# A Mobility-Assisted Localization Algorithm for Three-Dimensional Large-Scale UWSNs
## 4 Mobility-Assisted Localization Scheme  
### Phase I  
In this section, a novel mobility-assisted localization scheme with time-synchronization-free for 3D large-scale UWSNs is proposed. Since it is assumed that all sensor nodes are equipped with UPS, the 3D spatial localization of sensor nodes can be transformed into 2D planar localization. If an ordinary sensor node obtains three projected distances from different anchor nodes, it can begin to estimate its position. Some underwater localization papers estimate the location of sensor nodes by using the LS method. It is assumed that the ordinary sensor node receives the projection distances of \(n\) different anchor nodes, because the depth information can be obtained by UPS. Hence, Equation (16) can be established. By the least square estimation method, Equation (16) can be converted into the form \(AX=b\), where \(AX\) is shown in Equation (17), and \(b\) is shown in Equation (18). The planar coordinates of ordinary sensor nodes can be estimated, as shown in Equation (19). \[AX=\left[\begin{array}{cc}2\left(X_{b_{n}}-X_{b_{  
of ordinary sensor nodes in Phase I, cut costs, and expand the valid area covered by anchor nodes. Mobile anchor nodes need to be deployed effectively.  
Since the sensor node is configured with UPS, the sensor node can locate itself by receiving messages from three different non-collinear anchor nodes. As shown in Figure 7, the shaded part is the intersection region of three non-collinear anchor nodes, and the sensor nodes in this region can locate themselves. This shaded area can be referred to as a valid area. In general, however, the valid area of this arrangement is small. When three non-collinear anchor nodes are close to each other, the valid area can be approximated to the communication area of a single anchor node. However, if the distance between anchor nodes is too close, its function is equivalent to that of a single anchor node, which is not conducive to the localization of sensor nodes.  
In this paper, it is assumed that the length and width of the monitoring area are \(l\). The communication diameter of the mobile anchor node is \(R\). Then, the monitoring area plane is divided into \(m^{2}\) region grids on average; \(m\) is shown in Equation (20).  
\[m=\left\lceil\frac{l}{R}\right\rceil \tag{20}\]  
To facilitate the elaboration of ideas, the anchor node deployment is divided into two layers, as shown in Figure 8. In the first layer, to enable most sensor nodes in the monitoring area to receive messages from anchor nodes at least once, anchor nodes are deployed at the center of each uniform grid and the intersections of the grids. Moreover, the number of anchor nodes is \(m^{2}+\left(m-1\right)^{2}\). According to the analysis in Figure 7, to make most sensor nodes receive enough localization information from anchor nodes and weaken the collinear problem of anchor nodes, in the second layer, three anchor nodes are placed in each region grid, to form an equilateral triangle. \[l_{p}=k\frac{R}{2} \tag{21}\]  
The centroid of the triangle coincides with the center of the circle, and the distance between the anchor node and the center of the area is the same. Its distance is \(l_{p}\), which can be adjusted by \(k\in(0,1]\). Therefore, the total number of mobile anchor nodes arranged in the monitoring area is \(5m^{2}-2m+1\)  
Figure 8: Deployment of anchor nodes. Figure 7: Anchor node coverage analysis. The number of anchor nodes mainly depends on the communication radius of the node and the size of the monitoring area. When an ordinary sensor node obtains sufficient localization information, it can begin to estimate its position. In this paper, the optimal solution of the estimated position of sensor nodes is obtained by minimizing the localization error. It facilitates the solution of sensor node confidence values in Phase II.