## 3 Research Status of the Multipath Error Data Processing Algorithm
### Multipath Error Mitigation Methods Based on the Stochastic Model  
A stochastic model that reasonably weighs observations through the satellite's elevation, signal to noise ratio (SNR), and carrier-to-noise power density ratio (C/N0) can mitigate multipath errors and improve the positioning results. C/N0 reflects the quality of GNSS observations. [PERSON] et al. [29], based on the SIGMA-\(\Delta\) stochastic model using the measured C/N0, demonstrated the ability of the SIGMA-\(\Delta\) model to reduce signal diffraction effects on static GPS measurements and high-precision GPS railway measurements. This method improves the accuracy of GPS results by more than 50% over the standard GPS processing techniques. According to the correlation between the SNR and multipath effects, the oscillatory variation in the SNR can reflect the influence of the multipath effect. Reducing the weight or identifying and eliminating poor observation data can reduce the impact of multipath effects. [PERSON] et al. [30] used the signal to noise ratio as an evaluation index and verified through experimental data that reducing the weight of the observations affected by multipath effects can mitigate multipath errors. [PERSON] and [PERSON] [31] constructed a GPS-refined stochastic model using the correspondence between the variance in GPS observations and the signal to noise ratio. The measured data showed that the accuracy of baseline processing can be improved, which verifies the validity and necessity of GPS stochastic model refinement. GNSS observations with higher elevations are more precise. [PERSON] [32] added three models based on satellite elevation, signal to noise ratio, and least-squares residual error to the high-precision IGS station baseline vector calculation to improve the calculation accuracy. [PERSON] and [PERSON] [33] developed a multipath detector based on the signal to noise ratio of three frequencies, detected GNSS multipath errors by comparing the signal to noise ratio measurements of the three frequencies, and tested and verified its multipath detection capability in an urban environment. [PERSON] et al. [34] proposed a real-time adaptive weighting model based on satellite elevation and C/N0, which can reduce multipath errors, and applied it to simplified parallel process (SPP) and real-time differential (RTD). The test results showed that the adaptive model was better than the equal weight model, elevation model, and C/N0 model. [PERSON] [35] proposed a real-time multipath detection method using dual-frequency C/N0, which improves the reliability of multipath detection. [PERSON] et al. [36] analyzed the SNR characteristics of GPS and GLOASS, proposed an improved stochastic model based on the SNR, and reasonably established the link between carrier-phase accuracy and SNR observations. The improved model can be used in real time and can reasonably display carrier-phase accuracy with signal-to-noise ratio data, which is applicable to all GNSSs. [PERSON] et al. [37] proposed a multipath error identification method for GNSS observation data based on the prior information of the signal to noise ratio of reference stations. Satellite signal to noise ratio observations have a strong correlation with multipath errors. Poor data that are seriously affected by multipatheffects can be identified by the inter-station difference of SNR observations, and they are eliminated to resist the multipath effects' influence on monitoring complex environments.  
The equal-weight model assumes uniform accuracy for each observation, overlooking the impact of errors such as elevation and multipath effects on observation accuracy and deviating from the real conditions. Stochastic models that use elevation, SNR, or C/N0 to determine the weight are more in line with the actual situation and reflect the quality and precision of the observations. Some popular stochastic models are presented in Table 2.