# Local Batch Normalization-Aided CNN Model for RSSI-Based Fingerprint Indoor Positioning
## 4 Numerical Results
### Simulation Results  
The simulation was conducted using Jupyter Notebook (version 6.5.3) as the software platform, with Python version 3.11.7 (released on 4 December 2023) and TensorFlow version 2.14.0 (released on 27 September 2023). Previous research has established the effectiveness of grouping different techniques across various layers in CNNs. For example, [PERSON] et al. (2017)  
Figure 7: Fingerprint technique. used the CIFAR-10 and CIFAR-100 datasets and evaluated the performance of different regularization techniques (L1) and normalization methods (BN, LN, and denormalization (DN)) without modifying the network's layer structure [33]. [PERSON] et al. (2018) compared activation functions in a deep convolutional neural network (DC-NN) based on the MNIST dataset and found that the ReLU function provided the best classification performance [34]. [PERSON] et al. (2020) demonstrated that varying the type or position of activation functions within the same CNN architecture leads to different outcomes, helping to identify optimal configurations [35]. In their subsequent 2023 study, they further explored the stochastic selection of activation layers [36]. Building on these insights, we conducted a comparative analysis of BN, LN, and LBN, which were applied to the 1 st, 2 nd, and 3 rd layers of a CNN model. To systematically evaluate the contribution of each normalization method, we performed an ablation study, where different normalization techniques (BN, LN, and LBN) were incorporated separately into the CNN model for comparison. The simulation was divided into three parts, each containing an experimental section: CNN + BN (first experimental section), CNN + LN (second experimental section), and CNN + LBN (third experimental section). A separate baseline evaluation using only the CNN model was conducted for comparative purposes. For each experimental section, both the accuracy and loss metrics were evaluated. This approach generated three distinct accuracy values and three corresponding loss values for each part of the simulation. In total, each part of the experiment was characterized by six evaluation components. These results are shown in Tables 4 and 5. The simulation demonstrated that the CNN model integrated with BN achieved a maximum accuracy of 93.21%. The model incorporating LN reached 91.83%, and the model incorporating LBN achieved a higher accuracy of 94.69%. In terms of simulation results, among the four models in Layer 1 (Table 5), the CNN + LBN model in Layer 1 (Table 5) exhibited the highest test accuracy and the lowest loss. Initially, the loss values of the CNN + LBN, CNN + LN, CNN + BN, and CNN models were 2.20, 2.27, 3.07, and 2.24, respectively. After 200 epochs of training, these values decreased to 0.14, 0.22, 0.18, and 0.25. The decline in loss indicated the continuous improvement of the models' performance over the training process. The highest accuracy of each model, used as the benchmark in the final simulation results, was as follows: CNN + LBN reached a maximum accuracy of 94.69% after 195 epochs (loss = 0.14), CNN + LN reached a \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Model Name**} \\ \hline Layer 1 & CNN + BN & CNN + LN & CNN + LBN \\ Layer 2 & CNN & CNN + BN & CNN + LN & CNN + LBN \\ Layer 3 & & CNN + BN & CNN + LN & CNN + LBN \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Classification of the simulation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Accuracy (MAX)** & **CNN** & **CNN + BN** & **CNN + LN** & **CNN + LBN** \\ \hline Layer 1 & & 0.9321 & 0.9183 & 0.9469 \\ Layer 2 & 0.9054 & 0.9060 & 0.9055 & 0.9180 \\ Layer 3 & & 0.9291 & 0.9104 & 0.9365 \\ \hline Loss (MIN) & CNN & CNN + BN & CNN + LN & CNN + LBN \\ \hline Layer 1 & & 0.1898 & 0.2214 & 0.1489 \\ Layer 2 & 0.2589 & 0.2530 & 0.2573 & 0.2252 \\ Layer 3 & & 0.1943 & 0.2301 & 0.1740 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the simulation.