\left| \begin{array}{l} {x_3} - {x_1}\;\;\;\; - ({x_4} - {x_3})\\ {y_3} - {y_1}\;\;\;\; - ({y_4} - {y_3}) \end{array} \right|\\ \mu = \frac{1}{\Delta }\left| \begin{array}{l} {x_2} - {x_1}\;\;\;\; - ({x_3} - {x_1})\\ {y_2} - {y_1}\;\;\;\; - ({y_3} - {y_1}) \end{array} \right| \end{array} \right.$ (5)

 $\left\{ \begin{array}{l} {g_{{a_{主}}}} = {g_{{a_1}}} + \lambda \left( {{g_{{a_2}}} - {g_{{a_1}}}} \right)\\ {g_{{a_{副}}}} = {g_{{a_3}}} + \mu \left( {{g_{{a_4}}} - {g_{{a_2}}}} \right) \end{array} \right.$ (6)

 ${g_{{a_p}}} = {g_{{a_{主}}}} - {g_{{a_{副}}}}$ (7)

1.2 测线交叉点搜索

 图 2 主副测线点示意图 Fig. 2 The main and sub line points schematic

pi(xi, yi)和pj(xj, yj)(i=1, 2, …, n; j=1, 2, …, m)表示主副测线上的观测点，以pi为搜索窗口的中心，然后遍历整条副测线，判断pj是否落在窗口内。为了减小交叉点搜索范围，可依据测量时的飞行速度v来确定搜索窗口的大小。比如航向近似为南北向时，搜索窗口的大小可取1.5v或更大一些。副测线点落入窗口的判断准则为：

 $\left\{ \begin{array}{l} {x_i} - \Delta x \le {x_j} \le {x_i} + \Delta x\\ {y_i} - \Delta y \le {y_j} \le {y_i} + \Delta y \end{array} \right.$ (8)

 $\left\{ \begin{array}{l} {x_{{I_0}}} - \Delta x \le {x_i} \le {x_{{I_0}}} + \Delta x\\ {y_{{I_0}}} - \Delta y \le {y_i} \le {y_{{I_0}}} + \Delta y \end{array} \right.$ (9)

2 测线交叉点计算程序实现 2.1 测线交叉点计算流程

 图 3 交叉点计算流程 Fig. 3 Intersection calculation process
2.2 试验分析

 图 4 测区概况 Fig. 4 Measuring area introduction

 图 5 交叉点搜索结果 Fig. 5 Intersection search results
3 结语

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A New Method for Searching Intersection of Airborne Gravity Survey
WEI Jiancheng1,2,3     XIAO Yun2,4     WANG Li1,2,3     MENG Ning1,2     ZOU Jiasheng1,2
1. School of Geological Engineering and Geomatics, Chang'an University, 126 Yanta Road, Xi'an 710054, China;
2. State Key Laboratory of Geographic Information Engineering, 1 Mid-Yanta Road, Xi'an 710054, China;
3. Engineering Research Center of Geographic National Conditions Monitoring, NASMG, 1 Mid-Yanta Road, Xi'an 710054, China;
4. Xi'an Research Institute of Surveying and Mapping, 1 Mid-Yanta Road, Xi'an 710054, China
Abstract: Considering shortcomings of conventional search methods in airborne gravity measurement data processing, such as slow search speed, low correct rate and poor applicability, a new method, the 'sliding window search method' is proposed. The main line point is regarded as the search center and the main and sub line points are searched in a certain width of search box. The adjacent measuring points detected in the main and auxiliary lines form a line segment, and the intersection and discrepancy are determined. Through practical examples, the sliding window search method is discussed and analyzed from the aspects of search time and accuracy. The results show that the proposed method is simple and efficient, the searching efficiency of cross-point is improved and the workload is reduced significantly.
Key words: airborne gravity survey; intersection; discrepancy; sliding window search method