# Comparison Analysis on the Accuracy of Galileo PPP Using Different Frequency Combinations in Europe
## 1 Introduction  
Precise point positioning (PPP) can achieve high positioning accuracy on regions such as mountains, deserts, or oceans without the support of external reference stations [1]. However, a long initialization period of about 30 min is still necessary for the dual-frequency kinematic PPP to achieve a reliable solution, which can be shortened to 15 min using the ambiguity-fixing method or multi-system combination [2, 3]. With the modernization of the Global Navigation Satellite System (GNSS), triple- or multi-frequency signals have become available for the emerging BDS and Galileo, as well as the new generation of GPS and GLONASS satellites [4]. Therefore, the utilization of multi-GNSS and multi-frequency signals to shorten the convergence time and improve the position accuracy has been intensively investigated. The mathematic models of PPP mainly contain the traditional ionosphere-free (IF) model and the undifferenced and uncombined (UC) model. The IF model can obtain the three-dimensional coordinates in the International Terrestrial Reference Frame (ITRF) by eliminating the first-order ionospheric delay, and it is widely used in airborne andmarine applications. In comparison, the UC model additionally estimates the ionospheric delay and can be used for ionospheric scintillation monitoring. Moreover, the UC model avoids the noise amplification and correlation between observations and can be easily extended for multi-frequency data processing. It has been demonstrated that the UC model provides the best performance if an external ionosphere model is applied [5]. However, the accuracy of the external ionospheric delay corrections is affected by the temporal and spatial characteristics of the ionosphere activity. In the regions with more active ionospheric condition (equatorial or polar regions), or during the time when solar activity level is high, global ionosphere models [6; 7; 8] cannot characterize the real ionospheric condition. To achieve high accuracy with shorter convergence time in these scenarios, accurate post-processed or real-time products should be applied [9]. The Chinese BDS-3 achieved its global constellation in 2020; results indicated that the satellite-induced code biases have been eliminated in the new constellation, and the measurement quality of BDS-3 outperforms the BDS-2 [10]. The positioning errors for static BDS PPP on a global scale were also analyzed, and they indicated that comparable performance can be achieved with respect to the GPS [11]. Moreover, the BDS-3 and Galileo constellations provide observation frequency on more than three frequencies, which bring opportunities to improve the performance of PPP. The benefits of triple-frequency observations for rapid PPP ambiguity resolution (AR) are first demonstrated by [12] based on the simulated experiment. The use of the triple-frequency BDS and Galileo observations can achieve comparable results as the dual-frequency PPP model and is not affected by the time-dependent phase hardware delays [13]. Besides, using more frequencies can improve the performance of Galileo kinematic PPP [14]. Moreover, if proper spatial and temporal ionospheric constraints are available, the triple-frequency PPP with the raw observation model can achieve better performance than the traditional dual-frequency ionospheric-free PPP [15]. The benefits of triple-frequency observations for PPP ambiguity resolution (AR) have also been analyzed. An optimal linear combination model is proposed by [16] using triple-frequency observations to improve the ambiguity resolution performance and time-to-first fix of PPP. A unified modeling strategy for triple-frequency PPP AR was proposed by [17] and indicated that that the contribution of the third frequency observations can improve the float PPP solutions and the reliability of PPP AR. Concerning the contribution of more frequencies to PPP AR, E1/E5/E6 triple-frequency signals can achieve the best performance, and the use of quad- and five-frequency only bring a 1 min benefit for the Galileo PPP [18].