# Estimating and Analyzing Long-Term Multi-GNSS Inter-System Bias Based on Uncombined PPP
## 1 Introduction  
With the implementation and improvement of multi-GNSS constellations, precise point positioning (PPP) is rapidly developing from traditional GPS-only dual frequency systems to multi-system-multi-frequency systems. PPP is widely used in many areas, e.g., seismic rescue and ocean exploration [1; 2; 3; 4; 5]. As of 4 June 2019, there are 115 globally distributed satellites form the four different systems that can provide user location services. GPS and GLONASS, as completed constellation systems, can provide comprehensive GPS timing navigation (PNT) services [6]. Built in 1999, the GALILEO system represents a new generation of civilian global satellite navigation systems. The full GALILEO system constellation will consist of 30 satellites and will distribute over three orbital planes. Currently, 26 medium Earth orbit(MEO) satellites are in orbit to provide positioning and navigation services. GALILEO satellites transmit signals at five different frequencies, i.e., E1 (1575.42 MHz), E5a (1176.45 MHz), E5b (1207.14 MHz), E5 ab (1191.795 MHz) and E6 (1278.75 MHz). The BeiDou Navigation Satellite System (BDS) is the first navigation system [7] in which all satellites transmit tri-frequency signals, i.e., B1 (1561.098 MHz), B2 (1207.14 MHz) and B3 (1268.52 MHz). Currently, thereare 33 BDS satellites at the working phase and another six (1 GEO + 3 IGSO + 2 MEO) are under the in-orbit test phase [8]. When jointly processing multi-GNSS data, it is necessary to properly deal with the different receiver clocks. Existing methods could be generally divided into two types. The first type selects a reference system (mostly GPS), and only a single receiver clock difference parameter is built, and the ISB parameter is generated at the same time [9; 10]; The second approach sets separate receiver clock parameters for each system [11]. The advantage of the second approach is that ISB is not considered, and parameters to be estimated are not increased or decreased. With regard to the ISB parameter, when we select GPS as the reference system, the time reference is aligned to the GPS time in the joint processing function model; however, for multiple systems, the satellite reference clocks selected in the calculation process still differ, which also results in differences of the reference clock [12]. In addition, because of the satellite type, standard, frequency and other system specifications, the signals will be processed through different channels when the signals are received. This means that the signal hardware delays of different satellite systems will be inconsistent, relative to the receiver [13; 14]. In summary, ISB parameters are related to satellite reference clock differences and hardware delay biases, due to different receiver configurations. Research has been conducted to investigate ISB by single point positioning (SPP) technology. In the SPP function model, ISB parameters also include the two elements mentioned above [13]. [PERSON] et al. studied the ISB parameters between the GLONASS, GALILEO, BDS and GPS systems using SPP, and analyzed its influence on the positioning results [15]. However, the accuracy was poor, and only the variation of ISB on a single day were analyzed. [PERSON] et al analyzed the characteristics of BDS-GPS ISB using SPP and designed a statistical method based on a hypothesis test to evaluate the stability of ISB parameters. Results confirmed the correlation between ISB parameters and receiver type [13]. However, their method only includes the ISB between BDS and GPS, while that of the GALILEO and GLONASS were not considered. In addition, a long-term ISB instead of a single day analysis should be conducted. [PERSON] and [PERSON] used SPP technology to investigate the ISB parameters between GLONASS and GPS from five international GNSS service (IGS) tracking stations. Results indicated that, the variation of ISB parameter can be up to 40 ns over a single day [16].