## 5 Discussion  
The proposed approach is designed to effectively approximate the original waveform with a Gaussian mixture model while ensuring that initially detected OPs are not missed and allowing for the estimation of potential returns that were not detected. The time difference between the OPs and EPs is utilized to determine whether the decomposed model sufficiently represents the original waveform. This criterion can prevent the neglect of low-intensity return components during Gaussian curve fitting. Figure 12a shows the decomposition results when only R\({}^{2}\) > 0.95 was applied as the termination condition of iteration. The residual-based termination conditions inevitably include the possibility of missing weak returns. Figure 12b shows the results when the time difference criterion from the OP is used in addition to the R\({}^{2}\) criterion. The results indicate that even a weak bottom return can be decomposed into components. However, it may be vulnerable in distinguishing noise from weak returns. If noise is falsely detected as a  
Figure 11: Bottom point extraction results at test site 2: (**a**) overview of LBASSD result; (**b,c**): close-up views of boxes in (**a**); (**d**) overview of PGD result; (**e,f**): close-up views of boxes in (**d**).  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Method** & **AZ Error (m)** \\ \hline Site 1 & LBASSD & \(-\)0.684 \(\pm\) 0.395 \\  & PGD & \(-\)0.315 \(\pm\) 0.427 \\  & LBASSD & 0.033 \(\pm\) 0.457 \\ Site 2 & PGD & 0.109 \(\pm\) 0.501 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of geolocation accuracy of bottom point clouds based on echo-sounding data.  
peak or if a weak peak that should have been detected is missed, incorrect decomposition could result. The limitation is related to noise removal performance, which can be improved through component verification with neighboring waveforms. Hence, this warrants further investigation.  
The proposed approach can effectively decompose irregular and various ABL waveform types without a data-specific adjustment process. Existing ABL waveform decomposition techniques, which decompose the waveform into three fixed components (water surface, water column, and bottom), require separate classification and modeling for very shallow or deep water. However, PGD does not require such data-specific procedures or parameter adjustment according to the environment, thus simplifying and unifying the entire waveform processing. The approaches employing a fixed decomposition model can simultaneously label the water surface and bottom points during decomposition, but this is limited to typical ABL waveforms. Actual ABL data may include waveforms in which the bottom return is not received and noise may not be completely removed during waveform preprocessing. Consequently, whether the first component represents the water surface and the last one represents the bottom cannot be definitively determined. Therefore, we are investigating water labeling by utilizing various waveform features (e.g., amplitude, center, width, and return number) from the decomposed Gaussian components. The waveform features can also be used for classifying different underwater objects [18; 44].