Propagation of uncertainty by Monte Carlo simulations in case of basic geodetic computations

• Autorzy: Wyszkowska P.

Identyfikatory

DOI

10.1515/geocart-2017-0022

• Języki publikacji: EN

Abstrakty

EN

The determination of the accuracy of functions of measured or adjusted values may be a problem in geodetic computations. The general law of covariance propagation or in case of the uncorrelated observations the propagation of variance (or the Gaussian formula) are commonly used for that purpose. That approach is theoretically justified for the linear functions. In case of the non-linear functions, the first-order Taylor series expansion is usually used but that solution is affected by the expansion error. The aim of the study is to determine the applicability of the general variance propagation law in case of the non-linear functions used in basic geodetic computations. The paper presents errors which are a result of negligence of the higher-order expressions and it determines the range of such simplification. The basis of that analysis is the comparison of the results obtained by the law of propagation of variance and the probabilistic approach, namely Monte Carlo simulations. Both methods are used to determine the accuracy of the following geodetic computations: the Cartesian coordinates of unknown point in the three-point resection problem, azimuths and distances of the Cartesian coordinates, height differences in the trigonometric and the geometric levelling. These simulations and the analysis of the results confirm the possibility of applying the general law of variance propagation in basic geodetic computations even if the functions are non-linear. The only condition is the accuracy of observations, which cannot be too low. Generally, this is not a problem with using present geodetic instruments.

Słowa kluczowe

EN

variance propagation law; Monte Carlo simulation; nonlinear functions

PL

funkcja nieliniowa; metoda Monte Carlo; prawo propagacji

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Geodesy and Cartography
• Rocznik: 2017
• Tom: Vol. 66, no. 2
• Strony: 333--346
• Opis fizyczny: Bibliogr. 21 poz., tab., wykr.

Twórcy

autor

Wyszkowska P.

• University of Warmia and Mazury in Olsztyn Institute of Geodesy 1 Oczapowskiego St., 10-719 Olsztyn, Poland

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)