## 4 Algorithm Characterization
### Simulation Analysis of Positioning Success Rate  
Using a pseudo-light source for positioning during the positioning process will lead to incorrect positioning information, resulting in a positioning failure. Therefore, this section simulates the localization success rate of four different positioning algorithms when pseudo-light sources are present.  
The simulation environment is as follows: \(W\ \times W\) light source arrays are evenly distributed on a ceiling with a size of 20 m \(\times\) 20 m, the spacing of the sub-light sources in the light source array is 20 cm, and the distance from the ceiling to the ground is 3 m. The receiver is randomly placed in the range of 20 m \(\times\) 20 m, the height is fixed to 1 m, and the receiver attitude is free.  
There are two prerequisites for successful positioning. First, the information of the pseudo-light source is not used in the positioning process for positioning. Second, there are at least three sub-light sources on the imaging plane for imaging. Based on the above premise, the following comparative experiment is carried out, and the simulation results are shown in Figure 6. \(W\) is the density of the light source, and \(P_{w}\) is the probability of successful positioning.  
System 1 does not use an authentication algorithm and directly uses the spot information in the imaging plane for localization. In System 2, real and pseudo-light sources both have the same ID. If there are light sources with the same ID on the imaging plane, it means that the real light source and the pseudo-light source appear on the imaging plane at the same time. Therefore, the light sources with the same ID are discarded, and the remaining light sources on the imaging plane are used for positioning. This system experiment is based on [21]. System 3 is the light source authentication algorithm based on the delay and sum of the light source emission sequence proposed in this paper. System 4 uses the pseudo-light source identified by the algorithm in the process of positioning. In System 2,  
Figure 5: Simulation diagram of the range of the delayed addition algorithm.  
Figure 6: Comparison of positioning success rates of different algorithms.  
all light sources with the same ID are discarded. When the light source density is small, the number of real light sources available for positioning is small, so the positioning success rate can only be slightly improved. System 3 is equipped with the detection algorithm and can utilize most true light sources. Therefore, when the light source density is small, it is more advantageous, and the positioning accuracy rate is greatly improved. From Figure 6, it can be seen that the algorithm in System 3 yields an improvement of 15% to 30% compared with the existing algorithm at \(W\leq 10\). The smaller the density of the light source, the greater the advantage. Even when the light source density is large, it yields the same success rate as the existing algorithm. \(W=10\) indicates that there are 100 light source arrays in the environment. Therefore, in a normal-sized environment, the number of light source arrays can fully meet the needs of lighting and positioning. In System 4, we use a pseudo-light source for positioning, but the simulation results are not ideal. The reason for this is occasional errors in judgment. Therefore, it is necessary to design a correction method for the authentication algorithm on the basis of the error rate estimation function to enable the use of a pseudo-light source.