## 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
[77] compared the sidereal filtering method based on the coordinate domain and the observation domain, and the results showed that the accuracy of the observation domain was slightly higher than that of the coordinate domain, but the calculation efficiency of the coordinate domain was higher, and the processing time of the observation value domain was longer. When using the sidereal filtering method based on the coordinate domain to reduce the multipath effect, the coordinates are obtained from different satellite solutions. The coordinates are mixed with the influence of different satellite signals on the coordinate data. Especially when different constellations are used for multi-system joint positioning, the repeat period of different satellites is very different, which is not conducive to weakening the multipath error. Therefore, multipath modeling should be performed on each system satellite separately in the observation domain. Compared with the two methods, the sidereal filtering based on the observation domain can take into account the multipath error repeat period of each satellite and is more suitable for the reduction in multipath errors of BDS with heterogeneous constellations. The multipath error correction of SF based on the observation domain is divided into two aspects. Firstly, the SF multipath model is constructed based on the first-phase GNSS observation data; then, the SF model is used to perform multipath error correction on the second-phase GNSS observation data. The algorithm flow of the SF multipath model to correct the multipath error is shown in Figure 3. The algorithm includes the following six steps:  
1. According to the first phase of GNSS navigation ephemeris data, the average angular velocity of different satellites is calculated and the time offset of the repeat period of different satellites is obtained. 2. According to the GNSS baseline observation data of the first phase, errors such as satellite clock error, receiver clock error, satellite orbit error, tropospheric delay, and ionospheric delay are eliminated by constructing a double-difference observation equation. The double-difference ambiguity is fixed using the LAMBDA algorithm. 3. Double-difference residuals are converted to single-difference residuals based on the \"zero-mean assumption\"; wavelet analysis, EMD, or other filters are used to process the signal, and low-frequency components of single-difference residuals are extracted. 4. Using the obtained satellite repetition cycle time offset, the satellite single-difference residual time series is time-corrected based on GPST to obtain the single-difference residual low-frequency component correction model for the next repetition cycle. Finally, the SF model of the observation domain for multipath error mitigation in the next period is obtained. 5. According to the GNSS baseline observation data of the second phase, the satellite single-difference observation equation is constructed, and the corresponding satellite multipath error correction value in the sidereal filtering multipath model is extracted based on the GPST timestamp. The single-difference observation equation weakened by the multipath error is reconstructed into a satellite double-difference observation equation. 6. The Kalman filter is used to estimate the floating-point solution of the ambiguity, and the LAMBDA algorithm is used to fix the double-difference ambiguity. The double-difference ambiguity is substituted into the solution equation to obtain a fixed-point solution for the baseline solution, which mitigated the multipath error. Figure 3: Flowchart of the SF algorithm based on the observation domain. The geometric relationship between the satellite and the station is used to model and correct the multipath error. The modeling methods based on the repeatability of the multipath spatial domain mainly include the multipath spherical harmonic model, multipath stacking (MPS), and MHM.