## 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  
The multipath error is related to the geometric relationship among the measuring station, the reflector, and the satellite position. In a static environment, the multipath error presents a repeating regularity in time domain and spatial domain as the position of the satellite moves [56]. In an unobstructed observation environment, the satellite single-difference residual sequence theoretically presents the characteristics of white noise and is related to the satellite elevation. The satellite single-difference residual sequence under the influence of the multipath effect presents a low-frequency fluctuation trend, and the low-frequency component is the observation domain error caused by the multipath effect. There is a strong correlation between the low-frequency components of different satellite repeat periods. The achievement of multipath error correction in the time domain is divided into three steps: extracting the low-frequency component of the single-difference residual of each satellite; calculating the time offset of the satellite repeat period; and correcting the observations in the next satellite repeat period. [PERSON] et al. [57] proposed an algorithm to convert double-difference residuals to single-difference residuals based on the \"zero-mean assumption\". By establishing a reference period single-difference multipath model for each satellite, and using the periodicity of multipath errors, multipath error correction is performed on the observations in the following periods. v experimental results showed that the method is applicable to different GPS satellites and can effectively correct long-period and short-period multipath errors. [PERSON] et al. [58] proposed three methods for calculating satellite repetition shift times, which are the broadcast ephemeris method (BEM), the correlation coefficient method (CCM), and the aspect repetition time method (ARTM). [PERSON] et al. [59] compared the performance of ASF with modified sidereal filtering (MSF) to evaluate the ability to weaken the multipath error, and the performance of ASF was slightly higher than that of MSF. [PERSON] et al. [60] discussed how to model multipath errors in the observed range and evaluated the accuracy of the model algorithm using real-time deformation monitoring data. In order to accurately estimate the repeat period of multipath errors, [PERSON] et al. [61] proposed a real-time window matching method, combined with SF, to achieve near real-time positioning. In order to achieve the extraction of the low-frequency component of the satellite single-difference residual under the influence of multipath effects, where single difference refers to the between-station difference of the carrier-phase measurements for the same satellite, it is necessary to use the filtering method. The classical methods include wavelet analysis, EMD, and the Vondrak filter. [PERSON] and [PERSON] [62] applied wavelet decomposition to GPS double-difference residuals to extract GPS carrier-phase multipath errors. This multipath error component was then removed directly from the GPS carrier-phase observations in subsequent days of observation data. [PERSON] [63] conducted a comprehensive evaluation of different wavelet techniques that can be used to attenuate multipath errors and proposed a new method based on the wavelet detrending technique to attenuate carrier-phase multipath errors in the observation domain. [PERSON] et al. [64] proposed a new unscented Kalman filter (UKF) to estimate the multipath parameters of weak GPS signals. The simulation results demonstrated the effectiveness of the method for estimating the multipath parameters of weak GPS signals with a carrier-to-noise ratio as low as 21 dB-Hz. [PERSON] et al. [65] used the Kalman filter (KF) and Rauch-Tung-Striebel smoother (RTSS) to extract multipath error sequences from the single-difference residuals of observations and compared it with the wavelet technique and EMD.