## 5 Simulation Results and Discussions
### Comparison of Detect Ratio  
In our proposed CSLT, the weight values chosen for trust update are not constants, which are decided based on the knowledgeable of current network situation and directly impact the performance of CLST. Thus, we first simulate the weight value's on the algorithm performance, e.g., the detect ratio of malicious nodes. As shown in Figure 6, the detection ratio of malicious nodes rises step by step along the simulation progresses. When \(n_{1 new}>n_{1 old}\), choosing \(\omega_{old}\) as \(0.5\leq\omega_{old}<1\) can detect more malicious nodes. This is because all the malicious nodes which intentionally to increase their values can be effectively detected. When \(n_{1 new}<n_{1 old}\), choosing \(\omega_{old}\) as \(0\leq\omega_{old}<0.5\) can performance better. This is because, in this case, mainly using the current calculated trust as reference to update trust can well punish the behaviors of malicious nodes.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Simulation region size & 500 m \(\times\) 500 m \(\times\) 500 m \\ The number of unknown nodes & 500 \\ Communication range & 100 m \\ Node placement & Randomly deployed \\ Initial trust value & 1 \\ Acoustic channel bandwidth & 100 Kbps \\ The modulation mode for acoustic communication & BPSK modulation \\ Mobility model & The Meandering Current Mobility (MCM) model \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation Parameters.  
Figure 6: \(Cont.\)Our secure localization is proposed based on MANCL [29], ReTrust [31], and RFSN [34], thus CSLT is compared with the three references. As shown in Figure 7, nine types of malicious nodes are detected. They are (1) signal interference attacks; (2) link collision attacks; (3) DoS attacks; (4) selective forwarding attacks; (5) Sybil attacks; (6) wormhole attacks; (7) sinkhole attacks; (8) flooding attacks and (9) packet tampering attacks. Simulation results show that our proposed CSLT can well detect the nine types of malicious nodes with more than 95% detection ratio. However, we cannot find malicious node with 100%. This is because some malicious nodes which cause packet error or loss of the surrounding nodes' instead of in their own communication cannot be efficiently found out. MANCL cannot detection all the malicious attacks because it does not use any secure mechanism in the process of localization. RFSN and ReTrust are only effective against selective forwarding attacks, since they just consider packet loss to evaluate trust for sensor nodes. Therefore, they cannot detect the rest types of malicious nodes, e.g., Sybil attacks, wormhole attacks and packet tampering attacks. However, ReTrust works better than RFSN in terms of malicious node's detection ratio. This is because in RFSN, only direct trust are calculated and only one-hop neighbor nodes' behaviors can be monitored, while in ReTrust, neighbor nodes' recommendation are also taken into account to evaluate trust. Relatively specking, ReTrust is much more reliable and robust against malicious attacks than RFSN.  
Figure 6: The performance of detection ratio. (a) \(n_{1 new}>n_{1 old}\); (b) \(n_{1 new}<n_{1 old}\).  
Figure 7: Comparison of detect ratio.