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 3 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.