## 3 Research Status of the Multipath Error Data Processing Algorithm
### Multipath Error Mitigation Method Based on the Function Model  
The multipath mitigation method based on the function model refers to the construction of the corresponding multipath error correction model by using the physical or geometric relationship between the observation value or coordinate value in the GNSS data and the multipath error. Based on the time domain repetition characteristics of multipath errors, the time domain multipath error modeling method using the calculated satellite orbit repeat period is called sidereal filtering (SF). Another classic modeling method based on the repeatability of the multipath spatial domain is the multipath hemisphere map (MHM). [PERSON] and [PERSON] [38] first proposed sidereal filtering, using the satellite orbit repeat period, and established a multipath error correction model by calculating the satellite repeat period. [PERSON] et al. [39] studied the repeat period of the GPS orbit and found that the repeat period is different for each satellite. [PERSON] and [PERSON] et al. [40] used the orbital period and the topological center position of the satellite to calculate the repetition time and found that the repeat period of the satellite constellation is variable. Modified sidereal filtering (MSF) uses the average of the orbital repetition times of all satellites as the multipath repetition time. However, due to differences in satellite repeat periods, individual multipath modeling for each satellite is most efficient, called advanced sidereal filtering (ASF). Sidereal filtering has been applied to the coordinate domain and the observation domain. The multipath error is extracted from the previous coordinate sequence by the filtering method, and the multipath error of the coordinate sequence in the next cycle is corrected according to the calculated repeat period to obtain the corrected coordinate sequence. This coordinate domain-based sidereal filtering is suitable only for data post-processing and cannot correct multipath errors in real time. The time domain multipath model in the observation domain utilizes the correlation of the observation residuals in the satellite orbit repeat period and extracts the multipath error components in the observation residuals through the time series analysis method to achieve multipath error correction for observations in the next satellite orbit repeat period [41], which corresponds to the sidereal filtering method based on the observation domain.  
Sidereal filtering (SF) exerts a substantial impact on mitigating multipath errors in static environments. However, it proves unsuitable for dynamic scenes as it necessitates the advance calculation of the satellite repeat period, involving extensive modeling and intricate calculations. Compared with the coordinate domain, SF in the observation domain is more suitable for BDS containing three orbit types. MHM can significantly weaken the multipath error in the observation domain, and can be applied to precise point positioning and dynamic scenes, where the surrounding scenes remain unchanged. MHM is particularly adept at low-frequency multipath error correction rather than high-frequency multipath error correction. In addition, it is not well-suited for conventional receivers.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Type** & **Contributions** & **Year** & **Scholar** \\ \hline \multirow{2}{*}{C/N0} & Construction of the SIGMA-\(\Delta\) model based on C/N0 & 1999 & [PERSON] [29] \\  & dual-frequency C/N0 & 2019 & [PERSON] [35] \\ \hline \multirow{2}{*}{SNR} & Validation of the effectiveness of the SNR method to & 2003 & [PERSON] [30] \\  & refine a stochastic model for GPS & 2003 & [PERSON] [31] \\ \hline \multirow{2}{*}{Elevation} & Refined stochastic model for multi-GNSS & 2020 & [PERSON] [36] \\  & real-time adaptive weighting model & 2018 & [PERSON] [34] \\ \hline \hline \end{tabular}
\end{table}
Table 2: A summary of stochastic models.