GPS satellite sky distribution: Impact on the propagation of some important errors in precise relative positioning

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This research is a study of the impact of Global Positioning System (GPS) satellite sky distribution on the propagation of some important errors in precise static relative positioning, for baselines shorter than about 100 km. Even the full operational GPS constellation of 24 satellites will not provide a uniform distribution of the visible satellites in the observer's sky. The satellite sky distribution is a function of site latitude, because GPS satellite orbits have inclinations different than 90°. Covariance matrix behaviour and the effects of some important systemic errors on precise relative positioning are studied as a function of GPS Satellite sky distribution, using an improved an expanded simulation technique originally suggested by Geiger of ETH Zürich. Unknowns considered are the station coordinates, the relative receiver clock parameter and the relative tropospheric zenith delay parameter. Biases analysed are: relative tropospheric refraction, absolute ionospheric refraction, offset in the horizontal coordinates of the fixed station and offset in the height of the fixed station. The simulation results agree with those obtained from real GPS data processing with an associated error of about ±25%. Orientation and shape of the confidence ellipsoid an correlation among the selected unknowns, are used to monitor the behaviour of the covariance matrix. Systematic errors introduced in the station network by the biases are represented as station coordinate discrepancies and affine transformation parameters. Numerical values of these parameters are presented for satellite configurations produced by both the prototype and the full GPS constellations. The study has yielded an appreciation of the behaviour of the covariance matrix and the variations in the effects of systematic errors as a function of the satellite sky distribution and the elevation mask angle selection. The magnitudes of the effects of the studied biases on relative positioning are up to 10 cm for baseline length independent errors and up to 10 ppm for baseline length dependent errors. Applications of this technique are suggested for planning (pre-analysis) and assessment (post-analysis) in GPS production surveys.