## 4 Conclusions  
Geographic information services and geoprocessing services require BDS high-precision positioning technology to provide accurate spatial and temporal services. However, in severe urban environments, frequent shading will lead to multipathing, which will cause cycle slips of BDS observations, and the positioning accuracy is affected by these frequent cycle slips. To enhance the capability of the geoprocessing services and solve the problem of the cycle slips' detection and repair of the BDS-3 dual-frequency observation in severe multipath environments, an AMG method for the detection of cycle slips is proposed in this paper. Firstly, pseudorange observations unaffected by the multipath are used as the training quantity; an AR model based on the sliding-window method is constructed to predict the reliable pseudorange observations in a severe multipath environment. Then, the cycle slips' detection was carried out combining AR with the MW + GF method, and a derivation model and completeness monitoring indicators are derived to verify the effectiveness of the algorithm in theory. The field test results show that when the MW + GF combination fails in the severe multipath environments, the AMG combination still maintains a powerful detection and repair ability. Compared with the MW + GF method, the cycle slips' repair success rate of the AMG method is increased by 36%, and the cycle slips false detection rate and the missed detection rate are reduced by 64.5% and 42.0%, respectively. The specific contribution of this paper is:  
1. Compared with the traditional MW + GF method, the advantages of our method are: (1) the influence of the multipath effect on the MW observation equation has been significantly weakened, the probability of the false detection and missing detection of the cycle slips has been dramatically reduced, the more accurate estimation of the cycle slips has been obtained, and the success rate of the cycle slips' detection is more accurate. (2) The AMG method effectively solves the failure of the cycle slips' collection and repair in severe multipath conditions and restores the pseudorange in the multipath environment through an AR prediction. The cycle slips' estimation is not affected by the residual of the pseudorange multipath, and the success rate of the cycle slips' collection and repair is higher. 2. For the simulated cycle slips in the B1c and B2a dual-frequency observations of two types of BDS-3 satellites, the results show that the conventional MW + GF combination fails. After adopting the method in this paper, the detection and repair ability of the cycle slips has been significantly improved and reached the practical level. The false detection rate is 0.29%, the missed detection rate is 0.01%, the detection success rate is 99.9%, and the repair success rate is 99.9%. 3. The AMG method proposed in this paper has been verified experimentally in the severe multipath environment. However, the AMG method proposed in this paper needs to be trained with clean pseudorange data in advance, which has limitations in the practical real-time application of the cycle slips' detection and repair. In the future, we will consider this shortcoming and constantly improve the practicability of the AMG method. What calls for special attention is that the values presented in the conclusion were obtained for the field data conditions analyzed in this paper. The multipath can vary greatly according to the environment and these values of the PF and PA will not remain constant depending on their test environment. Conceptualization, Y.N. and J.C.; methodology, D.C.; software, W.Z. ; validation, J.C. and D.C.; formal analysis, W.Z. ; investigation, Y.N. ; resources, W.Z. ; data curation, J.C.; writing--original draft preparation, J.C.; writing--review and editing, J.C.; visualization, Y.N. and Y.S. ; supervision, J.X. and S.W; project administration, J.X. and S.W. ; funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript.