GPS-Network Analysis with BLIMPBE: An Alternative to Least-Squares Adjustment for Better Bias Control

Abstract

Geodetic networks, when derived solely from observed GPS baseline vectors, have an inherent datum deficiency of dimension three due to the respective unknown translation parameters. Thus, estimated coordinates from a (weighted) least-squares adjustment will not be unique, although the adjusted baseline vectors are. Uniqueness, without affecting the adjustment as such, can be achieved by introducing a minimum number of constraints for the coordinates, or by applying an objective function on the set of least-squares solutions (LESS) that fulfill the so-called normal equations. In both alternatives, bias control for some (or all) coordinate estimates has so far been treated only as a secondary issue. Here it is shown that the recently introduced estimator of type BLIMPBE—although generally not a LESS—can indeed be expected to be superior to all other linear estimators that minimize the bias for certain coordinates. This performance is demonstrated in a GPS network that includes GPS receivers at several continuously operating reference stations.