# Modeling and Assessment of GPS/BDS Combined Precise Point Positioning
## 1 Introduction  
To prepare for the next phase of generating products for all GNSS available, the IGS [1] initiated the IGS Multi-GNSS Experiment (MGEX) campaign. The MGEX campaign focuses on tracking the newly available GNSS signals including the Chinese BeiDou Navigation Satellite System (BDS). BDS had been providing regional service since December 2012 with five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Satellite Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Many studies are being carried out and much progress has been achieved in BDS-only and GPS/BDS-combined precise data analysis. Precise BDS orbits/clocks are currently available at many institutes and several IGS analysis centers [2; 3; 4; 5].  
Many publications demonstrate the daily static Precise Point Positioning (PPP, [6] using BDS observations, and precise orbits/clocks could reach a precision of a few cm [5; 7; 8]. With the additional tracking of BDS constellations and therefore, a significant increase of observed satellites, GPS/BDS combined PPP could improve solution availability and accuracy by improving tracking geometry with a reduction of the position dilution of precision (PDOP) [9], especially in environments like urban canyons and ravines where there are limits in sky view. [PERSON] et al. [10] demonstrated that near real time GPS/BDS combined PPP solution show a higher degree of precision and better robustness, whichis very important for tsunami early warning. Also, for GNSS-based precipitable water vapor retrieval, GPS/BDS combined PPP could obtain more accurate and reliable water vapor estimates than GPS-only or BDS-only PPP [11]. [PERSON] et al. [12] evaluated the orbit and clock of different GNSS systems from different analysis centers comprehensively and has shown the accuracy improvement of Multi-GNSS PPP rather than single-system PPP.  
Compared to the GPS-only and BDS-only PPP, the key issue in GPS/BDS PPP is the handling of inter system bias (ISB). Station-wise GPS/BDS inter-system bias includes two parts, one is the difference between system time GPST and BDT, and the other comes from the station-wise instrument hardware delay difference when tracking satellites of different systems. For most geodetic receivers and antennas, the instrument hardware delay is not calibrated and it will be assimilated into the receiver clock. Thus, the GPS/BDS inter-system bias shows up as the receiver clock differences between GPS-only and BDS-only PPP. For GPS/BDS combined PPP, two kinds of parameterization strategies are widely implement: (1) two receiver clock parameters at each epoch; (2) epoch-wise receiver clock and ISB parameter. Since for one station, the difference of hardware delay between different satellite systems is over one day interval [13; 14; 15], ISB is usually treated as a daily constant [9; 16; 17; 18]. [PERSON] et al. [19] developed a new simplified multi-GNSS PPP model, which does not include ISB parameter and observations of different GNSS systems could be treated in a unique way. [PERSON] et al. [20] demonstrated that a priori constraint of predicted ISB in GPS/BDS combined PPP could shorten convergence time and also, improve positioning accuracy slightly. Furthermore, many studies have been carried out over the handling of ISB in multi-GNSS data processing, including GPS/BDS inter-ambiguity resolution [21], GPS/BDS single-frequency short baseline RTK [22; 23] and long baseline relative positioning [24], GPS/BDS/GLONASS/Galieo/QZSS ISBs analysis with different types of receivers [25], BDS/Galileo/QZSS and GPS single-frequency RTK [26].  
In this paper, we present and evaluate GPS/BDS PPP models, where single system and combined PPP models are discussed. In the following, Section 2 presents the traditional and simplified GPS/BDS PPP model; Section 3 presents data analysis and compares daily positioning qualities; Section 4 compares the solved parameters between the traditional and simplified combined PPP models; finally, Section 5 summarizes the main points of this paper.