## 4 Experiments and Results Analysis
### Comparison with Similar Location Methods  
To evaluate the performance of the IPSOGWO-MSVR localization algorithm, we compare it with three methods. These methods are GWO-SVR, GWO-MSVR, and a hybrid optimization algorithm without improvements, which we refer to as normal-PSOGWO-MSVR. The preset parameters for the different methods are consistent with IPSOGWO-MSVR, as Section 3.3.3 describes. After 250 iterations of training, Figure 10 illustrates the RMSE trends of the four methods in the two scenarios.  
As Figure 10 shows, the RMSEs of the GWO-SVR and GWO-MSVR algorithms are relatively high in both scenarios after the iterations have converged. Specifically, their  
Figure 10: Number of iterations and RMSE. (**a**) Scenario 1; (**b**) Scenario 2.  
Figure 9: Comparison of results of different dimension reduction algorithms.  
values are 0.747, 0.613, and 0.654, 0.592 for the two scenarios, respectively. This indicates that whether it is SVR or MSVR, the efficiency of using a single algorithm for parameter optimization is low. Moreover, it is prone to falling into local optima and cannot escape. However, the RMSEs of the two algorithms reveal that MSVR's predictions are superior to SVR's. A smaller RMSE indicates that the predicted target points by the algorithm are closer to the actual values. This also demonstrates that using MSVR in place of SVR as a localization algorithm is feasible. From the convergence curves in both scenarios, the post-convergence RMSEs of IPSOGWO-MSVR and normal-PSOGWO-MSVR algorithms are notably lower than those utilizing single optimization methods. Specifically, they are 0.232, 0.43, and 0.377, 0.508, respectively. However, the local search capability of normal-PSOGWO-MSVR is not as good as that of IPSOGWO-MSVR, with the latter being able to escape local optima to achieve a smaller RMSE. It can be concluded from the figure that IPSOGWO-MSVR has stronger optimization capabilities. Table 3 shows the optimal parameter combinations of the four models in the two scenarios.  
The optimal hyperparameter combinations determined by each of the four methods were applied to the model training, and then the data collected during the localization phase were pre-processed in the same way before being input into the model to obtain the final prediction results, as Figures 11 and 12 show.  
Figures 11 and 12 show that the improved PSOGWO-MSVR algorithm outperforms the other three in both scenarios. In Scenario 1, the prediction results of most of the test points are close to the real position and evenly distributed. In Scenario 2, the average RMSE of the 15 test points for the four algorithms are as follows: 2.05 m, 1.99 m, 1.62 m, and 1.12 m. Notably, the RMSE of the improved PSOGWO-MSVR remains below 1.5 m. It can be seen that the localization model constructed by Multi-Output Support Vector Regression is more accurate relative to the single-output regression model. This is because the multi-output model considers the intrinsic connection between output variables. It treats errors holistically during training, achieving an optimal fit for each component. In contrast, the single-output model handles each component's output separately, amplifying errors upon combination and reducing localization accuracy.