## 4 Conclusions  
To realize the accurate detection of complex top-coal structures, we propose a novel multi-frequency GPR data-fusing method using a joint sliding window and wavelet transform-weighting method. It possesses both the merits of high resolution and great detection depth and has the ability to integrate multi-frequency GPR data into one composite profile to interpret the internal structure information of top coal in detail. Also, we developed an edge detection algorithm to improve the fusion efficiency of the wavelet transform so as to realize the effective fusion of multi-frequency GPR data. Furthermore, we established a reflection intensity model of multi-frequency GPR signals traveling in top coal and interpreted the detailed top coal structure. The experimental results prove that, compared with the genetic method, the time-varying method and the wavelet transform method, the fusion results for our proposed method in terms of the IE, SF and LG evaluation criteria have improved by \"12.74%, 11.46% and 11.97%\"; \"13.59%, 11.47% and 11.96%\"; and \"12.77%, 8.51% and 10.64%\" and \"15.72%, 44.89% and 19.11%\"; \"10.77%, 9.47% and 12.13%\"; and \"14.08%, 7.04% and 12.61%\" in laboratory and field environments, respectively. Moreover, our method can also accurately interpret the internal structure of top coal.  
Although the proposed multi-frequency GPR data fusion method possesses many merits in detecting top-coal structures, there are still some issues that should be addressed in further research: (1) In fusion experiments, we only selected two kinds of GPR frequencies to evaluate fusion effectiveness; thus, in future work, multiple frequencies of GPR will be considered and compared. (2) More fusion performance assessments and evaluations of multi-frequency GPR data fusion will be conducted for further applications to deal with more challenging scenarios.  
Writing--original draft, Z.G.; writing--review and editing, W.L.; All authors have read and agreed to the published version of the manuscript. This research was funded by the Industry and Information Technology Development Program of Foundation Reconstruction and Manufacturing Industry High-Quality Development of China (TC220A04W-1-167Z) and the National Natural Science Foundation of China (52274161).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & **100 MH** & **270 MH** & \begin{tabular}{c} **Our** \\ **Proposed** \\ **Method** \\ \end{tabular} & \begin{tabular}{c} **Genetic** \\ **Method** \\ \end{tabular} & \
\begin{tabular}{c} **Time-Varying** \\ **Method** \\ \end{tabular} &
\begin{tabular}{c} **Wavelet** \\ **Transform** \\ **Method** \\ \end{tabular} \\ \hline _IE_ & 10.11 & 7.86 & 13.87 & 11.69 & 12.72 & 11.22 \\ _SF_ & 39.49 & 42.32 & 64.27 & 57.35 & 59.18 & 56.47 \\ _LG_ & 0.55 & 0.46 & 0.71 & 0.61 & 0.68 & 0.62 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The comparison results for our proposed method with the genetic, time-varying and wavelet transform methods using 100 MHz and 270 MHz GPR data.  
Data Availability Statement: The data are contained within this article.  
The authors would like to thank the editors and the reviewers of this journal.  
The authors declare no conflicts of interest.