# WiFi Positioning in 3 GPP Indoor Office with Modified Particle Swarm Optimization
## 5 Simulation Results
In addition, the black triangle is the user's final position obtained by performing the PSO algorithm. In other words, this is the position of the particle with the smallest value by evaluating the fitness of each particle after the PSO algorithm is ended. That position can be used as the UE's final estimated position and compared to the UE's actual location. The simulation is performed a total of 10,000 times, and the position of the UE is changed randomly during iterations. The final positioning error is determined by averaging all the values from the 10,000 different locations of the UE. Figure 8 shows the result of comparing the proposed scheme with the existing positioning algorithm. To perform the performance comparison, positioning errors are compared while changing the distance between SPs. The PSO algorithm ends when the maximum number of iterations T is reached. In Figure 8, WFM is a result of estimating the location of the UE through a WFM algorithm. The cosine similarity (CS) is a result of estimating the location of the UE through a CS scheme [29]. MLE-PSO is the result of estimating the location of the UE through the combination of MLE and a PSO scheme [19]. Finally, the range-limited (RL)-PSO executes the PSO algorithm within a limited region. The simulation result is the result of measuring the positioning error while changing the distance between the SPs. The WFM algorithm  
Figure 6: Result of four SPs by WFM. is the result of determining the final location of the UE based on the closeness weight. It can be seen that the smaller the spacing between the SPs, the higher the accuracy achieved. However, as can be seen in Table 2, the number of SPs increases rapidly as the distance between SPs decreases. This causes a complexity problem when building a database in the fingerprinting scheme. The CS is the result of estimating the final position of the UE through a CS scheme. The CS is a method of calculating the similarity between the fingerprinting database of SPs measured at each AP and the RSSI of the real user. After that, the location of the SP with the highest similarity to the actual user is mapped to the user's estimated location. As can be seen from Figure 8, the positioning error increases as the distance between SPs increases. Additionally, it is confirmed that the result obtained through fuzzy matching is the same when the four SPs adjacent to the actual user are derived based on the CS. The MLE-PSO is a method of estimating the position of the UE through MLE and limiting the initial region of the PSO algorithm based on a circle centered on the estimated location. It can be seen that this scheme also shows a constant positioning error irrespective of the distance between the SPs in the same way as PSO only. In addition, it can be confirmed that the MLE-PSO scheme achieves higher accuracy when the distance between the SPs is increased compared to the scheme that depends on the distance between the SPs. However, it is difficult to allow an error of about 4 m in an indoor environment. To summarize the previous information, the positioning accuracy and the number of SPs are in a tradeoff relationship. Therefore, research is needed to improve the indoor positioning accuracy by fusing several single algorithms, as in the method proposed in this paper. As can be seen in Figure 8, the RL-PSO scheme proposed in this paper achieves the highest positioning accuracy. With the RL-PSO, as mentioned above, if the initial search region of the PSO is limited, faster convergence speed and higher positioning accuracy can be achieved. This result was verified through simulation. Furthermore, we confirmed that we achieved high positioning accuracy performance when using a single algorithm by fusing it rather than using a single algorithm such as WFM or CS. Figure 7: Result of final SP by using PSO. Table 4 shows the processing time required to achieve a positioning error of 1 m through each scheme.