## 3 Experiment and Result
### Result and Analysis
Because the algorithm needs time to process one frame, during which the target may already move to other positions. The process of positioning is always slower than the moving of the target. Our proposed algorithm utilizes the unscented Kalman filter algorithm to predict the most possible position of the target in the current frame. Then let the mean shift algorithm search for the target from the predicted position. This method increases the highest allowable motion speed of the positioning terminal. Theoretically, our proposed algorithm can track targets with any speed if enough priori information is given. However, if the target moves too quickly within one frame, the LED will exceed the maximum capture scope of the image sensor. To simplify the calculation of the theoretical maximum motion speed of the positioning terminal, we assume that the LED in the image starts moving from the left edge in frame N with no velocity and the motion path is parallel to the x-axis. Because the unscented Kalman filter algorithm can handle variable motion with arbitrary acceleration, we assumed that the UKF algorithm predicts the position according to the uniform acceleration motion model and ignores the effect of the target's previous positions except its last position. The first maximal moving distance allowed is the diameter of the LED. Then the UKF obtains its speed and accelerated speed to predict its position in the next frame. In frame N + 1, the maximum allowable moving distance is the predicted moving distance plus the diameter of the LED. The steps for the next frame are the same. Then the maximum motion speed can be calculated in frame N + 2, because the predicted moving distance has exceeded the border of image in this frame. The process is shown in Figure 16.  
The maximum motion speed of the target is defined as:  
\[\
u_{\rm max}\ =\ \rm{s/t} \tag{47}\]  
in which s represents the maximum allowable moving distance of the positioning terminal between two successful frames, while t stands for the algorithm's average processing time. Based on the proportional relationship between images coordinates and world's coordinates, the relationship can be expressed as:  
\[\rm{s/r=D/d} \tag{48}\]  
\[D=\sqrt{\left(X-X_{r}\right)^{2}+\left(Y-Y_{r}\right)^{2}} \tag{44}\]0 The cumulative distribution function (CDF) of positioning error. where r represents pixel length of moving distance, D stands for the actual diameter of the LED, and d is the pixel length of the LED. In our experiment, we calculated the average processing time of 87 successful frames without shielding, which is 24.93 ms. By contrast, the algorithm's average processing time of one frame in our previous work [9] was 0.162 s. The actual diameter of the LED was 150 mm, whose diameter in the image was 60 pixels. Besides, the pixel length of the image was 800 pixels in our experiments. Also, in our algorithm, if the predicted position of the UKF algorithm exceeded the border, the final output of predicted position will be tangent with the edge of image. Supposing that the LED is tangent with the right edge of the image in frame N + 2, the moving distance is 440 pixels compared with frame N + 1, in other words, r is 440. Therefore, the theoretic maximum allowable motion speed of the positioning terminal is 44.12 m/s \(\approx\) 158.84 km/h according to the definition, which not only meets the requirement of indoor dynamitic positioning, but also satisfies the needs of some outdoor positioning circumstances such as traffic systems in channels. The theoretical maximum allowable motion speed of the positioning terminal in Reference [1] was 48 km/h, much slower than the proposed method. Robustness is also significant for VLP systems in practical VLP situations, which is often ignored in most existing research. In this article, we especially set-up an experiment measuring the performance of our proposed algorithm under the circumstance of a shielding effect and background interference. Besides, to simplify the analysis, we considered the case that only one LED existed.