# Local Batch Normalization-Aided CNN Model for RSSI-Based Fingerprint Indoor Positioning
## 4 Numerical Results
### Experimental Results  
This section evaluates four methods for the CNN-based positioning system: Method 1 employs the original CNN model, Method 2 integrates BN into the CNN model, Method 3 integrates LN into the CNN model, and Method 4 incorporates LBN into the CNN model. The performance of these methods was validated through online experiments. During testing, a mobile device captured real-time RSSI information, including MAC addresses, from various APs at different RPs. These data were transmitted to a positioning server, where it was processed by a classifier model to predict the device's position. The experimental setup involved moving the mobile device to each RP within a predefined environment (from RP1 to RP74) and collecting data five times at each RP. The classifier model on the server analyzed the collected data to calculate localization accuracy. The interval between consecutive RPs in this study is 2 m, resulting in a positioning precision of 4 m. To evaluate simulation outcomes, three different margins (0, 1, and 2) were applied. A margin of 0 indicates that the decision made at a specific RP is completely accurate. A margin of 1 means the positioning decision falls within the range of RP \(-\) 1 to RP + 1, while a margin of 2 implies the decision lies within RP \(-\) 2 to RP + 2. Since the database contains 74 RPs and n tests were conducted at each RP, the total number of samples is a multiple of 74. The accuracy probability is calculated using the following formula [9]:  
\[Probability\ of\ accuracy\ [\%]=\frac{success\ count}{total\ samples}\times 100 \tag{12}\]  
The online test results are summarized in Table 6. The real-time localization accuracy of the CNN model was 87.84%, slightly lower than its simulated accuracy of 90.54% (Table 5). Similarly, the CNN + BN model achieved a real-time accuracy of 91.89%, which is lower than its simulated result of 93.21%. The CNN + LN model achieved a real-time accuracy of 89.73%, which is lower than its simulated result of 91.83%. The CNN + LBN model recorded the highest real-time accuracy of 92.97%, though it still fell short of its simulated performance of 94.69%. Figure 8: Principal component analysis (PCA) visualizations: (**a**) CNN baseline without normalization; (**b**) with BN applied in the CNN; (**c**) with LN applied in the CNN; (**d**) with LBN applied in the CNN. Blue points represent training data, and orange points represent test data. In the WiFi fingerprint-based indoor positioning experiment using RSSI signals, additional error metrics were calculated for all models in Table 7. The CNN model showed a mean error of 2.21 m, a variance of 12 m\({}^{2}\), and a standard deviation of 3.46 m. By incorporating BN, the CNN + BN model significantly improved these results. It achieved a mean error of 1.48 m, reducing the error by 0.73 m. Its variance was reduced to 4.3 m\({}^{2}\) (a decrease of 7.7 m\({}^{2}\)), and the standard deviation dropped to 2.07 m (a reduction of 1.39 m). After the integration of LN, the model exhibited a mean error of 2.07 m, a variance of 7.61 m\({}^{2}\), and a standard deviation of 2.75 m. While LN improved the variance and standard deviation compared to the baseline CNN model, it was less effective than BN in reducing the mean error. The CNN + LBN model demonstrated even greater improvements over both the CNN and CNN + BN models. It achieved a mean error of 1.27 m, reducing the error by 0.94 m compared to the CNN model. Its variance decreased to 3.97 m\({}^{2}\), an improvement of 8.03 m\({}^{2}\), while the standard deviation was reduced to 1.99 m, representing a decrease of 1.47 m. These results clearly indicate that the LBN approach is more effective than BN in processing RSSI data for fingerprint-based positioning systems.