## 4 Experimental Results
### Experimental Result Evaluation
#### 4.2.4 Positioning Performance Analysis  
To evaluate the performance of our proposed positioning method with respect to the positioning accuracy, we conducted an experiment in the evenly distributed test points and randomly distributed test points. For evenly distributed test points, 32 evenly distributed real test positions were created at the height of 2 m from the ceiling to ground. Each position was tested twice, and the experiment for the estimated position involved 64 positions. The even distributions of the positioning results are shown in Figure 13a. As shown in Figure 13a, the estimated positions matched well with the real positions, which proved that our proposed positioning system provided high positioning accuracy. To observe the performance of the random movement of the user, we also conducted the experiment with 11 randomly distributed test points at the same height. The random distributions of the positioning results are shown in Figure 13b. The results of the system show that the estimated positions matched well with the real positions for the random movement cases. The experimental result shows that the average positioning accuracy was 2.44 cm, and the maximum error was 4.60 cm for the evenly distributed test points. Meanwhile, for the randomly distributed test points, the average positioning accuracy was 2.41 cm with maximum error of 4.50 cm, which was almost the same as the evenly distributed test results. For a better visualization of the performance, Figure 14a,b shows the cumulative distribution function (CDF) of the positioning error for the evenly and randomly distributed test points, respectively. The cumulative distribution function is defined in terms of the probability of a random positioning error (\(\epsilon\)), whose value is less than or equal to the positioning accuracy \(Pa\), such that the CDF can be expressed as \((Pa)=P\left(\epsilon\leq Pa\right)\). As shown by the histograms in Figure 14c,d, the average errors are 2.44 and 2.41 cm, where all the positioning errors are within 4.60 and 4.50 cm for the evenly and randomly distributed test points, respectively. Therefore, it is perceivable that the proposed positioning method can yield a highly accurate positioning performance. Finally, a comparative analysis of the proposed system with other practically implemented VLC- and image sensor-based indoor positioning systems is shown in Table 3. The major drawback of the other system  
Figure 12: (**a**) Decoding accuracy vs. vertical distance; (**b**) decoding accuracy vs. horizontal distance.  
is its small testbed with inadequate accuracy and high cost. By applying the proposed localization method with VLC combined with an image sensor, a high-accuracy low-cost indoor positioning system was obtained.  
Figure 14: (**a**) CDF vs. error for evenly distributed test points; (**b**) CDF vs. error for randomly distributed test points; (**c**) histogram of error for evenly distributed test points; (**d**) histogram of error for randomly distributed test points.  
Figure 13: Positioning results for evenly and randomly distributed test points: (**a**) for evenly distributed test points, positioning result at height 2 m; (**b**) for randomly distributed test points, positioning result at height 2 m.