Least Square Approach to Estimate 3D Coordinate Transformation Parameters: A Case of Three Reference Systems in Sweden

• Seven parameters of Helmert transformation are estimated using three-dimensional Cartesian coordinates in Sweden. Here, two cases are studied. Cartesian coordinates of RT90 and SWEREFF 93 in mm level accuracy for Case A are generated from secondary source. However for Case B, coordinates have been obtained by a field measurement. Trimble differential GPS has been used to measure coordinate in both SWEREFF 99 TM and RT90 reference systems in Gothenburg region, Sweden. It provides the coordinates in decimeter level accuracy. Helmert transformation parameters are estimated by applying MATLAB code. Seven parameters of Helmert transformation between RT90 and SWEREFF 93, and RT90 and SWEREFF 99 TM, and vice-versa are estimated. The average variance-covariance and, difference between measured and transformed coordinates in Case A is estimated to 3.86e-7 and 0.082 meter, respectively. However in Case B, the estimated transformation parameters is poor due to low level accuracy of measured coordinates and not fit in proper Cartesian system since the height component in 3D coordinate system provides geoid height which does not correspond to Cartesian coordinate. Therefore it gives high average variance-covariance as to 0.2165 and difference between measured and transformed coordinates to 5.498 meter. So estimation of Helmert transformation parameters requires Cartesian coordinates with high accuracy.

Ämnesord

NATURVETENSKAP  -- Geovetenskap och miljövetenskap -- Annan geovetenskap och miljövetenskap (hsv//swe)

NATURAL SCIENCES  -- Earth and Related Environmental Sciences -- Other Earth and Related Environmental Sciences (hsv//eng)

Nyckelord

Cartesian coordinate

Helmert transformation parameters

Bursa-Wolf mathematical model

SWEREFF 93

SWEREFF 99 TM

RT90

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)