Abstract
This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference.
Highlights
GNSS precise point positioning (PPP) has proven to be capable of providing positioning accuracy at the sub-decimeter and decimeter levels in static and kinematic modes, respectively
GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model
Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference
Summary
GNSS precise point positioning (PPP) has proven to be capable of providing positioning accuracy at the sub-decimeter and decimeter levels in static and kinematic modes, respectively. To simplify Equations (17)–(20), the receiver and satellite clock errors can be written as: dt rG = cdtrG + brP dt Gs = cdtGs + bPS dt rE = cdtrE + brE dt Es = cdtEs + bES dt rGΦ = cdtrGΦ + brΦ dt GsΦ = cdtGs Φ + bΦS dt rEΦ = cdtrEΦ + brEΦ dt EsΦ = cdtΦs + bESΦ where dt Gs , dt Es , dt Gs Φ , and dt Es Φ are the decoupled satellite clock errors for the pseudorange and carrier phase measurements of both GPS and Galileo systems, respectively. As shown in Equations (21)–(24), the assumption of having a separate receiver clock error for the pseudorange and the carrier phase observables is more complex in the case of GPS/Galileo PPP model. GIFDC and Φ EIFDC are the ionosphere-free linear combinations of the pseudorange and carrier-phase observables after applying the above corrections; zpdw is the wet component of the tropospheric zenith path delay; mf troposphere mapping functions; The ambiguity parameters of the decoupled clock PPP model are given by:. It can be concluded that either satellite clock corrections or un-calibrated satellite hardware delays drift over time or even both change over time
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