# A Post-Processing Multipath/NLoS Bias Estimation Method Based on DBSCAN
## 5 Conclusions  
This study proposed a post-processing method to calculate the pseudorange biases resulting from multipath/NLoS effects. Leveraging the physical models and corrections from IGS, pseudorange leftover terms were computed. The application of the DBSCAN algorithm facilitated the separation of the receiver clock parameters. The novelty of this paper can be summarized in three key aspects. Firstly, the paper defined a novel leftover term derived from insights into the pseudorange equation. Secondly, through theoretical analysis, two probability models for this leftover term were established under conditions with and without multipath/NLoS effects. The analysis demonstrates that leftover terms without multipath/NLoS effects can form a cluster. Finally, the paper proposed a post-processing procedure based on a clustering algorithm for estimating multipath/NLoS biases. The experimental results, derived from two real-world datasets in challenging GNSS scenarios for both static and dynamic conditions, demonstrate the effectiveness of the proposed method. Firstly, the successful estimation of receiver clock parameters \(\hat{dt}_{\text{rcv}}\) was achieved using the DBSCAN method. Secondly, the pseudorange biases due to multipath/NLoS effects were isolated from the leftover terms. Finally, compensating for the estimated pseudorange biases in the measurement results in a significant improvement in 3D positioning accuracy. The 3D positioning RMSE was reduced by 78% (from 13.9217 m to 3.0121 m) and by 79% (from 26.0103 m to 5.5094 m) for the static dataset and dynamic dataset, respectively. The experimental results highlight the effectiveness of the proposed method. While the proposed method has demonstrated promising results, as outlined earlier, its application is subject to certain limitations. For instance, in scenarios where the interference leading to multipath/NLoS effects is particularly strong, biases may affect all the measurements. Under such extreme conditions, the clustering algorithm may fail as there may be insufficient measurements unaffected by the influence of multipath/NLoS effects. In the future, several aspects will be considered for extending the proposed multipath/NLoS estimation method, including its application to multi-constellation GNSS  
Figure 17: CDFs of positioning errors before and after pseudorange multipath/NLoS compensation in horizontal and vertical directions. systems. Additionally, it would be valuable to explore the factors that influence the accuracy of the clustering algorithms employed in this context. Conceptualization, Y.G. ; methodology, Y.G. ; software, Y.G. ; validation, Y.G., S.Z., P.D. and F.D. ; formal analysis, S.Z. and F.D. ; resources, P.D. ; data curation, P.D. ; writing--original draft preparation, Y.G. ; writing--review and editing, S.Z. and F.D. ; supervision, F.D. All authors have read and agreed to the published version of the manuscript. This research was funded by the Chinese Scholarship Council (grant code 202008310182). Not applicable. The static GNSS data used in this research are available from [PERSON] ([EMAIL_ADDRESS]) upon reasonable request; The dynamic GNSS data can be downloaded from [[https://github.com/weisongwen/UrbanNavDataset](https://github.com/weisongwen/UrbanNavDataset)]([https://github.com/weisongwen/UrbanNavDataset](https://github.com/weisongwen/UrbanNavDataset)) (accessed on 25 October 2023). [PERSON] acknowledges the help from [PERSON] (Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy) for the discussion regarding the clustering algorithms. The authors declare no conflicts of interest. Appendix A Shapiro Effect Correction for \(\delta\mathbf{t}_{\text{stc}}^{s,\text{rel}}(\mathbf{t})\)  
Earth's gravitational field causes the Shapiro effect, which results in a time delay for GNSS signal propagation.