Enhanced model for precise point positioning with single and dual frequency GPS/Galileo observables

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-2, 2014 ISPRS Technical Commission II Symposium, 6 – 8 October 2014, Toronto, Canada ENHANCED MODEL FOR PRECISE POINT POSITIONING WITH SINGLE AND DUAL FREQUENCY GPS/GALILEO OBSERVABLES A. Afifi, A. El-Rabbany Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada – (akram.afifi, ) Technical Commission II KEY WORDS: GNSS, PPP, GPS, Galileo, Single frequency, Dual frequency ABSTRACT: This paper introduces a newly developed model for both single and dual-frequency precise point positioning (PPP), which combines GPS and Galileo observables. As is well known, a drawback of a single GNSS system is the availability of sufficient number of visible satellites in urban areas. Combining GPS and Galileo systems offers more visible satellites to users, which is expected to enhance the satellite geometry and the overall positioning solution. However, combining GPS and Galileo observables introduces additional biases which require rigorous modelling, including the GPS to Galileo time offset (GGTO) and the inter-system bias. This research introduces a new ionosphere-free linear combination model for GPS/Galileo PPP, which accounts for the additional errors and biases. An additional unknown is introduced in the least-squares estimation model to account for the additional biases of the GPS/Galileo PPP solution. It is shown that a sub-decimeter level positioning accuracy and 20% reduction in the solution convergence time can be achieved with the newly developed GPS/Galileo PPP model. 1. INTRODUCTION Precise point positioning (PPP) technique allows a user with a standalone single and dual-frequency global navigation satellite system (GNSS) receiver to determine his or her position at the decimeter level accuracy. The accuracy of PPP depends on the ability to mitigate all errors and biases, which can be achieved through modeling, estimation, and combination of the GNSS observables. PPP relies essentially on the availability and use of precise satellite products, namely orbital and clock corrections. At present, a number of organizations such as the International GNSS Service (IGS) and the Cooperative Network for GIOVE Observations (CONGO) network provide the user with such precise products. A drawback of a single GNSS system such as GPS is the availability of sufficient number of visible satellites in urban areas. With the addition of Galileo satellites, a PPP solution based on the combined GPS/Galileo measurements becomes more feasible. Combining the two satellite constellations offers more visible satellites to users, which in turn enhances the satellite geometry and is expected to improve the overall positioning solution (Hofmann-Wellenhof et al., 2008). Combining GPS and Galileo, however, comes at the expense of introducing additional biases to the observations mathematical models. These include the GPS to Galileo time offset, and Galileo satellite hardware delay. Recently, the European Space Agency (ESA) estimated the GPS to Galileo time offset (GGTO), which was found to be approximately 50ns, or equivalently 15m range error (ESA, 2013). As well, the IGS estimated the code system bias of the GPS/Galileo systems at different stations with different receiver types which has range between -30 and 35 nanoseconds (IGS, 2013). Afifi and El-Rabbany (2013) showed that combining GPS and Galileo observations in a PPP solution enhances the positioning solution convergence and precision in comparison with GPSonly PPP solution. Their work, however, was limited to singlefrequency data, which is expected to have a relatively longer convergence time for the PPP solution. Melgard at al. (2013) showed that combining multi-constellation in a PPP solution improves the positioning accuracy, especially when the system biases are calibrated. As well, Odijk and Teunissen (2013) showed that prior correction of the differential GPS/Galileo (GIOVE) inter-system biases significantly increases the success rate of instantaneous ambiguity resolution for short baselines. Likewise, Paziewski and Wielgosz (2013) showed that combining GPS/Galileo observables in a double-differenced carrier-phase and pseudorange technique improves the success rate of instantaneous ambiguity resolution in comparison with GPS-only solution. Unfortunately, however, their work was limited to differential positioning techniques. This paper develops a GPS/Galileo PPP model, which rigorously accounts for the additional combination biases, namely the GPS to Galileo time offset, and Galileo satellite hardware delay. These additional biases are lumped and considered as a new unknown parameter, commonly known as inter-system bias, in the PPP mathematical model. The GPS hardware delay is lumped to the receiver clock error in both GPS-only and GPS/Galileo PPP models. Galileo signals E1/E5b and E1/E5a are combined with the GPS L1/L2 signals in a dualfrequency ionosphere-free linear combinations, respectively. In addition, GPS L1 is combined with Galileo L1 signal in a single-frequency PPP analysis. Sequential least-squares estimation technique is used to get the best estimates for the inter-systems bias parameter. The positioning results of the newly developed GPS/Galileo PPP model showed a subdecimeter accuracy level and 25% convergence time improvement in comparison with the GPS-only PPP results. 2. GPS AND GALILEO COMBINATION MODELS Generally, the accuracy of PPP depends on the ability to mitigate all errors and biases. GNSS pseudorange and carrierphase measurements are both affected by several types of random and systematic errors. These errors may be classified as those originating at the satellites, those originating at the receiver, and those that are due to signal propagation through the atmospheric layers (El-Rabbany, 2006). GNSS errors attributed to the satellites include satellite clock errors, orbital errors, satellite hardware delay, satellite antenna phase centre variation, and satellite initial phase bias. Errors attributed to signal propagation include the delays of the GNSS signal as it This contribution has been peer-reviewed. doi:10.5194/isprsarchives-XL-2-173-2014 173 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XL-2, 2014 ISPRS Technical Commission II Symposium, 6 – 8 October 2014, Toronto, Canada passes through the ionospheric and tropospheric layers. Errors attributed to receiver/antenna configuration include, among others, the receiver clock errors, multipath error, receiver noise, receiver hardware delay, receiver initial phase bias, and receiver antenna phase center variations. In addition to the above errors and biases, combining GPS and Galileo observation in a PPP model introduces additional errors such as GGTO due to the fact that each system uses a different time frame. GPS system uses the GPS time system, which is referenc (...truncated)