Msplit estimation. Part II: Squared Msplit estimation and numerical examples

• Autorzy: Wiśniewski Z.

Warianty tytułu

PL

Msplit estymacja. Część II. Kwadratowa Msplit estymacja i przykłady numeryczne

• Języki publikacji: EN

Abstrakty

EN

The present paper consists of two parts. The first part presents theoretical foundations of Msplit estimation with reference to the previous author’s paper (Wiśniewski, 2009). This time, some probabilistic assumptions are described in detail. A new quantity called f-information is also introduced to formulate the split potential in more general way. The main aim of this part of the paper is to generalize the target function of Msplit estimation that is the basis for a new formulation of the optimization problem. Such problem itself as well as its solution are presented in this part of the paper. The second part of the paper presents some special case of Msplit estimation called squared Msplit estimation (also with reference to the mentioned above paper of the author). That part presents a new solution and development in the theory of this version of Msplit estimation and some numerical examples that show properties of the method and its application scope.

PL

Msplit estymacją. Funkcja celu jest tutaj ustalana na podstawie wypukłych funkcji kwadratowych. Przedstawiono teoretyczne podstawy squared Msplit estymacji, jej algorytm oraz kilka przykładów numerycznych.

Słowa kluczowe

EN

geodetic adjustment; M-estimation; split potential of an observation set

PL

geodezja; kartografia

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Geodezja i Kartografia
• Rocznik: 2009
• Tom: Vol. 58, no 1
• Strony: 23--48
• Opis fizyczny: Bibliogr. 7 poz., tab., wykr.

Twórcy

autor

Wiśniewski Z.

• Institute of Geodesy, University of Warmia and Mazury 1 Oczapowskiego St., 10-957 Olsztyn, Poland

Bibliografia

• Hampel E.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A., (1986): Robust statistics. The approach based on influence functions, John Wiley & Sons, New York.
• Kadaj R., (1988): Eine verallgemeinerte Klasse von Schatzverfahren mit praktischen Anwendungen, Zeitschrift fur Vermessungswesen, Vol. 113, No 4, pp. 157-166.
• Rao C.R., (1973): Linear statistical inference and its applications, John Wiley & Sons, Inc.
• Teunissen P.J.G., (1990): Nonlinear least squares, Manuscripta Geodaetica, Vol. 15, pp. 137-150.
• Wiśniewski Z., (2008): Split estimation of parameters in functional geodetic models, Technical Sciences, Vol. 11, pp. 202-212.
• Wiśniewski Z., (2009): Estimation of parameters in asplit functional model of geodetic observations (Msplit estimation), Journal of Geodesy, Vol. 83, pp. 105-120.
• Yang Y., (1991): Robust Bayesian estimation, Bulletin Geodesique, Vol. 65, pp. 145-150.