# A Novel Localization Technique Using Luminous Flux
## 5 Simulation Setup, Results, and Discussion
The resultant matrix provides a solution that reduces the sum of squares of the residuals or errors. We collected the residuals in a vector that was used to compute the cumulative distributive function of the Student's t-distribution. The residuals or error were used to calculate the RMSE for positional changes. The RMS delay spread parameter is the only metric that relates to positional accuracy based on the impulse response. The spatial coordinates are Cartesian products, while the LED luminous flux is in the spherical coordinates; since it is considered to be a solid angle, the delay spread variation gives the positional variations. Appendix A shows the analytical method of RMS delay spread and measured luminous flux. Here, we have the power distribution in the form of t-statistics, with \"t\" giving the relative error in comparison to the null hypothesis. The \"p-value\" provides the statistical significance of measured values against theoretical values. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Room Size & \(6\) m \(\times\) \(6\) m \(\times\) \(6\) m \\ \hline Reflectance (\(\rho\)) of ceiling & 0.35 \\ \hline Reflectance (\(\rho\)) of wall & 0.8 \\ \hline Reflectance (\(\rho\)) of floor & 0.60 \\ \hline Coordinates of LED Sources for Scenario 1 & A (0,0,6), B (6,0,6) \\  & C (0,6,6), D (6,6,6,) \\ \hline Coordinates of LED Sources for Scenario 2 & A (2,2,6), B (4,2,6) \\  & C (0,6,6), D (6,6,6) \\ \hline Transmitted power & 16 w \\ \hline Center luminous flux & 300 lm \\ \hline Height of LED source & 5.15 m \\ \hline Receiver detection area & 100 m\({}^{2}\) \\ \hline Height of receiver & 0.085 m \\ \hline FOV of receiver & 70\({}^{\circ}\) \\ \hline Elevation of receiver & 90\({}^{\circ}\) \\ \hline \end{tabular} Note: LED = light-emitting diode; FOV = field of view.  
\end{table} 
Table 1: Simulation parameters. Figure 4: Different orientations of transmitters and receivers for different scenarios. Figure 5: _Cont._  
As seen in Table 1, for our 2 different scenarios, we calculated the sum of square errors, \(t,p\), and RMSE. We considered the power from LED-A as the reference power value, with corresponding \(t\) and \(p\)-values. Tables 2 and 3 provide the SSE, t, p, and RMSE values for both cases. The RMSE value of \(1.4054\times 10^{-6}\) and \(1.13\times 10^{-6}\) is a comparison considering the overall volume of room dimensions, which is enhanced by 24%, as mentioned in Appendix A. Finally, proportional references are cited for comparison purposes in terms of cost, availability, energy efficiency, and complexity. As can be seen in Table 4, the performance of this work is far better than the other state of the art indoor localization techniques involving DoP metrics. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Evaluation of Frame Work**} \\ \hline
**References** & **DoP (Indoor Positioning)** & **Cost** & **Availability** & **Energy Efficiency** & **Complexity** \\ \hline
[44] & GDoP & High & Low & Low & High \\
[45] & DoP & Moderate & High & Low & High \\
[46] & HDoP, VDoP & High & Low & Moderate & Moderate \\ This work & PDoP & Low & Moderate & High & Low \\ \hline \hline \end{tabular} Note: VDoP = vertical DOP; GDoP = geometric DOP; PDoP = positional DOP; HDoP = horizontal DOP.  
\end{table} 
Table 4: Comparative evaluation in terms of application of dilution of precision (DoP) metrics in indoor positioning. Figure 5: Proximity of light sources. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **LED-A** & **LED-B** & **LED-C** & **LED-D** \\ \hline SSE & 0 & 0.3492 & 0.1845 & 0.2814 \\ \(t\) & \(-\)2.4217 & \(-\)1.6456 & 0.8489 & 2.5946 \\ \(p\) & 0.0193 & 0.1064 & 0.4002 & 0.0125 \\ RMSE & \(1.4054\times 10^{-6}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scenario 1. Least squares estimation of PDoP values for received signal strength (RSS) localization. RMSE = root means square errors.