## 6 Simulations
### Results and Discussions
#### 6.3.2 Numerical Results of Semi-Supervised Learning-Based Method  
In this simulation, we conducted tests with a very small sample size, specifically using 3000 or fewer samples to evaluate the performance. On the basis of supervised learning, we first verified the effectiveness of the proposed data augmentation methods. From Figure 7, it can be observed from four performance curves with different numbers of labels that the number of samples is positively correlated with the positioning accuracy. Additionally, from the comparison of Figure 7a-c, it is clear that both proposed data augmentation methods can effectively improve the positioning accuracy for all test samples in supervised learning (SL) methods, with the most significant improvement observed for sample sizes ranging from 500 to 2000. This demonstrates that our proposed data augmentation methods can adapt to scenarios with very few labeled data and meet practical needs. In terms of the effectiveness of the two data augmentation methods, amplitude scaling is significantly better than temporal shifting when the number of labels is 500, and it also performs slightly better than the temporal shifting for other sample sizes. To judge whether the unlabeled data are effective for a performance improvement in DSSL methods, we obtain the positioning accuracy of AMT to compare with the performance of purely supervised learning using a few labeled data to train the model. After verifying the effectiveness of two data augmentation methods in the SL method, we conduct the AMT model by using the two proposed augmentation methods. By comparing Figure 8a,b to Figure 7b,c), we observe that the performance of AMT significantly improves in four cases compared to purely supervised learning methods, while it applies two proposed data augmentation techniques. Additionally, similar to purely supervised learning, the use of the random amplitude scaling augmentation method attains better performances than random temporal shifting in four cases. Furthermore, the AMT method in the case of small sample sizes demonstrates more significant improvement, specifically when the number of labeled samples is less than 2000. A visualization example to show the performance of AMT using 1000 labeled samples is present in Figure 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method for Indoor Positioning**} & \multicolumn{3}{c}{**CDF Percentile of Position Errors (m)**} & \multirow{2}{*}{**ME (m)**} \\ \cline{2-2} \cline{4-6}  & **50\%** & **67\%** & **80\%** & **90\%** \\ \hline CIR-based fingerprint positioning & 0.28 & 0.35 & 0.45 & 0.54 & 0.31 \\ TOA-based fingerprint positioning & 0.36 & 0.46 & 0.57 & 0.69 & 0.40 \\ TDOA-based fingerprint positioning & 0.38 & 0.49 & 0.60 & 0.74 & 0.41 \\ RSS-based fingerprint positioning & 0.30 & 0.41 & 0.52 & 0.68 & 0.38 \\ CHAN & 10.35 & 16.01 & 22.08 & 31.14 & 14.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of position accuracy based on supervised learning Furthermore, we verify the effectiveness of the proposed AMT model by comparing it with several reference algorithms under 1000 labeled samples. In order to facilitate better horizontal comparison, we will use some DSSL methods that have similar training frameworks and steps to AMT as benchmark algorithms. One reference algorithm is the \(\Pi\) Model and the other is the Temporal Ensembling. Both two algorithms are advanced consistency regularization methods, and the same data augmentations are used for the three approaches. In addition, we also compare the performance of the pseudo label to verify the effectiveness of our method because it is widely used for positioning. As numerical results are shown in Table 4, we can observe that the three consistency regularization methods significantly outperform the pseudo label in positioning accuracy. Moreover, among the three consistency regularization methods, the AMT model achieves the highest accuracy. Figure 8: Performance of AMT with different augmentations.