Alternative transformation from Cartesian to geodetic coordinates by least squares for GPS georeferencing applications
The inverse transformation of coordinates, from Cartesian to curvilinear geodetic, or symbolically (x,y,z)?(?,?,h) has been extensively researched in the geodetic literature. However, published formulations require that the application must be deterministically implemented point-by-point individually. Recently, and thanks to GPS technology, scientists have made available thousands of determinations of the coordinates (x,y,z) at a single point perhaps characterized by different observational circumstances such as date, length of occupation time, distance and geometric distribution of reference stations, etc. In this paper a least squares (LS) solution is introduced to determine a unique set of geodetic coordinates, with accompanying accuracy predictions all based on the given sets of individual (x,y,z) GPS-obtained values and their variancecovariance matrices. The (x,y,z) coordinates are used as pseudo-observations with their attached stochastic information in the LS process to simultaneously compute a unique set of (?,?,h) curvilinear geodetic coordinates from different observing scenarios.
geodetic coordinates least squares inverse transformation cartesian coordinates