# A Maximum Likelihood Estimation Method for Underwater Radiated Noise Power
## 8 Conclusions  
Underwater radiated noise measurement plays a crucial role in assessing the radiated noise levels of marine vessels. Unlike measurement methods based on array beamforming, this paper approaches the problem from a probabilistic perspective, proposing a MLE method for underwater radiated noise power. Assuming white Gaussian noise, the PDF representation of the hydrophone array received data is established, and the radiated noise power estimation under the maximum likelihood criterion is derived.  
Theoretical derivation proves that this estimate is a MVUE, satisfying the CRLB. Numerical simulation results indicate that the proposed method exhibits reduced susceptibility to ambient noise and maintains optimal power estimation performance even under low  
Figure 10: (**a**) The estimated powers and (**b**) estimation biases of the LFM signal at different frequencies.  
Figure 9: (**a**) The estimated powers and (**b**) estimation biases of the CW signal with different snapshot numbers.  
SNR conditions. Experimental data further verifies the effectiveness of this estimation method in practical measurement applications.  
Additionally, when the source location is unknown, the method can still locate the source and estimate its power by searching for the peak value within a specified area. However, due to the necessity of employing the ambient noise covariance matrix, the method is more suitable for fixed measurement sites with stationary ambient noise, as the statistical covariance matrix of ambient noise can be obtained through prolonged monitoring.  
For future work, (1) it is necessary to consider that ship-radiated noise sources are not a point source in realistic scenarios, but rather volume sources composed of multipoint sources; and (2) considering the fluctuations in ocean environmental parameters, the robustness of this method to changes in environmental parameters needs to be analyzed.  
Conceptualization, G.J. and M.L.; methodology, G.J. and M.L.; software, G.J., Z.L. and L.S.; validation, G.J. and Z.L.; formal analysis, G.J. and L.S.; investigation, G.J.; resources, G.J.; data curation, G.J. and Z.L.; writing--original draft preparation, G.J.; writing--review and editing, G.J. and M.L.; visualization, G.J.; supervision, Q.W.; project administration, Q.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors are grateful to the anonymous reviewers.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} MLE & Maximum Likelihood Estimation \\ MVUE & Minimum Variance Unbiased Estimation \\ CRLB & Cramer-Rao Lower Bound \\ SNR & Signal-to-Noise Ratio \\ PDF & Probability Density Function \\ MFP & Matched-Field Processing \\ CBF & Conventional BeamForming \\ NFBF & Near-field Focused BeamForming \\ VLA & Vertical Linear Array \\ RPCA & Robust Principal Component Analysis \\ \end{tabular}