Positional Accuracy Improvement Using Empirical Analytical Functions

Abstract

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 116 m to 48 m. Other problems with similar math requirements are the transformation between geodetic control networks.