# Estimating and Analyzing Long-Term Multi-GNSS Inter-System Bias Based on Uncombined PPP
## 1 Introduction
[PERSON] et al., studied the relationship between the globally distributed IGS tracking station receivers and ISB parameters [17]. The main problem of the SPP approach is that the accuracy is relatively low. Nevertheless, after correcting the ISB parameter, the SPP positioning accuracy of multiple systems can still be improved [18]. With the development and application of PPP technology, more researchers have started to use PPP technology to investigate the ISB parameter [19; 20; 21] or have adopted multi-system PPP with ISB corrected for practical application [22; 23]. [PERSON] et al., proposed a four-system combined PPP algorithm with ISB parameters based on GPS, GLOASS, GALILEO and BDS. Based on the ionosphere-free combination model, this algorithm obtains the ISB parameters of between GLONASS, BDS, GALILEO and GPS through a static processing of seven Multi-GNSS Experiment (MGEX) tracking stations data. The results demonstrate that ISB shows a moderate slight intra-day variation that is related to the receiver type. The multi-day ISB time series also includes irregular jumps, which can be up to 20 ns [12]. However, this algorithm is based on the ionospheric-free combination model, and the process noise is amplified by approximately three times, which may affect ISB parameter estimation. In addition, this method is not applicable to ISB estimation and analysis on a day when the ionosphere changes significantly. [PERSON] et al., studied multi-GNSS PPP considering ISB parameters based on an uncombined model and discussed different processing strategies for ISB parameters, however, the characteristics of ISB parameters were not investigated or analyzed [19]. [PERSON] et al., applied multi-system PPP considering ISB in precision agriculture. Compared to the single GPS system, the dynamic and static positioning accuracy are decreased from 19 mm and 126 mm, to 6 mm and 35 mm, respectively, and ISB parameters were estimated as a constant within a day [24]. Up to now, a detailed long-term analysis and comparison of ISB parameters of the four systems based on the uncombined model has not been conducted. To analyze the characteristics of multi-system ISB parameters, the four-system uncombined PPP function model was first deduced, followed by the specific definitions of ISB parameters. It is worth noting that we specifically consider the processing of the pseudo range frequency deviation of the GLONASS system. After formula derivation and separation, we set an inter-frequency-biase (IFB) parameter for each epoch, which is conducive to eliminating the influence of pseudo range IFB parameter on positioning. Compared with the method of setting the IFB parameter one by one for the GLONASS satellite, the model produced in the manuscript can greatly reduce the number of parameters to be estimated for each epoch, greatly enhance the structural strength of the model, and improve the efficiency of model estimation. We then introduce the experimental scheme and data processing method. First, we analyze the advantages of multi-system PPP in the number of available satellites, dilution of precision (DOP) value and positioning accuracy, so as to provide a better reliability guarantee for the analysis of ISB parameter characteristics in subsequent experiments. Next, the intra-day and inter-day variation characteristics of three groups of ISB parameters and their relationship with the receiver type of the station are presented in detail. Finally, conclusions and future prospects are summarized.