Article
MSC:
62J02,
62J05,
62M20,
65C99,
65D10,
86A30 | MR 0678114 | Zbl 0511.65011 | DOI: 10.21136/AM.1982.103991
Full entry |
PDF
(1.8 MB)
Feedback
PDF
(1.8 MB)
Feedback
Keywords:
least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix
least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix
Summary:
Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
References:
[1] Torben Krarup: A contribution to the mathematical foundation of physical geodesy. Geodaetisk Institut, Meddelelse No 44, København 1969. MR 0250524
[2] Lubomír Kubáček: Universal model for adjusting observed values. Studia geoph. et geod. 20 (1976), 103-113.
[3] Lubomír Kubáček, Lea Bartalošová, Ján Pecár: "Pandora-Box" matrix in the calculus of observations. Studia geoph. et geod. 21 (1977), 227-235.
[4] Lubomír Kubáček, Ludmila Kubáčková: The present approach to the least-squares method. Studia geoph. et geod. 22 (1978), 140-147.
[5] Lubomír Kubáček, Ludmila Kubáčková: Filtration and prediction of inhomogeneous geophysical potential fields. Studia geoph. et geod. 22 (1978), 330-335.
[6] Alois Kufner: Geometrie Hilbertova prostoru. SNTL, Praha 1973.
[7] Helmut Moritz: Least-squares collocation. DGK Bayer. Akad. d. Wiss., R. A. Nr. 75, München 1973. MR 0456320
[8] Emanuel Parzen: Time series analysis papers. Holden-Day, S. Francisco 1967, MR 0223042
[9] C. Radhakrishna Rao, Sujit Kumar Mitra: Generalized inverse of matrices and its application. J. Wiley, N. York 1971. MR 0338013
[10] František Štulajter: The linear filtration and prediction of indirectly observed random processes. Kybernetika 12 (1976), 316-327. MR 0446688
Search
Partner of
