## 3 Experiment and Result
### Result and Analysis  
Positioning accuracy is a vital index measuring the performance of VLP systems. Though the LED may be shielded or broken sometimes, in most cases the whole LED is captured by the positioning terminal. Besides, an interferential lamp was introduced into our experiment to test if our LED-ID algorithm could successfully detect the position of the LED and obtain its ID with the world's coordinates. The result was successful as shown in Figure 10. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Camera Specifications**} \\ \hline Model & MV-U300 \\ Spectral Response Range/nm & 400–1030 \\ Resolution & 800 \(\times\) 600 \\ Frame Rate/FPS & 46 \\ Dynamic Range/dB & \textgreater{}61 \\ Signal-to-noise Ratio/dB & 43 \\ Pixel(H \(\times\) V) & 2048 \(\times\) 1536 \\ Pixel Size/\(\upmu\)m\({}^{2}\) & 3.2 \(\times\) 3.2 \\ Time of Exposure/ms & 0.0556–683.8 \\ Sensitivity & 1.0 V/lux-sec 550 nm \\ Optical Filter & 650 nm Low Pass Optical Filter \\ Type of Shutter & Electronic Rolling Shutter \\ Acquisition Mode & Successive and Soft Trigger \\ Working Temperatures/\({}^{\circ}\)C & 0–50 \\ Support Multiple Visual Software & OpenCV, LabView \\ \hline \multicolumn{2}{c}{**Turtlebot3 Robot Specifications**} \\ \hline Processor Module & Raspberry Pi 3 B \\ CPU & Quad Core 1.2 GHz Broadcom BCM2837 \\ RAM & 64 bit CPU \\ \multicolumn{2}{c}{1 GB} \\ operating system & Ubuntu mate 16.04 \\ \hline \multicolumn{2}{c}{**Experimental Platform Specifications**} \\ \hline Size (L \(\times\) W \(\times\) H)/ cm\({}^{3}\) & 190 \(\times\) 100 \(\times\) 190 \\ \hline \multicolumn{2}{c}{**LED Specifications**} \\ \hline Coordinates (x, y, z)/cm & LED2(100,45,190) \\  & LED3(0,145,190) \\  & LED4(0,45,190) \\ \hline The half-power angles of & 60 \\ LED/deg(\(\psi\)1/2) & \\ \hline \multicolumn{2}{c}{**Circuit Board Specifications**} \\ \hline Drive chip & DD311 \\ Drive current/A & 0.1 \\ Drive voltage/V & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of experimental facilities and platform. We define positioning error as:  
\[D=\sqrt{\left(X-X_{r}\right)^{2}+\left(Y-Y_{r}\right)^{2}} \tag{44}\]  
\[\text{Error of }X(Y)=\left|\text{Value}_{\text{predicted}}-\text{Value}_{\text{ actual}}\right| \tag{45}\]  
where (X, Y) is the position located by our proposed algorithm and (X\({}_{r}\), Y\({}_{r}\)) is the actual position. The maximal positioning error of x coordinates is less than 1 cm, and that of y coordinates less than 0.8 cm. Also, the value of maximal positioning error does not exceed 1.2 cm. Besides, the average value of positioning error in x coordinates, the average value of error in y coordinates, the average positioning error were 0.31 cm, 0.21 cm, and 0.42 cm, respectively. Cumulative distribution function (CDF) is the integral of the probability density function, which can be used to analyze the probability distribution of the tracking error, error in the direction of coordinate axis x and coordinate axis y. The cumulative distribution function of positioning error is shown in Figure 14. The definition of cumulative distribution function is:  
\[F_{X}(x)=P(X\leq x) \tag{46}\]  
In other words, the cumulative distribution function represents the sum of the probability of all values less than or equal to x for the discrete variable. As the Figure 15 indicates, more than 90% of positioning error D, the positioning error of x coordinates, and the positioning error of y coordinates were less than 0.75 cm, 0.67 cm, and 0.57 cm,  
Figure 14: The tracking error D.  
Figure 13: The error of position value of y coordinates. respectively. If we can bear the 10% uncertainty, the positioning error of our algorithm is only 0.75 cm. In contrast, the positioning error of our previous work [9] was two times more than that of our new method. The real-time ability is also important for VLP systems, which determines the maximum motion speed of the positioning terminal allowed. The running time and complexity of the algorithm both affect the real-time ability of VLP algorithms prominently.