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DOI
Warianty tytułu
Języki publikacji
Abstrakty
A new optimization method presented in this work – the Least m-Order Central Moments method, is a generalization of the Least Squares method. It allows fitting a geometric object into a set of points in such a way that the maximum shift between the object and the points after fitting is smaller than in the Least Squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track or gantry rails. The theoretical properties of the proposed optimization method are analyzed. The computational problems are discussed. The appropriate computational techniques are proposed to overcome these problems. The detailed computational algorithm and formulas of iterative processes have been derived. The numerical tests are presented, in order to illustrate the operation of proposed techniques. The results have been analyzed, and the conclusions were then formulated.
Rocznik
Tom
Strony
39--49
Opis fizyczny
Bibliogr. 25 poz., tab., wykr.
Twórcy
autor
- Katedra Geodezji, Uniwersytet Warmińsko-Mazurski, ul. Oczapowskiego 1, 10-719 Olsztyn
autor
- Department of Geodesy, University of Warmia and Mazury in Olsztyn
Bibliografia
- Avriel M. 2003. Nonlinear Programming: Analysis and Methods. Dover Publishing.
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- Cellmer S. 2014. Least fourth powers: optimisation method favouring outliers. Survey Review, 47(345): 417. DOI: https://doi.org/10.1179/1752270614Y.0000000142.
- Chang X.W., Guo Y. 2005. Huber’s M-estimation in relative GPS positioning: computational aspects. Journal of Geodesy, 79: 351–362. DOI: https://doi.org/10.1007/s00190-005-0473-y.
- Duchnowski R., Wiśniewski Z. 2012. Estimation of the shift between parameters of functional models of geodetic observations by applying M split estimation. Journal of Surveying Engineering, 138: 1–8. DOI: 10.1061/(ASCE)SU.1943-5428.0000062.
- Fletcher R. 1987. Practical methods of optimization. 2nd ed. John Wiley & Sons, New York.
- Hampel F.R., Ronchetti E., Rousseeuw P.J., Stahel W.A. 1986. Robust statistics: the approach based on influence function. Wiley, New York.
- Huber P.J. 1981. Robust statistics. Wiley, New York.
- Kadaj R. 1988. Eine verallgemeinerte Klasse von Schätzverfahren mit praktischen Anwendungen. Z Vermessungs-wesen, 113(4): 157–166.
- Kamiński W., Wiśniewski Z. 1992. Analysis of some, robust, adjustment methods. Geodezja i Kartografia, 41(3-4): 173-182.
- Koch K.R. 1996. Robuste Parameterschätzung. Allgemeine Vermessungs-Nachrichten, 103(11): 1–18.
- Liew C.K. 1976. Inequality constrained least squares estimation. Journal of the American Statistical Association, 71: 746–751.
- Martins T.C., Tsuzuki M.S.G. 2009. Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing. Bulletin of the Polish Academy of Sciences. Technical Sciences, 57(3): 273-280.
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- Neumann J. von, Morgenstern O. 1947. Theory of games and economic behavior. Princeton Univ. Press. Princeton, New Jersey.
- Nocedal J., Wright S.J. 1999. Numerical Optimization. Springer-Verlag, Berlin.
- Skała-Szymańska M., Cellmer S., Rapiński J. 2014. Use of Nelder-Mead simplex method to arc fitting for railway track realignment. The 9th International Conference Environmental Engineering, selected papers. DOI: 10.3846/enviro.2014.244.
- Werner H.J. 1990. On inequality constrained generalized least-squares estimation. Linear Algebra and its Applications, 27: 379–392. DOI: http://dx.doi.org/10.1179/1752270614Y.0000000142.
- Wiśniewski Z. 2009. Estimation of parameters in a split functional model of geodetic observations (M split estimation). Journal of Geodesy, 83: 105–120. DOI: https://doi.org/10.1007/s00190-008-0241-x.
- Wiśniewski Z. 2010. M split(q) estimation: estimation of parameters in a multi split functional model of geodetic observations. Journal of Geodesy, 84: 355–372. DOI: https://doi.org/10.1007/ s00190-010-0373-7.
- Xu P. 1989. On robust estimation with correlated observations. Bulletin Géodésique, 63: 237–252.
- Yang Y.1999. Robust estimation of geodetic datum transformation. Journal of Geodesy, 73: 268–274. DOI: https://doi.org/10.1007/s001900050243.
- Yang Y., Song I., Xu T. 2002. Robust estimation for correlated observations based on bifactor equivalent weights. Journal of Geodesy, 76: 353–358. DOI: https://doi.org/10.1007/s00190-002-0256-7.
- Zhong D. 1997. Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights. Journal of Geodesy, 71: 552–561. DOI: https://doi.org/10.1007/ s001900050123.
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Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a43bee3d-b222-4af8-b588-8eceb77469cd