Accession Number:

ADA030302

Title:

Covariance Functions in Least-Squares Collocation,

Descriptive Note:

Corporate Author:

OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE

Personal Author(s):

Report Date:

1976-06-01

Pagination or Media Count:

85.0

Abstract:

The report consists of two parts. Part A deals with the mathematical structure of covariance functions. The properties of isotrophy, harmonicity and positive definiteness are discussed, and it is suggested that a covariance function may be characterized by three essential parameters the variance, the correlation length and a curvature parameter. Finally some spatial covariance models planar and spherical are considered. Part B treats the influence of covariances on the results of collocation. Formulas are developed for the standard error of collocation results when using non-optimal covariance functions, also for the case of stepwise collocation. Finally the behavior of interpolation errors with and without the additional use of horizontal gradients is studied by means of power series expansions for covariance functions and by means of Gaussian covariance functions. It is seen that non-optimal covariance functions have relatively little influence on the interpolated values but a very strong effect on covariances as calculated using the conventional formulas. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE