## 3 Experimental Results and Analysis
### Simulation of Positioning Errors  
When \(SNR=\) 10 dB, the localization results of the IRS-RFL algorithm in this study are shown in Figure 6, where the asterisk indicates the estimated location of the point to be located, and the hollow point indicates the real location of the point to be located. Figure 5: Comparison of computational complexity between IRS-URFL algorithm and IRS-RFL algorithm. Figure 6: Schematic of the localization result of the IRS-RFL algorithm. As shown in Figure 6, the point to be located that was estimated by the proposed IRS-RFL algorithm was similar to or overlapped with most of the real locations. This indicated the highly accurate localization results of the proposed IRS-RFL algorithm. Positioning error analysis plots of the traditional fingerprint localization (traditional RSS) algorithm [49; 50; 51], the intelligent reflective surface for unreconstructed fingerprint localization (IRS-URFL) algorithm, and IRS-RFL algorithm are shown in Figure 7.  
In Figure 7, the horizontal coordinate, vertical coordinate, blue curve, red curve, and yellow curve indicate the SNR (dB), positioning error (m), positioning error of the traditional RSS algorithm, positioning error of the IRS-RFL algorithm, and positioning error of the IRS-URFL algorithm, respectively. The results show that at \(SNR=5\) dB, the error of the traditional RSS algorithm is 3.35 m, the error of the IRS-RFL algorithm is 0.97 m, and the error of the IRS-URFL algorithm is 0.92 m; at \(SNR=25\) dB, the error of the traditional RSS algorithm is 1.41 m, the error of the IRS-RFL algorithm is 0.60 m, the error of the IRS-URFL algorithm is 0.92 m, and the IRS-URFL algorithm has an error of 0.57 m. All three localization algorithms show better localization results as the SNR increases. Among these three algorithms, the IRS-URFL algorithm has the highest positioning accuracy and the smallest positioning error, and the IRS-RFL algorithm has a higher positioning accuracy than the traditional RSS algorithm. First of all, both the IRS-URFL algorithm and IRS-RFL algorithm use APEM fingerprints; this type of fingerprint contains more information compared to RSS fingerprints, and the correspondence between this information and spatial location is stronger, which is conducive to improving the system's localization accuracy, so the localization error of the traditional RSS algorithm is higher than the IRS-URFL algorithm and IRS-RFL algorithm's positioning error. In addition, because the IRS-RFL algorithm uses the LMafit reconstruction algorithm, there is a certain error between the reconstructed fingerprint database and the fingerprint database that is directly collected without reconstruction; therefore, the IRS-RFL algorithm has a larger localization error than the IRS-URFL algorithm compared to the IRS-RFL algorithm. The localization errors for different numbers of IRS and SNRs are shown in Figure 8.  
Figure 7: Positioning error of different positioning methods. As shown in Figure 8, the X, Y, and Z coordinates indicate the number of IRSs, SNRs (dB), and localization errors (m), respectively. The figure shows that with an increase in the SNR number of IRSs, the localization error of the IRS-RFL algorithm gradually decreases. For IRS \(M=6\), the localization error was less than 1 m, and it decreased gradually with an increase in SNR; when \(SNR=15\), the localization error decreased gradually with an increase in IRS. This shows that both SNR and the number of IRSs have a highly significant effect on the localization accuracy. In the wireless communication system, SNR indicates the power ratio of the received signal to the noise, and the larger the SNR, the stronger the useful signal in the received signal and the smaller the interference generated by the noise. In this case, the fingerprint APEM will be inaccurate, and the final localization error of the IRS-RFL algorithm in this study will be larger. In contrast, the smaller the SNR, the less useful the signal received.