# Research on Localization Algorithms Based on Acoustic Communication for Underwater Sensor Networks
## 3 Localization Algorithm
### The State of the Nodes
#### Hybrid  
In this part, we still first consider the active messaging properties based on the hybrid state. In [59], a 3D Underwater Localization (3 DUL) algorithm is shown. Three anchor nodes float at the surface. It is a distributed and iterative algorithm and does not require time synchronization. Three surfaces' buoys are employed for localization initially. The 3 DUL can be described in two steps. In the first step, the sensor node whose location is unknown determines the distances to neighboring anchors. In the second step, the anchor is projected into the horizontal level for which the unknown sensor node is located by utilizing the pairwise distances and depth information. After the location of the sensor node is known, it becomes an anchor and helps to locate other nodes. Then, we discuss the silent messaging properties based on the hybrid state. In [60], the authors present a silent positioning method. Both a pressure sensor and an accelerometer are equipped with an each sensor. Hence, the purpose of using a pressure sensor is the same as with other algorithms to measure the depth estimation. The accelerometer is used for sensor orientation estimation. In addition,the EKF is employed to overcome the state estimation problem. In [61], a range-free localization scheme is proposed. This scheme first finds two estimated locations of the sensor node by geometry. Finally, one estimated location is selected as the final results. The sensor node locates itself without any help from the other nodes and consists of two steps, namely, selecting three beacon points and estimating the location of a unknown node. In the first steps, the sensor node within the transmission range can receive the beacons from the mobile beacon, and the received beacons are projected in the plane parallel to where the sensor node is located. The first received beacon is selected as a beacon point, and the last received beacon within a predefined time is selected at another point beacon. Hence, this scheme needs at least three beacon points. In the second phase, three beacon points are not exactly on the projected transmission circle of the sensor node. Considered that the beacon distance is \(d\), and the projected transmission range of the sensor node is \(r^{\prime}\), then distance points are located between the distance \(r^{\prime}-d\) and \(r^{\prime}\) from the sensor node. The authors use the middle value of the range, i.e., \(r^{\prime}-d/2\), to minimize the error of the estimated distance. Hence, solving the following equations can obtain the estimation location of the sensor node:  
\[\left\{ \begin{array}{l}\{(x-x_{1})^{2}+(y-y_{1})^{2}=(r^{\prime}-d/2)^{2},\\ \{(x-x_{2})^{2}+(y-y_{2})^{2}=(r^{\prime}-d/2)^{2},\\ \{(x-x_{3})^{2}+(y-y_{3})^{2}=(r^{\prime}-d/2)^{2},\end{array} \right. \tag{5}\]  
where \((x,y)\) are the coordinates of the sensor node, and \((x_{i},y_{i})\) are the coordinates of the beacon \(B_{i}\). Two intersection points of the two equations can be obtained and described as \(P_{m}\) and \(Q_{m}\). Hence, the third equation is needed to determine which ones are the true coordinates of the sensor node. If \(||B_{3}-P_{m}||-(r^{\prime}-d/2)\ |<|\ ||B_{3}-Q_{m}||-(r^{\prime}-d/2)|\) is satisfied, the location \(P_{m}\) is used for the estimation of the sensor node; otherwise, select the \(Q_{m}\). In this subsection, we have discussed the state of nodes and the difference between the stationary UWSNs, mobile UWSNs, and hybrid UWSNs. We use some papers to show the different characteristics of the three kinds of UWSNs. Furthermore, we summarize these papers that use the state of nodes to achieve the positioning in Table 5. We mainly compare the coverage, localization time, accuracy, computational complexity, and energy consumption. According to the following table, the reader can choose the suitable algorithm for doing some application or doing some improvement.