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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

Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.
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