Journal of Surveying Engineering

A noniterative transformation of earth-centered, earth-fixed (ECEF) Cartesian coordinates to geodetic coordinates of a point is presented. The transformation is based on ellipsoidal coordinates. The ECEF Cartesian coordinates of a point are first transformed to the ellipsoidal coordinates by closed formulas. Second, the reduced latitude referred to the reference ellipsoid takes the approximation to the reduced latitude referred to a confocal ellipsoid. Third, the approximation can be improved by a correction for the purpose of higher accuracy. The accuracy of the transformation is analyzed in the paper and it is shown that the derived geodetic coordinates are sufficiently accurate for the most geodetic purposes.

Formulae for judging a priori the influences of individual observations on the unknown parameters and the mean network precision are presented. The influences of an observation on the parameters and the mean network precision are measured by the influence index and the percentage share, respectively. The larger the redundancy number, or the smaller the parameter number of the observation, the smaller the influence index will be and hence the less influence the observation will have on the estimate of an unknown parameter vector. A larger parameter number ensures a high percentage share in the mean network precision. The numerical example of the first-order leveling network of Taiwan seems to indicate that a better weighting scheme tends to produce more homogeneities among the individual parameter numbers and their corresponding influence numbers.

Software for processing single vectors is often used to densify geodetic networks based upon global positioning system (GPS) data. When operating more than two GPS receivers in the same survey session, the covariance information among vectors is not readily available for the subsequent network analysis. A procedure is suggested for regenerating full covariance information for the mathematically independent vectors using all single vectors. As opposed to the approach of using all combinations of vectors, the suggested procedure has the advantage of not introducing false reliability into the network analysis.