GNSS Carrier-Phase Multipath Modeling and Correction: A Review and Prospect of Data Processing Methods  
[PERSON]  
1 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (L.Z. ); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (D.Z.) [PERSON]  
1 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (L.Z. ); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (D.Z.) [PERSON]  
1 School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (L.Z. ); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (A.S.); 1s21160021a31 [EMAIL_ADDRESS] (D.Z.) [PERSON]  
2 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; 2 [EMAIL_ADDRESS] 2  
[PERSON]  
1 School of Architecture, Building and Civil Engineering, Loughborough University, Loughborough LE11 3 TU, UK; 1s21160021a31 [EMAIL_ADDRESS] 1s21160021a31 [EMAIL_ADDRESS]. Leveraging its unique advantages, GNSS observation technology finds widespread application in deformation monitoring and user position navigation and positioning. The GNSS receiver captures both direct signals from the satellite and signals reflected from the surrounding environment. The superimposition of the reflected signals onto the direct signals introduces errors in the positioning results [4]. The resulting positioning error is termed multipath error. GNSS positioning involves various errors, including satellite ephemeris error, satellite clock error, multipath error, ionospheric delay, and tropospheric delay [5]. In short baseline relative positioning, double-difference observations can mitigate or eliminate the influence of various errors, such as satellite and receiver clock errors and ionosphere and tropospheric delay errors. However, multipath errors, being associated with the station's surrounding environment, cannot be mitigated by double-difference methods [6]. Particularly in complex environments, like deep mountains, woods, canyons, slopes, lakes, and urban areas, the presence of unavoidable reflectors leads to the generation of numerous satellite reflection signals, causing significant multipath effects. At this time, the multipath error becomes the primary source of errors affecting the accuracy of GNSS data processing in deformation monitoring and navigation positioning. GNSS multipath errors are categorized into two types: satellite-side multipath errors and station-side multipath errors. Satellite-side multipath errors refer to the measurement errors caused by the multipath effect, which is caused by the signal reflected by the satellite itself [7]. Station-side multipath errors mean that there are reflectors in the environment around the station, and the reflected signals enter the receiver antenna and interfere with the signals directly from the satellite, making the observed value deviate from the true value. Satellite-side multipath errors are systematic errors, which are related to satellite elevation and can be eliminated by the fitting modeling method [8]. Station-side multipath errors are related to the surrounding environment of the station, and the surrounding environment of the station is their direct cause. GNSS multipath errors are classified using observations into two types: pseudo-range multipath errors and carrier-phase multipath errors. Under line-of-sight conditions, for the coarse acquisition (C/A) code, the impact of the multipath may reach 10-20 m, and in the most serious case, it may be as high as 100 m. The maximum impact on the precise code can be about 10 m. Under line-of-sight conditions, theoretically, the maximum value of the carrier-phase measurement error caused by the multipath effect is 1/4 of the carrier wavelength [9].