TY - JOUR
N2 - The aim of the paper is the comparison of the least squares prediction presented by Heiskanen and Moritz (1967) in the classical handbook “Physical Geodesy” with the geostatistical method of simple kriging as well as in case of Gaussian random fields their equivalence to conditional expectation. The paper contains also short notes on the extension of simple kriging to ordinary kriging by dropping the assumption of known mean value of a random field as well as some necessary information on random fields, covariance function and semivariogram function. The semivariogram is emphasized in the paper, for two reasons. Firstly, the semivariogram describes broader class of phenomena, and for the second order stationary processes it is equivalent to the covariance function. Secondly, the analysis of different kinds of phenomena in terms of covariance is more common. Thus, it is worth introducing another function describing spatial continuity and variability. For the ease of presentation all the considerations were limited to the Euclidean space (thus, for limited areas) although with some extra effort they can be extended to manifolds like sphere, ellipsoid, etc.
L1 - http://journals.pan.pl/Content/105914/PDF/art2.pdf
L2 - http://journals.pan.pl/Content/105914
PY - 2010
IS - No 2
DO - 10.2478/v10277-012-0002-0
KW - least squares prediction
KW - kriging
KW - semivariogram
KW - covariance function
KW - random field
A1 - Ligas, Marcin
A1 - Kulczycki, Marek
PB - Commitee on Geodesy PAS
VL - vol. 59
DA - 2010
T1 - Simple spatial prediction - least squares prediction, simple kriging, and conditional expectation of normal vector
UR - http://journals.pan.pl/dlibra/publication/edition/105914
T2 - Geodesy and Cartography
ER -