應用純數二元二次聯立方程式解析以後方交會模式求測站坐標

Apply Mathematics binary quadric form analysis to solve the instrumental station coordinates using the resection mode

圖根點為辦理數值區土地複丈業務之基準，惟近來本所轄區數起公共建設造成所謂永久性圖根點不再永久，因此從源頭改變方式建構永久性圖根點概念，實為本所目前應思考重要課題。因此若能建構前述的現場建物特徵，以較永久性建物及設施（非地面）為已知標的點，爾後只要在該標的點附近自由擺設測站，就能快速得到測站坐標，此也為傳統後方交會基本概念。
前述相關作業方式已討論多年，業界也有一些廣泛作法，如後方交會法、自由測站、e-gnss等方式。惟本試驗樣本是採用二元二次聯立方程式，以純數概念去推導出向量結構關係，期待能以快速、簡化並能立刻得到可用之相對應坐標，而且不受都市內密集巷道及房屋遮蔽所影響為實驗目的。
經研究結果顯示，經現場以二元二次聯立方程式解算與經緯儀後方交會功能分析比較結果，在不同測站及各個不同角度下所呈現結果差異性略有不同。依本次4個測試場域，以經緯儀功能操作後方交會模式下，當角度較尖銳時，其誤差量將隨之增大，另以純數二元二次聯立方程式解算則受夾角及幾何圖形影響較小。

mapping control point is the basis for handling digital number Land Resurveying business. However, several recent public constructions in this jurisdiction have caused the so-called permanent mapping control point to be no longer permanent. Therefore, the method of constructing permanent mapping control point has been changed from the source. The concept of graph root point is indeed an important issue that our institute should consider at present. Therefore, if the aforementioned on-site building characteristics can be constructed, relatively fixed buildings and facilities (not on the ground) are used as known targets. In the future, as long as any instrumental station is placed near the target, the instrumental station coordinates can be quickly obtained. This is also the basic concept of the traditional resection.
The above-mentioned related operation methods have been discussed for many years, and there are also some common practices in the industry, such as resection, method of free station, e-gnss and other methods. However, this test sample uses binary quadric form and uses Mathematics concepts to deduce vector structure relationships. It is expected that the corresponding coordinates can be quickly, simplified, and immediately available, and will not be affected by The impact of dense alleyways and housing shelters in the city is for experimental purposes.
The research results show that the results of the on-site binary quadric form solution and the total station own resection function analysis and comparison results are presented at different instrumental station and at different angles. The results vary slightly. According to the 4 test field modes this time, in the total station function operation resection mode, when the angle and geometry are sharp, the error amount will increase accordingly. In addition, when the Mathematics binary quadric form is less affected by included angles and geometric figures.