Effect of Mathematical Correlation on GPS Network Computation

Abstract

The precision and accuracy of positions obtained from the least-squares adjustment of Global Positioning System (GPS) data are dependent on the fidelity of the algorithms used to model the data. They are also dependent on the a priori covariance matrix of the data that is used in the adjustment. This matrix describes not only the uncertainty of the data but also the correlation among them—both mathematical and physical. In this paper we present a summary of a study of the effect of mathematical correlations on GPS position determination in network mode using carrier-phase double-difference observations. For our analysis, a network with baselines of hundreds to thousands of kilometers in length was processed, applying three distinct cases of observation correlations: case a—the correlations were ignored; case b—only the correlations within baselines were taken into account; and case c—all correlations, including those between baselines, were considered. This analysis used both broadcast and postfitted orbits. It is shown in this study that the proper modeling of mathematical correlations typically yields better reliability of baseline component estimates and more realistic formal error estimates.