Astronomical School’s Report, 2019, Volume 15, Issue 2, Pages 38–42
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UDC 528.11

Optimal use of quadratic programming method for alignment of geodesic networks

Goncharenko O.S.1, Gladilin V.N.2, Šiaudinytė L.3

1Taras Shevchenko National University of Kyiv, Hlushkova Avenue 2a, 03127 Kyiv, Ukraine
2National Aviation University, Kosmonavta Komarova Avenue 1, 03058 Kyiv, Ukraine
3Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania


In the theory of measurement errors, gross measurements include measurements, when blunders occur, or measurements, whose errors exceed the marginal errors for measurement condition. Gross errors can occur not only during the measurement process, but also during the calculation process. Results that have gross errors should be excluded from the calculations. When designing geodetic measurements, they select devices and measurement methods which have errors within the predefined acceptable values. The detection of gross errors is a special task in modern geodesy and is relevant for automated data collection, since gross errors may not be noticed by the operator during the measurement process, so the rejection of gross errors does not always satisfy the required measurement accuracy. Currently, an important problem is adjustment with a large number of determined unknowns, as well as taking into account systematic errors and errors of the original data. The least squares method used in adjustment limits the nature of information, used in equalization, only by equations and does not permit the combined effect of random and systematic errors that have the form of inequality. The solution of the adjustment problem with accounting the equalities and inequalities is performed using the mathematical programming method. The robust adjustment method determines the presence of gross and systematic errors using the Huber loss function, which is used in robust regression and is low sensitive to outliers, i.e. to gross errors.

Keywords: gross and systematic errors; adjustment


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