## 7 Conclusions  
In this study, a convolutional neural network (CNN) based multipath detection method has been proposed to detect multipath in kinematic GPS positioning. The proposed method has been validated with simulated and real GPS data. The proposed method uses a CNN with a Sparse Auto-Encoder (SAE) for feature extraction. The performance of two classifiers, softmax and random forest, are compared. The results show that the softmax classifier performs better on static data and the random forest classifier performs better on kinematic data. This is because uncertainty is involved (e.g., rapid changing of environment) in kinematic multipath data, decision tree based random forest outperforms because of its high robustness. The trained detector can detect multipath contaminated measurement in real time based on the data from the current epoch and its previous successive observations. The test results with kinematic simulated data show that the proposed method can detect direct and multipath signals with accuracies of about 80%. Real kinematic data collected using a rotating arm rig (but no repetitive multipath errors) and real static data show that the method works well for GPS L1 C/A and L2 P(Y) signals with accuracies of about 70%. Real data collected near a building show that the well trained detector has an accuracy of about 60% when the training and test data are collected in two different multipath environments (close to a wall on a rooftop and near a building). In addition, the proposed method is validated in the position domain with an improvement of 18-30% in positioning accuracy using a simple linear down-weighting method, and the method outperforms a simple elevation model and SIGMA-\(\varepsilon\) model in both datasets. As a result, the tests with simulated and real data show that a multipath pattern can be detected by the proposed method, and machine learning is a feasible and promising way for detecting large GPS multipath errors. The proposed methods can be used in carrier phase based kinematic positioning, including Real-Time Kinematic (RTK) applications for improving kinematic positioning performance in difficult environments. Future work can further study the treatment of the detected multipath measurement and its effects on positioning accuracy. In addition, improving and applying the proposed methods to other GNSS (GLONASS, Galileo, and Beidou) and multi-GNSS data and high frequency (more than 1 Hz) data are suggested for further research work. Conceptualization, Y.Q. and L.L. ; Methodology, Y.Q. and L.L. ; Software, Y.Q. and C.Z. ; Validation, Y.Q., L.L. and G.W.R. ; Formal Analysis, Y.Q., L.L., G.W.R. and X.M. ; Investigation, Y.Q. and C.Z. ; Resources, L.L. ; Data Curation, Y.Q. and L.L. ; Writing-Original Draft Preparation, Y.Q. ; Writing-Review & Editing, L.L., G.W.R., X.M. and C.Z. ; Visualization, Y.Q. and C.Z. ; Supervision, L.L., G.W.R. and X.M. ; Project Administration, L.L. ; Funding Acquisition, L.L. This work was carried out at the International Doctoral Innovation Centre (IDIC). The authors acknowledge the financial support from the Ningbo Education Bureau, the Ningbo Science and Technology Bureau, China's Ministry of Science and Technology and the University of Nottingham. This research was \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**RMS Error [mm]**} & \multicolumn{2}{c}{**Standard Least**} & \multirow{2}{*}{**Elevation Model**} & \multirow{2}{*}{**SIGMA-\(\varepsilon\) Model**} & \multirow{2}{*}{**Proposed Method**} \\  & **Square Solution** & & & \\ \hline Horizontal & 13.8 & 11.7 & 11.8 & 11.7 \\ Vertical & 27.2 & 22.1 & 24.2 & 22.1 \\
3D & 30.5 & 25.1 & 26.9 & 25.0 \\ \hline \multicolumn{4}{c}{\%improvement} & & & \\ \hline Horizontal & - & 14.6 & 14.1 & 15.0 \\ Vertical & - & 18.7 & 11.3 & 18.9 \\
3D & - & \(-\)3.9 & 22.4 & 30.4 \\ \hline \hline \end{tabular}
\end{table}