## 3 Collaborative Secure Localization Algorithm
### Network Model and Assumptions  
We assume there are three types of sensor nodes in the UWSNs: surface buoys, mobile AUVs, and unknown nodes, as shown in Figure 1. Surface buoys are floating on the ocean surface, which can directly obtain their positions by GPS and localize unknown nodes in their communication ranges. The AUV can first obtain its location on the surface, then dives into water to localization unknown nodes in the deep water. The sensor node which can first obtain its own location information and then help unknown nodes with localization is named as an anchor node. Therefore, both the surface buoys and the AUVs are anchor nodes. In this paper, we assume that all the anchor nodes can accurately obtain their positions from GPS as some previous underwater localization algorithms did. The GPS accuracy impacts on localization are not within the scope of this paper. All unknown nodes have the same initial energy level, the same capability of communication, computation and storage.  
In the UWSN, there are \(n\) unknown nodes, denoted by \(u_{i}\in S\), where \(U=\{u_{i}\}_{i=1}^{n}\). Each unknown node \(u_{i}\) is randomly deployed at the position \(p_{i}\) with the communication range \(r\). Only when the distance \(d(p_{i},p_{j})\) between two neighbor node \(u_{i}\) and \(u_{j}\) satisfies \(d(p_{i},p_{j})\leq r\), the two neighbor unknown nodes can directly communicate with each other. We call them one-hop neighbor nodes. Similarly, there are two-hop and multi-hop neighbor nodes. In this paper, two-hop neighbor nodes will be used in the secondary localization. In addition, there are many malicious attacks in the process of localization, as summarized in Table 1. All the malicious attacks are compared and analyzed in terms of existing countermeasures, attack behaviors and attack results.  
Figure 1: The structure of network model.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Layers** & **Attacks** & **Countermeasures** & **Attack Behaviors** & **Results** \\ \hline Physical & Stealing & The perception mechanism for physical damage, encryption algorithm, _etc._ & Signal eavesdropping and tampering & packet error and packet loss \\ Layer & Jamming & Multi-frequency communication, binding different transmission priority, _etc._ & Send jamming signal on the working frequency & packet loss \\ \hline Data Link & Collision & Forward Error Correct (PFC) code. & Report to send messages & packet loss \\ Layer & Eshaustion & Limit the transmission speed and retransmission times of packets & Send a lot of useless messages & packet loss \\ Layer & Undlares & Avoid using pose packets, redistributing transmission priority of packets, _etc._ & Dislureable use up the channel & packet loss \\ \hline \multirow{4}{*}{Network} & DS attacks & Detection of energy consumption & Repeatedly send many messages to exhaust energy & packet loss \\  & Selective forwarding & Multi-path routing, reputation and trust model, _etc._ & Selectiveforward packets & packet loss \\ Layer & Spill & Identity authentication of sensor nodes & Have multiple identities & packet error \\  & Wornble & Construction of network topology & Shorten distance & packet error \\  & Shishoke & Traffic monitoring, identify authentication, multi-path routing, _etc._ & Maliciously tamper with routing & packet loss \\ \hline \multirow{4}{*}{Transport Layer} & Flooding & Limit the broadcast range of sensor nodes & Establish false connections & packet loss \\  & Tampering & Data encryption and node authentication. & Tampering localization beacons & packet error \\ \hline \hline \end{tabular}
\end{table}
Table 1: Analysis on malicious attacks against localization in Underwater Wireless Sensor Networks (UWSNs).