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.
Highlights
Precise point positioning (PPP) using global navigation satellite systems (GNSS) measurements was initially proposed in [1] in order to solve the high computation burden of the network approach.The PPP technique only employs a single receiver to determine its position without explicitly using reference stations
Precise orbit and clock are needed to enable absolute positioning of high accuracy [2]. This technique has been intensively developed from static to kinematic positioning [3], from post-processing to real-time service [4,5], from using global positioning system (GPS) only to using multi-constellation systems [6], from ambiguity-float to integer ambiguity-fixed solution [7,8,9,10], from decimeter to centimeter accuracy [11]
GNSS measurements with 1 s interval from selected IGS sites are downloaded from the IGS
Summary
Precise point positioning (PPP) using global navigation satellite systems (GNSS) measurements was initially proposed in [1] in order to solve the high computation burden of the network approach. The common point for these two approaches is that their ambiguity parameters do not have integer nature, as a double-difference cannot be formed using a single receiver. In this case, the satellite hardware delay cannot be separated or eliminated from the ambiguities in the PPP mode. There are exceptional occasions where some satellites, like GPS IIF, could have large errors up to meters in their predicted orbits [22] These errors could significantly worsen the clock bias estimation and satellite phase bias estimation as well as PPP integer ambiguity resolution in user side, in particular for real-time users.
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