# A Method for Estimating Source Depth Based on the Adjacent Mode Group Acoustic Pressure Field
## 5 Conclusions  
This study simulated and analyzed the effectiveness of obtaining the AMG acoustic pressure field and combined it with singular value decomposition mode extraction technology to obtain the AMG acoustic pressure field based on SACLANT test data. These data were used as a comparative parameter for the source depth estimation method based on the AMG acoustic pressure field proposed in this paper. In addition, in this study, we conducted a simulation and experimental verification using the proposed source depth estimation method. Under the conditions of the simulation environment, the average estimation error rate of the method was as low as 0.24%, and with increases in the temperature coefficient and Markov chain length, the average estimation error rate of the method decreased. In the experimental environment, setting the algorithm-related parameters resulted in an average estimation error of 0.45% for the method.  
Without the need for accurate modeling of underwater acoustic channels, the proposed method achieved a higher localization accuracy. However, the method proposed in this paper has also some limitations. For example, we need to make sure that the mode extraction process is accurate; if the mode information contains errors, this will lead to AMG acoustic pressure field deviation, resulting in increased experimental error. In addition, the proposed method uses SVD to extract the mode information and uses a simulated annealing algorithm to find the optimal solution iteratively, which increases the computation amount.  
Although our method was validated through simulation and experiments, further research on reducing the size of the vertical array, using other iterative algorithms to reduce the computation or improving the precision of mode extraction is required. The smaller the vertical array, the less difficult it is to operate. Inevitably, SVD is used to extract accurate mode information, but in order to reduce the computation amount, other iterative algorithms can be selected instead of the simulated annealing algorithm to estimate the source depth. Thus, comparative experiments will be conducted in the future between this method and other excellent source depth estimation methods.  
[PERSON] initiated the idea; [PERSON] contributed to the experiment; [PERSON], [PERSON], [PERSON] and [PERSON] contributed to the statistical analysis of data. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National key R&D Program (2022 YFB4703403), the NSF of China (Grant No. 12274113), and in part by the Research Fund from Science and Technology on Underwater Vehicle Technology Laboratory (No. 6142215200102).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are presented in the article.  
**Acknowledgments:** The authors would like to express their gratitude for the support provided by the University of HoHai.  
**Conflicts of Interest:** The authors declare no conflict of interest.