## 3 Research Status of the Multipath Error Data Processing Algorithm
### Multipath Error Mitigation Method Based on the Function Model
#### 3.2.2 Multipath Error Mitigation Method Based on the Observation Domain
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Scenario** & **System** & **Year** & **Scholar** \\ \hline Multipath spherical harmonic model & Baseline positioning & GPS & 1991 & [PERSON] [78] \\ MPS & PPP & GNSS & 2015 & [PERSON] [79] \\ MHM & Baseline positioning & GNSS & 2016 & [PERSON] [80] \\ T-MHM & Baseline positioning, PPP & GNSS & 2019 & [PERSON] [82] \\ M-MHM & PPP & GNSS & 2019 & [PERSON] [84] \\ MHGM & Baseline positioning & GPS & 2020 & [PERSON] [85] \\ AT-MHM & Baseline positioning, PPP & GNSS & 2020 & [PERSON] [83] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: A summary of MHM models. MHM can significantly mitigate multipath errors; thus, this type of model is of great value for evaluating multipath errors, and this is also one of the current research hotspots. The multipath error correction of MHM is divided into three aspects. Firstly, the multipath error sequence of the GNSS observation data is extracted, and then the MHM model is constructed according to the elevation and azimuth. Finally, the obtained MHM model is used to correct the multipath error of the second-phase GNSS observation data. The algorithm flow of the MHM model to correct the multipath error is shown in Figure 4, and the algorithm includes the following six steps:  
1. Single-difference residual low-frequency components are extracted using the filtering method from the first-period observation data. 2. For different satellite constellations, different hemisphere geometric models are established. Based on the minimum elevation, maximum elevation, azimuth angle, minimum grid latitude, and minimum grid longitude, the hemispherical geometric model of GPS/BDS IGSO/BDS MEO satellites is established; based on the minimum elevation, maximum elevation, minimum azimuth, maximum azimuth, minimum latitude interval, and minimum longitude interval, the semi-celestial geometric model of the BDS GEO satellite is established. 3. Based on the instantaneous elevation and azimuth of the satellite, the low-frequency components of the instantaneous single-difference residual of the satellite are divided into the corresponding grids of the hemispherical geometric model (HGM)/GEO hemispherical geometric model (GEOHGM). 4. The mean value of the low-frequency component of the satellite single-difference residual in each grid is calculated, that is, the parameter fitting of the semi-celestial spherical grid. Finally the MHM/MHMGEO corresponding to HGM/HGMGEO is obtained. 5. The second-phase GNSS baseline monitoring data are used to construct a single-difference observation equation. The grid parameters of the MHM model are obtained based on the satellite azimuth and elevation of the current epoch and the multipath error correction of the single-difference observation equation is conducted. 6. The single-difference observation equation that was weakened by multipath errors was reconstructed into a satellite double-difference observation equation. The LAMBDA algorithm is used to fix the double-difference ambiguity and the double-difference ambiguity is substituted into the solution equation to obtain a fixed-point solution for the baseline solution.