## 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
Based on the principle of superposition, [PERSON] and [PERSON] [78] used spherical harmonics as a calibration function and applied this calibration model to GPS measurements to weaken multipath errors. [PERSON] et al. [79] proposed MPS that considers geometric and statistical aspects, is able to detect far-field and near-field multipath signals, can be used in real time and for post-processing, and is applicable to all satellite systems. When the observation environment remains basically unchanged, the change characteristics of the single-difference residual of the satellite carrier observation value are related to the azimuth and elevation, and the change characteristics are consistent in the spatial domain. The single-difference residuals of the carrier observations in different satellites and the different frequencies of the same satellite have different variation characteristics. The MHM model with the receiver as the origin, the elevation as the latitude, and the azimuth as the longitude for grid division can express satellite single-difference residual spatially varying characteristics. Based on the single-receiver multi-antenna hardware and unified time system, [PERSON] et al. [80] directly constructed a single-difference observation equation, taking into account the altitude angle and azimuth angle of each satellite, and established the MHM model suitable for real-time deformation monitoring, which significantly mitigated the impact of multipath errors. [PERSON] et al. [81] extended MHM to the kinematic shipboard environment, conducted static and kinematic tests, and proved the feasibility of MHM. On the basis of MHM, [PERSON] et al. [82] proposed an MHM model based on the trend surface analysis method, called T-MHM, focusing on the correlation of multipath errors in the satellite spatial domain, which effectively mitigated multipath errors. In the baseline E, N, and U directions, T-MHM has a higher positioning accuracy than MHM. To solve the problem of the multicollinearity and overfitting of the fitting parameters in the T-MHM, [PERSON] et al. [83] proposed the AT-MHM method. Theoretically, this method can be applied to carrier-phase multipath error correction. Aiming to obtain the multipath error characteristics of satellites with different elevation values, [PERSON] et al. [84] proposed an improved MHM, which reduces the influence of multipath errors on precise point positioning under static conditions. [PERSON] et al. [85] proposed a multi-point hemispherical grid model (MHGM) to directly model the double-difference residual, which can be applied to common receiver hardware equipment. [PERSON] et al. [86] presented the MHM_V model based on variational mode decomposition (VMD) and MHM. They using the VMD algorithm to extract multipath errors from the single-difference residuals and to correct the original observations of the carrier phase within a few days after implementation according to the principle of recent elevation and azimuth angles to mitigate multipath effects. [PERSON] and [PERSON] [87] used ensemble empirical mode decomposition (EEMD) to accurately extract the multipath errors in the observation domain and combined with the MHM model to correct the multipath errors in real time, indicating the importance of the accurate extraction of multipath errors. The development of the MHM method is presented in Table 4.  
These methods are adaptable to multiple GNSS systems and can be applied to baseline positioning and precise point positioning. In a relatively constant observation environment,