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Abstract

The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.
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Abstract

The paper presents empirical methodology of reducing various kinds of observations in geodetic network. A special case of reducing the observation concerns cartographic mapping. For numerical illustration and comparison of methods an application of the conformal Gauss-Kr├╝ger mapping was used. Empirical methods are an alternative to the classic differential and multi- stages methods. Numerical benefits concern in particular very long geodesics, created for example by GNSS vectors. In conventional methods the numerical errors of reduction values are significantly dependent on the length of the geodesic. The proposed empirical methods do not have this unfavorable characteristics. Reduction value is determined as a difference (or especially scaled difference) of the corresponding measures of geometric elements (distances, angles), wherein these measures are approximated independently in two spaces based on the known and corresponding approximate coordinates of the network points. Since in the iterative process of the network adjustment, coordinates of the points are systematically improved, approximated reductions also converge to certain optimal values.
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