On the Impact of the Coordinate Representation onto the Estimates in Least-Squares Adjustment

In geodesy and metrology several coordinate representations are known. The most important representations are polar coordinates and Cartesian coordinates. The coordinate representations are rigorously convertible into each other. Such functional relations are well-known as the direct (first) and the inverse (second) geodetic problem. Instruments like e. g. total station, laser scanner, or laser tracker are polar measurement systems. It is common practise especially in surface analysis, e. g. deformation analysis of the VLBI main reflector, to initially convert the obtained polar coordinates into their Cartesian representations. Instead of the polar measurements, the converted Cartesian coordinates are introduced to the least-squares adjustment. In this investigation, the impact of the chosen coordinate representation onto the estimates is studied. It is shown that the adequate transformation of the functional model and the stochastic model of the least-squares adjustment is not sufficient to obtain identical estimates.