## 5 Conclusions  
The mitigation of GNSS carrier-phase multipath errors is a hot topic with great research significance in the field of navigation signal error processing. Scholars globally have conducted considerable research on the mitigation of multipath errors from various perspectives. In over 30 years of development, there has been notable progress in the research on methods to mitigate GNSS carrier-phase multipath errors. This paper reviewed and summarized the research on GNSS carrier-phase multipath error mitigation in recent years,with a primary focus on introducing the mitigation method of carrier-phase multipath errors from the station side based on software data processing. At present, the sidereal filtering method based on the time domain repetition characteristics of multipath errors and the multipath hemispherical map method based on the spatial domain repetition characteristics of multipath errors are the future research hotspots of multipath error data processing methods. Future research directions of multipath error mitigation methods could focus on the following three aspects:  
1. Extend the current multipath error correction modeling method to the multi-frequency data of multi-GNSS systems, including GPS, BDS, Galileo, GLONASS, and other systems. [PERSON] et al. [115] extended the MHM method and proposed a MHGM (multi-point hemispherical grid model, MHGM) method suitable for multi-GNSS systems. This approach enabled the fusion of observation data from different GNSS systems for MHGM modeling, demonstrating a significant attenuation effect on the multipath errors of GNSS signals. At present, the fusion processing of multi-system and multi-frequency GNSS data has emerged as the future trend in satellite positioning [116]. Research into multipath error processing methods suitable for multi-system and multi-frequency GNSS data constitutes a focal point for future investigations. 2. Enhance the effectiveness of multipath mitigation methods in practical applications. In order to improve the positioning accuracy and operating efficiency in actual engineering practice, research on multipath error mitigation should be developed to achieve real-time application, intelligence [117], and engineering application, and the actual application scenarios should be extended to single-point positioning, dynamic scenes, and more complex environments with severe occlusions. 3. Integrate deep learning and machine learning technology into multipath error mitigation. [PERSON] and [PERSON] [118] used a combination of deep learning network long short-term memory network (LSTM) and EMD to predict and weaken the impact of multipath effects. [PERSON] et al. [119] constructed a time-frequency mask and convolutional neural network (TFM-CNN) model, which had a remarkable effect on separating the multiple paths of GNSS observation sequences in real-time deformation monitoring. [PERSON] et al. [120] used the K-means clustering algorithm from machine learning to distinguish direct signals and reflected signals in urban environments to achieve the purpose of improving positioning accuracy. By processing GNSS data through deep learning and machine learning technology, the strengths of these approaches are leveraged to improve the capability of handling GNSS data and enhance the accuracy and reliability of GNSS positioning results. Conceptualization, Q.Z. and L.Z. ; methodology, Q.Z. and L.Z. ; software, Q.Z. and L.Z. ; validation, Q.Z., L.Z., A.S. and X.M. ; formal analysis, Q.Z., L.Z. and A.S; investigation, Q.Z., L.Z., D.Z. and C.H. ; resources, Q.Z. ; data curation, Q.Z. and X.M. ; writing--original draft preparation, Q.Z. and L.Z. ; writing--review and editing, A.S. and C.H. ; visualization, L.Z. ; supervision, Q.Z. ; project administration, Q.Z. ; funding acquisition, Q.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. U22A20569, 42074226, and 42304046) and the Natural Science Foundation of Jiangsu Province (BK20221146).