Improving the relationship between reference frames by using the Thin-Plate Spline modelling

Abstract

The adoption of new geodetic reference systems and/or the availability of new reference frames occur, mainly, by the availability of new data sets. For the use of products in different reference frames, methods are necessary to transform the coordinates and modelling the distortions that compromise the transformation. In this paper a method is presented for three-dimensional coordinates transformation with modeling of distortions based on Thin-Plate Splines (TPS) mapping functions. Experiments were performed with real data of SAD 69 (South American Datum - 69) stations in the realization of 1996 (SAD69/96) and its homologous coordinates in SIRGAS2000. In the control points, the values of the root mean square error (RMSE) of the discrepancies in latitude and longitude, respectively, were 0.9 mm and 0.6 mm, and in the check points of 7.8 cm and 6.7 cm. By using distinct points of the network, the comparison of direct and inverse transformation results in the standard deviation were of 0.5 mm in latitude and 0.3 mm in longitude. In the comparison between the TPS model and the ProGriD, the statistical indicators were reduced by 97% (average), indicating that the proposed method is promising.