# Enhancing Unmanned Marine Vehicle Security: A Periodic Watermark-Based Detection of Replay Attacks
## 5 Conclusions  
This research has presented a method for detecting replay attacks on UMVs by employing periodic watermark and compensatory signals that adhere to a Gaussian signal. Unlike  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(J_{ave}\) & \(\beta_{1}\) & \(\alpha_{1}\) & \(\beta_{2}\) & \(\alpha_{2}\) \\ \hline Method in This Paper & 80 & 95–96\% & 1–2\% & 95–96\% & 1–2\% \\ \hline Method in [PERSON] et al. [30] & 80 & 92–94\% & 1–2\% & 92–94\% & 1–3\% \\ \hline Method in [PERSON] et al. [37] & 80 & 90–92\% & 3–5\% & 89–92\% & 3–4\% \\ \hline Method in [PERSON] et al. [32] & 80 & 82–84\% & 9–12\% & 79–80\% & 11–13\% \\ \hline Method in [PERSON] et al. [31] & 80 & 67–70\% & 16–19\% & 57–66\% & 22–27\% \\ \hline Method in [PERSON] et al. [36] & 80 & 65–70\% & 17–23\% & 53–62\% & 28–35\% \\ \hline \end{tabular}
\end{table}
Table 4: Comparison of Detection Efficiency and Control Cost Between Methods in This Paper and Other Papers under the Same Control Performance Loss  
Figure 12: Comparison between the performance index of the method proposed in this paper and others [30,36,37].  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(J_{ave}\) & \(\beta_{1}\) & \(\alpha_{1}\) & \(\beta_{2}\) & \(\alpha_{2}\) \\ \hline Method in This Paper & 24 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline Method in [PERSON] et al. [30] & 30 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline Method in [PERSON] et al. [37] & 55 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline Method in [PERSON] et al. [32] & 93 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline Method in [PERSON] et al. [31] & 167 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline Method in [PERSON] et al. [36] & 175 & 88–92\% & 4–6\% & 87–91\% & 6–10\% \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of Detection Efficiency and Control Cost Between Methods in This Paper and Other Papers under the Same Detection Efficiencyconventional approaches that use fixed thresholds to compare residual detection function magnitudes, this method has improved detection efficiency by evaluating the relative position across compensatory signals. The technique has not only achieved high detection rates but also reduced the variance of watermark signals, thus preserving system performance. However, when the attack delay aligns with an integer multiple of the watermark signal period, the method may produce some false positives. In the method used by [PERSON] et al. [30], although the method incurs a greater loss in control system performance compared to the paper, it does not produce false positives under these circumstances. Addressing this issue is planned for future research. Future research will also focus on designing new watermark signals to minimize their effect on system control performance further.  
Conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing--original draft preparation, writing--review and editing, visualization, supervision, project administration, funding acquisition, G.B. and X.G. All authors have read and agreed to the published version of the manuscript.  
This work is supported in part by the National Natural Science Foundation of China under Grants 52301418; Sichuan Science and Technology Program under Grants 2024 NSFSC0878; Joint Fund of Science and Technology Department of Liaoning Province and State Key Laboratory of Robotics under Grant 2022-KF-22-08.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The author declares no conflict of interest.