## 5 Results
### Accuracy Results
GRU achieves an average mean absolute error of 0.310 m and a root mean square error of 0.427 m, while MLP demonstrates slightly better performance in terms of root mean square error at 0.393 m. The worst model in this scenario is BPNN, with an average mean absolute error of 0.387 m and a root mean square error of 0.492 m.  
Figure 16: ML results for the second scenario: (**a**) MAE, (**b**) RMSE. Figure 15: ML results for the first scenario: (**a**) MAE, (**b**) RMSE. For the third scenario, GRU and MLP again perform best, with GRU achieving an average mean absolute error of 0.376 m and a root mean square error of 0.499 m, while MLP records an average mean absolute error of 0.377 m and a root mean square error of 0.475 m. The worst model is BPNN, which has an average mean absolute error of 0.447 m and a root mean square error of 0.569 m. Overall, the localization accuracy for the third scenario was not very high because the number of points obtained from RSSI values in the first and second scenarios is significantly lower than in the third. Consequently, in the third scenario, where the mobile robot follows a sinusoidal trajectory with high amplitude and frequency, odometry errors accumulate faster, leading to a noticeable decrease in localization accuracy. It is also evident that models incorporating the Kalman filter perform worse than those without the filter. Figure 18 presents the cumulative distribution of absolute errors (AE) by distance for various models across different scenarios. The left column shows the CDF results for the first, second, and third test scenarios, respectively. In all scenarios, the GRU and MLP models exhibit lower absolute error values, especially at shorter distances. However, when applying the EKF (shown in the right column), the absolute error increases slightly for each scenario, indicating that EKF performs poorly in this context. The MLP model shows a pattern of increasing AE across scenarios, with values of 0.396 m, 0.546 m, and 0.621 m for the first, second, and third scenarios, respectively. The kNN model achieves competitive results without EKF, with an AE of 0.390 m for the first scenario, 0.587 m for the second, and 0.640 m for the third. Other models such as RF and SVR follow this trend, where the average AE remains lower in the absence of EKF. For example, RF achieves AE values of 0.402 m, 0.553 m, and 0.641 m without EKF, but slightly higher values with the filter applied. The RNN and BPNN models also reflect these patterns. Without the filter, RNN achieves AE values of 0.441 m, 0.557 m, and 0.639 m across the three scenarios, showing a moderate increase as the trajectory complexity increases. BPNN, however, exhibits the highest errors among the tested models, with AE values of 0.467 m, 0.598 m, and 0.693 m without EKF. These results indicate the relatively weaker capabilities of BPNN compared to GRU, MLP, and kNN. The cumulative distribution of localization errors (CDF) highlights that GRU and MLP maintain a significant proportion of errors below 0.5 m for shorter trajectories, demonstrating their robustness in simpler scenarios. However, as trajectory complexity increases, the AE and error spread increase for all models. This is because, in the first and second scenarios, the number of points derived from the RSSI values is significantly lower than in the third. Consequently, in the third scenario, where the mobile robot follows a sinusoidal trajectory with high amplitude and frequency, the odometry errors accumulate, leading to a noticeable decrease in localization accuracy. Figure 17: ML results for the third scenario: (**a**) MAE, (**b**) RMSE. Overall, GRU and MLP stand out as the most robust models in all scenarios, achieving the lowest AE values. This indicates their suitability for trajectory prediction tasks, especially in cases involving moderate trajectory complexity.