Combination of spatial networks using an estimated covariance matrix |
| |
Authors: | Klaus-Peter Schwarz |
| |
Institution: | (1) Technical University, Graz, Austria |
| |
Abstract: | When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data.
It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not
necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The
problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices
are often used.
If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment.
The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework.
It is shown in which way improvements can be made using a modified approach of principal component analysis.
As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions
on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can
be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable
covariance function is suggested.
Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|