# A Mobile Anchor Node Assisted RSSI Localization Scheme in Underwater Wireless Sensor Networks
## 4 Simulation
### Simulation Results and Discussion
#### 4.2.2 The Error of a Node Projection on the Trajectory  
The PI scheme, the RuDT scheme and the scheme proposed in this paper must first determine the projection position of the node on the trajectory. Therefore, we first compare the error of one node projection of different schemes. As shown in Figure 12, the actual projected position of the node on the trajectory is the position corresponding to the highest point of the curve without noise (Blue curve). The PI scheme selects the position with the largest value on the RSSI curve with noise (Magenta curve with diamond) as the node projection. The DuRT scheme uses a polynomial fitting method to fit an increased curve (Green dotted line) to the left part and a decreased curve (Light blue dotted line with circles) to the right part. The position corresponding to the intersection of the increased curve and the decreased curve is the node projection determined by the DuRT scheme. The scheme in this paper uses SVR to fit a curve and select the position corresponding to the maximum value of this curve as the node projection. The actual projection position is 141. The projection positions determined by the PI scheme, the DURT scheme, and the scheme in this paper are 130, 155, and 140, respectively. The scheme in this paper has the least error of the three schemes.  
As shown in Figure 13, we compare the mean error of node projections for 100 nodes at different broadcast point intervals in three schemes. The mean error of the three schemes increases as the broadcast point interval increases. In the case of the same broadcast point interval, the mean error of the three schemes is sorted from biggest to smallest: the PI scheme, the RuDT scheme, and the scheme proposed in this paper. Due to the influence of noise, the broadcast position with the largest RSSI value is often not the closest broadcast position to the actual projection, as shown in Figure 13. Since the PI scheme only selects the broadcast position with the largest RSSI value, the PI scheme has a large error in determining the node projection. Although the polynomial curve fitting method can fit all RSSI values, the fitting effect is poor. Thus, the DuRT scheme fits the RSSI values on the left and right sides separately. When the left polynomial and the right polynomial have an intersection between the broadcast position with the largest RSSI value and the broadcast position with the second largest RSSI value, the DuRT scheme selects this intersection as the node projection. However, this intersection can only be controlled between two broadcast locations, and it is not possible to control the intersection to be close to the actual projection. Thus, the error of the DuRT scheme is smaller than the error of the PI method, but it is still very large. The scheme in this paper solves the noise problem and fits a good curve to all RSSI values. Therefore, our scheme is an effective scheme for reducing the error of the determined node projection.  
Figure 12: Determining the projection of one node on the trajectory by three schemes (\(\Delta L=10\) m).