## 5 Conclusions  
This paper illustrates a QPSO algorithm for an indoor location system based on hybrid raw RSS signals, namely those from WiFi and WSN sources. The proposed system considered the possibility of reducing the positioning error by performing a regular tessellation of the research area in which the raw signals were acquired. Each QPSO individual was identified as a vector of four values containing the tile size and offset, which unambiguously determined a tessellation geometry. A Multilayer Perceptron network was developed as a tool to heuristically predict the positioning error for each QPSO individual. The architecture of the MLP, as well as the initial raw signal weighting, were kept in agreement with our previous research, thus allowing a faster network setup and positioning error reduction. The final results of the optimization process allowed us to identify an optimal geometrical configuration of the regular surface tessellation in which the positioning error showed a marked reduction compared to our previous research using the same set of data. We achieved a final localization accuracy of 0.611 m, representing an improvement of at least 16% compared to our previous best results using the same dataset. This value also marks an improvement of at least 50% over our initial published analysis of these data. In addition to determining the overall positioning accuracy, a raw analysis of the spatial source of error was performed in order to identify the contribution along the horizontal and vertical directions. For every QPSO generation, in the horizontal direction, the error component was larger by roughly a factor of two compared to the vertical component, thus providing a large amount of the positioning error. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & \
\begin{tabular}{c} **Chosen Approach and** \\ **Implementation** \\ \end{tabular} &
\begin{tabular}{c} **Research Area and** \\ **Anchor Points (AP)** \\ \end{tabular} & **Error** \\ \hline [PERSON] et al. [40] & Source selection, WiFi + Bluetooth & 20 m \(\times\) 21 m, 26 AP & \textgreater{}4 m \\ [PERSON] [26] & K-NN modeling, WiFi + RSS & 15 m \(\times\) 40 m, 100 AP & 1.70 m \\ [PERSON]. [PERSON] et al. [41] & Particle filter, WiFi + RFID & 25 m \(\times\) 12 m, 80 AP & 1.60 m \\ [PERSON] et al. [28] & Optimization, IMU + WLAN & 90 m path, 113 AP & 1.48 m \\ [PERSON] et al. (same dataset) [33] & MLP modeling, WiFi + WSN & 6 m \(\times\) 24 m, 96 AP & 1.22 m \\ [PERSON] et al. (same dataset) [27] & Tessellation, WiFi + WSN & 6 m \(\times\) 24 m, 96 AP & 1.01 m \\ [PERSON] et al. (same dataset) [32] & Optimization, WiFi + WSN & 6 m \(\times\) 24 m, 96 AP & 0.725 m \\ This Research (same dataset) & Variable tessellation, WiFi + WSN & 6 m \(\times\) 24 m, 96 AP & 0.611 m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of our obtained results with previously published research. The goal of any indoor positioning algorithm consists of reducing the localization error in real-life scenarios in which randomly set wireless receivers are capable of precisely inferring their spatial coordinates. To this date, we have analyzed hybrid approaches with two sources, namely WiFi and WSN, and several algorithms, i.e., signal weighing with smooth research space and variable tessellation in this work. These results encourage further investigation, and in future work, all the developed approaches may be joined together, as well as including further techniques of spatial data analysis or an improved MLP training process that takes into account the different directional error contributions. Conceptualization, E.S., M.A.A.R., Z.F., S.A., and M.A. ; Data curation, M.A.A.R., Z.F., and M.A. ; Formal analysis, E.S. and Z.F. ; Funding acquisition, S.A. and M.A. ; Investigation, M.A.A.R., S.A., and M.A. ; Methodology, E.S. and M.A.A.R. ; Resources, M.A.A.R., Z.F., and M.A. ; Software, E.S. ; Supervision, M.A.A.R. ; Validation, M.A.A.R., Z.F., S.A., and M.A. ; Visualization, E.S. and M.A. ; Writing--original draft, E.S.