Variance component estimation applied to satellite laser ranging

Abstract

The variance component estimation (VCE) method as developed by Helmert has been applied to the global SLR data set for the year 1987. In the first part of this study the observations have been divided into two groups: those from ruby and YAG laser systems, and their weights estimated over several months. It was found that the weights of both sets of stations altered slightly from month to month, but that, not surprisingly, the YAG systems consistently outperformed those based on ruby lasers. The major part of this paper then considers the estimation of the variance components (i.e. weights) at each SLR station from month to month. These were tested using the F-statistic and, although it indicated that most stations had significant temporal variations, they were generally small compared with the differences between the stations themselves, i.e. the method has been shown to be capable of discriminating between the precision with which the various laser stations are operating. The station coordinates and baseline lengths computed using both a priori, and estimated, weights where also compared and this showed that changes in the weights can have significant effects on the estimation of the station positions, particularly in the z component, and on the baseline lengths - so proving the importance of proper stochastic modelling when processing SLR data.