## 3 Experimental Setup and Result Analysis
### Result and Analysis
#### 3.2.1 Accuracy Performance  
In order to demonstrate the accuracy performance of the proposed tracking algorithm to the maximum extent, two hundred successive frames (101 th to 300 th) of video sequences (with a white LED signal source) were chosen to process. The _total tracking error_ can be defined as:  
\[Total\;tracking\;error=\sqrt[2]{\left(x-x_{r}\right)^{2}+\left(y-y_{r}\right)^{2}} \tag{23}\]  
\[error\;of\;x\;(y)=\left|value_{tracking\;algorithm}-value_{actual}\right| \tag{24}\]  
Figure 7: Experimental system configuration. (**a**) Transmitter, (**b**) Receiver. where \((x,y)\) represents the proposed algorithm's calculated coordinate of the target signal source LED, and \((x_{r},y_{r})\) represents the actual coordinate of the target LED. From the proportional relationship between image coordinates and world coordinates, the actual distances can be obtained via a conversion. The tracking result is shown in Figure 8 where the blue dot represents the actual position and the red dot is the coordinate calculated by the proposed algorithm. Figure 8a is the total tracking result, Figure 8b,c is the tracking result in the \(x\)- and \(y\)-axis directions, respectively. As can be seen from the results, the performance of the tracking is good with small errors. To further illustrate the result and show the accuracy performance of the proposed algorithm in the round, Figure 9 shows the _total tracking error_, _error of_\(x\), and _error of_\(y\) coordinate, where Figure 9a is the _total tracking error_, and the blue solid line and purple dotted line in Figure 9b represents the _error of_\(x\) and the _error of_\(y\) coordinate, respectively. The maximum _total tracking error_ was 2.21 cm, and the average _total tracking error_ was 0.85 cm. Furthermore, the average tracking _error of_\(x\) was 0.20 cm and the average _error of_\(y\) was 0.81 cm. There are many reasons for the tracking error, such as image noise, camera-shaking, brightness vibration of target signal source LED, etc., which can affect the back-projection image, causing the color probability distribution map to be disturbed. However, in practical applications of OVLC systems, such errors, which are only a few centimeters or within one centimeter, are acceptable. Therefore, it can be concluded that the proposed tracking algorithm has a good accuracy performance and can extract the target signal source LED area accurately and completely, which is the premise of realizing communication in a CMOS-based VLC system. Figure 8: The calculated coordinate value and the actual coordinate value of the target signal source LED: (**a**) tracking result of the target signal source LED, (**b**) Tracking result of the \(x\) coordinate, and (**c**) tracking result of the \(y\) coordinate. The cumulative distribution function (CDF) is the integral of the probability density function, describing the probability of an event, the abscissa is variable and the ordinate is a probability value. Specifically, the ordinate of any point on the CDF curve indicates the probability of a variable that is less than or equal to the corresponding abscissa of the point. The CDF is defined as:  
\[F_{X}(x_{0})=P(X\leq x_{0}) \tag{25}\]  
If variable is discrete, the CDF is expressed as:  
\[F_{X}(x_{0})=P(X\leq x_{0})=\sum_{x_{i}\leq x_{0}}p_{i} \tag{26}\]  
where \(p_{i}\) is the probability of event \(x_{i}\). The CDF is a frequently-used index for error analysis, such as in References [4; 5; 22]. When evaluating the tracking or positioning accuracy, the abscissa represents the error and ordinate represents the probability. Furthermore, when the ordinate value is fixed, the smaller the abscissa, along with the error value, the more accurate the algorithm performs. Usually, the ordinate value is 90% or 95% as a judging standard. Figure 9: Tracking error of the target signal source LED: (**a**) total tracking error, and (**b**) tracking error of \(x\) and \(y\) coordinate. Therefore, the CDF is used in this paper to further elaborate the accuracy performance of the proposed algorithm.