Analysis of wide-lane ambiguities derived from geometry-free and geometry-based precise point positioning models and their implication for orbit and clock quality

Abstract

Orbit and clock products are used in real-time global navigation satellite systems (GNSS) precise point positioning (PPP) without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in a PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities coincide with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.