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Positional Accuracy Improvement Using Empirical Analytical Functions

机译：利用经验分析函数提高位置精度

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摘要

We define as Positional Accuracy Improvement the problem of putting together maps A and B of the same area, with B of higher planimetric accuracy. To do so, all objects in A might have to be slightly moved according to a mathematical transformation. Such transformation might ideally be of a specific type, like analytical or conformal functions. We have developed a theory to find a suitable analytical transformation despite it is not well defined because the only data available is the displacement vectors at a limited number of homologue control points. There exists a similar problem in fluid mechanics devoted on estimating the complete velocity field given just values at a limited number of points. We borrowed some ideas from there and introduced them into the positional accuracy improvement problem. We shall demonstrate that it is possible to numerically estimate an analytic function that resembles the given displacement at control points. As a byproduct, an uncertainty estimation is produced, which might help to detect regions of different lineage. The theory has been applied to rural 1:50.000 cartography of Uruguay while trying to diminish the discrepancies against GNSS readings. After the analytic transformation, the RMSE error diminished from 116m to 48 m. Other problems with similar math requirements are the transformation between geodetic control networks.
机译：我们将位置精度提高定义为将同一区域的地图A和B放在一起，而B的平面精度更高的问题。为此，可能必须根据数学转换稍微移动A中的所有对象。理想地，这种变换可以是特定类型的，例如分析或保形函数。尽管尚无很好的定义，但我们已经开发出一种理论来找到合适的分析变换，因为唯一可用的数据是有限数量的同源控制点处的位移向量。在流体力学中，存在一个类似的问题，即仅在有限数量的点上给出给定值的情况下，就估计整个速度场。我们从那里借来了一些想法，并将它们引入了位置精度改善问题。我们将证明有可能在数值上估计类似于控制点给定位移的解析函数。作为副产品，会产生不确定性估计，这可能有助于检测不同谱系的区域。该理论已应用于乌拉圭的1：50.000乡村制图，同时试图减少与GNSS读数之间的差异。解析转换后，RMSE误差从116m减小到48m。数学要求相似的其他问题是大地测量控制网络之间的转换。

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