## 5 Performance Evaluation
### Simulation Experiments
#### 5.1.1 Regular Deployment  
In this group of experiments, as shown in Figure 5, 405, 487 and 525 nodes are regularly deployed in the 600 \(\times\) 600 C-shaped, Z-shaped and S-shaped areas. Experiments select 30 to 60 nodes as anchor nodes. First, we examine the final localization results of the two ML-RELM methods (the number of anchor nodes in Figure 5 is 40), where the circle represents the unknown node, and the square represents the anchor node. Then, as shown in the Figure 5, we use a straight line to connect the real coordinates of the unknown node and its estimated coordinates. The longer the line, the greater the estimation error of nodes. It is obvious to observe from Figure 6 that the DV-hop method uses fixed hop-counts vs distances coefficients, and when there is an obstacle, the hop-count and the distance may deviate on converting. Although the PDM method can solve hop-distance deviation to a certain extent, it cannot deal with significantly different scales. For LSVR, the optimization of multiple parameters easily results in over-fitting (unknown nodes estimate an unknown trend to a curve). Nevertheless, estimation accuracy from the proposed ML-RELM is higher than from other localization methods. Figure 5: The regular distribution of nodes. Figure 6: The localization results of regularly distributed nodes. For each deployment area in the regular deployment network, Figure 7 shows the average RMS value for 50 experiments with 40 anchor nodes. The experimental results illustrated in Figure 7 show that the classical multi-hop localization method in the C-shaped, Z-shaped and S-shaped regions has low DV-hop performance, and the RMS values are 214.22, 169.75 and 246.65, respectively. The PDM and LSVR methods have better ability to obtain the relationship between the hop-counts and distances, so their performance is improved by 80.9% and 79.2% compared with the DV-hop method. ML-RELM has improved the prediction and fitting ability by using ELM as the core algorithm, so the ML-RELM localization performance is improved by 21.8% and 28.3% respectively compared with the PDM and LSVR methods. The ELM machine is very efficient, which only needs to calculate the weights (the computation complexity is \(O\big{(}\min\big{(}L^{3},N^{3}\big{)}\big{)}\)). So the ELM is often in a very short period of time able to complete the operation. Table 1 shows that the running time of our proposed ML-RELM algorithm is compared with that of multiple multi-hop distributed localization algorithms in a variety of regular deployment environments of 40 anchor nodes. Clearly, ML-RELM is proposed to be more efficient than LSVR, DV-hop and PDM. Bars in Figure 8 represent RMS values and standard deviations of the four algorithms varying with the number of anchor nodes in the three regular deployment areas of the C, Z, and S shapes. It is easy to see that DV-hop is not suited to non-convex environment (there are obstacles in the network) localization. We also notice that the LSVR algorithm is superior to PDM when the number of anchor nodes is less than 40, and the PDM algorithm is better than LSVR. This is due to the increase in the number of anchor nodes, resulting in the over-fitting, making the performance of LSVR degraded (shown in Figure 6).