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.
JO - Geodesy and Cartography
L1 - http://sd.czasopisma.pan.pl/Content/105914/PDF/art2.pdf
L2 - http://sd.czasopisma.pan.pl/Content/105914
IS - No 2
KW - least squares prediction
KW - kriging
KW - semivariogram
KW - covariance function
KW - random field
ER -
A1 - Ligas, Marcin
A1 - Kulczycki, Marek
PB - Commitee on Geodesy PAS
VL - vol. 59
JF - Geodesy and Cartography
T1 - Simple spatial prediction - least squares prediction, simple kriging, and conditional expectation of normal vector
UR - http://sd.czasopisma.pan.pl/dlibra/docmetadata?id=105914
DOI - 10.2478/v10277-012-0002-0