Abstract
This paper introduces a new precise point positioning (PPP) model, which combines single-fre- quency GPS/Galileo observations in between-satellite single-difference (BSSD) mode. In the absence of multipath, all receiver-related errors and biases are cancelled out when forming BSSD for a specific constellation. This leaves the satellite originating errors and atmospheric delays un- modelled. Combining GPS and Galileo observables introduces additional biases that have to be modelled, including the GPS to Galileo time offset (GGTO) and the inter-system bias. This paper models all PPP errors rigorously to improve the single-frequency GPS/Galileo PPP solution. GPSPace PPP software of Natural Resources Canada (NRCan) is modified to enable a GPS/Galileo PPP solution and to handle the newly introduced biases. A total of 12 data sets representing the GPS/Galileo measurements of six IGS-MEGX stations are processed to verify the newly developed PPP model. Precise satellite orbit and clock corrections from IGS-MEGX networks are used for both GPS and Galileo measurements. It is shown that sub-decimeter level accuracy is possible with single-frequency GPS/Galileo PPP. In addition, the PPP solution convergence time is improved from approximately 100 minutes for the un-differenced single-frequency GPS/Galileo solution to approximately 65 minutes for the BSSD counterpart when a single reference satellite is used. Moreover, an improvement in the PPP solution convergence time of 35% and 15% is obtained when one and two reference satellites are used, respectively.
Highlights
The concept of precise point positioning (PPP) was first introduced by [1]
To verify the developed GPS/Galileo PPP model, GPS and Galileo measurements at six well-distributed stations (Figure 1) were selected from the International GNSS service (IGS) tracking network [28]. Those stations are occupied by GNSS receivers, which are capable of simultaneously tracking the GPS and Galileo constellations
Three different scenarios are considered when processing the data sets with the betweensatellite single difference (BSSD) model, namely (1) a GPS satellite is selected as a reference satellite for both GPS and Galileo observables; (2) a Galileo satellite is selected as a reference satellite for both GPS and Galileo observables; and (3) two reference satellites are selected: a GPS reference satellite for the GPS observables and a Galileo satellite for the Galileo observables
Summary
The concept of precise point positioning (PPP) was first introduced by [1]. Dual-frequency GPS PPP technique has been proven to be capable of providing positioning solution at the sub-decimeter level in static mode. Combining GPS and Galileo, comes at the expense of introducing additional biases to the observation mathematical models These include the GPS to Galileo time offset, and Galileo satellite hardware delay. It is shown that the use of a single reference satellite provides a sub-decimeter level positioning accuracy and 35% improvement in the convergence time, in comparison with the un-differenced single-frequency GPS/Galileo solution. Lk E1 are the BSSD non-integer ambiguity parameters lumped to the receiver and satellite hardware delays as shown in Equations (32) and (33) It should be noticed from the above equations that the modified receiver clock error (i.e., the common term d trG ) and the initial phase bias cancel out when forming BSSD with one satellite selected as a reference (i.e., tight combination). When forming per constellation BSSD, the modified receiver clock error, the intersystem bias, and the initial phase bias are all cancelled out
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