A Light Source Authentication Algorithm Based on the Delay and Sum of the Light Source Emission Sequence

Abstract

Indoor visible light positioning is susceptible to specular interference, which reduces the accuracy of positioning. From the perspective of increasing the number of identity documents (IDs), this paper proposes a light source authentication algorithm based on the delay and sum of the light source emission sequence. After obtaining the sub-light source emission sequence at the receiving end, the algorithm performs a cross-correlation operation on the adjacent sub-light source emission sequence in chiral order, and the emission sequence delay of the adjacent sub-light source can be obtained. Then, the relationship between the sum of the delays of all emitted sequences and the length of the sequence is calculated to identify the authenticity of the light source array. We conduct a simulation analysis of the light source authentication algorithm based on the delay and sum of the light source emission sequence. The results show that the algorithm can effectively improve the sequence utilization and localization success rate. Compared with the light source authentication algorithm based on the vector product, the number of light source IDs of the proposed algorithm is significantly increased. For example, when the number of light sources is 3 and the sequence length is 63, the number of light source IDs of the proposed algorithm is greater than that of the light source authentication algorithm based on the vector product by about 35. Therefore, the light source authentication algorithm based on the delay and sum of the light source emission sequence can effectively improve the utilization of the sequence.

1. Introduction

Positioning technology is widely used in people’s daily lives. In terms of indoor positioning, traditional indoor positioning includes Wi-Fi [1], Bluetooth [2], infrared [3], ultra-wideband [4], radio frequency identification (RFID) [5], ZigBee [6], and ultrasound [7]. However, there are many problems in traditional indoor positioning, such as poor positioning precision, a limited operating range, poor stability, and high construction costs. With the continuous improvements in lighting equipment, light-emitting diode (LED) light sources can also achieve communication under the premise of fulfilling the lighting function [8]. Visible light communication technology makes it possible to use visible light for indoor positioning. Compared with traditional indoor positioning technology, visible light positioning has the advantages of stability, convenience, and simple deployment. Because of the short wavelength and high frequency of visible light, it has a strong ability to resist electromagnetic interference. In addition, the accuracy of visible light positioning is also relatively high.

In visible light positioning technology, each LED in the environment is encoded. After the receiver decodes the information of multiple LED lights, these LED lights are used as a reference to obtain the location of the receiver. Marco et al. from Italy used the trilateral positioning method to achieve indoor positioning, which verified the feasibility of visible light communication (VLC) positioning technology [9]. Some researchers have proposed to use the light source image reflected by the floor for localization. This positioning method can avoid the problem whereby the front camera of the mobile phone is obscured by the user, resulting in an overly narrow viewing angle [10]. However, this method needs to limit the user’s posture to ensure that the pseudo-light source is collected. With the popularity of smartphones, many researchers can now obtain light source images collected through smartphone cameras and calculate the pose of the receiver to provide support for navigation services [11,12,13,14]. To date, most VLC indoor positioning studies have covered multi-light collaborative multi-access and interference suppression problems [15,16]. The receiving device for VLC can be implemented by a photosensitive device or camera. Despite the decreased price of photosensitive devices, with the popularity of smartphones, cameras have become more accessible VLC receiving devices. A camera captures more information than a photosensitive device. A higher rate of communication can be achieved through rolling shutter technology, and the frequency of light source flashing can even exceed the frame rate of the camera [17,18].

However, in real-world environments, the complexity of the indoor environment makes reflections common. For positioning, this reflection phenomenon, especially the specular reflection phenomenon, will form a pseudo-light source with the same ID and characteristics as the real light source, and receivers often cannot distinguish between the two. Therefore, the problem of the authentication of light sources is unavoidable and must be solved [19].

The light source authentication algorithm based on the vector product adopts a light source array composed of n (n ≥ 3) sub-light sources and assigns each sub-light source a different pseudo-random sequence as an emission sequence to identify the light source ID [20]. Then, through the method of vector outreach, the chirality of the light source is obtained, and the authenticity of the light source is judged. Considering the limit on the number of sequences, the light source authentication algorithm based on the vector product limits the number of light source IDs, making it suitable only for environments with a small number of light sources. Therefore, from the perspective of increasing the number of light source array IDs, this paper proposes a light source authentication algorithm based on the delay and sum of the light source emission sequence. The proposed algorithm increases the number of light source IDs while identifying the authenticity of the light source. Compared with the light source authentication algorithm based on the vector product, the number of ID sequences of the proposed algorithm increases by around 6% when the number of light sources is 3 and the length of the sequence is 63. As the sequence length and the number of light sources continue to increase, the number of light source ID sequences will continue to grow.

The remainder of this paper is organized as follows. The second section provides an introduction to the principles. This section elaborates on the light source design considered in the authenticity algorithm, describes the algorithm’s principles in detail, and presents the method of determining the light array ID under the algorithm. The third section simulates the number of light source IDs and derives the usable length of the emission sequence based on the rolling shutter characteristics. The fourth section analyzes the algorithm from the perspectives of the correct rate, the scope, and the positioning success rate.

2. A Light Source Authentication Algorithm Based on the Delay and Sum of the Light Source Emission Sequence

In the design of light sources, this algorithm adopts a chiral light source array composed of sub-light sources, and it uses light source arrays instead of point lights. The light array is set to a closed convex geometry consisting of n sub-lights that are tightly arranged. Chirality refers to the fact that the figure cannot be translated and rotated to coincide with the original figure after mirror symmetry. When using chirality to identify real and pseudo-light sources, in the case of less than three light sources in the environment, the chiral characteristics cannot be judged between the light sources, and the authenticity of the light source also cannot be judged. The sub-lights in the light array are assigned IDs in a preset chiral order. The sequence $H_r$ of positive integers composed of the delay of the emission sequence $h_j$, $h_{j+1}$, $h_{j+2}$,…, $h_n$,…, $h_{j-2}$, $h_{j-1}$ between adjacent sub-lights is called the ID of the light array. A small light source array represents an independent light source. Therefore, regardless of the number of light arrays in the environment, a single light array can also be used to determine the authenticity in an actual indoor environment. A complete array of light sources is shown in Figure 1. In Figure 1a, Sub-light 1, Sub-light 2,…, Sub-light n are arranged in counterclockwise order to form a circular light source array.

In order to identify the light source ID, usually, a different pseudo-random sequence is used for the emission sequence of each light source. However, the number of sequences is limited, which severely limits the number of light source IDs. Therefore, this paper considers different light sources using the same pseudo-random sequence as the emission sequence. This increases the available IDs of the light source and improves the sequence utilization. In order to increase the number of light source IDs, the sub-light sources in the light source array constructed in this part all use the same pseudo-random sequence. The emission sequence of each sub-light source in the light source array relies on the different cyclic shifts of the light source array sequence, thus distinguishing each sub-light source, as shown in Figure 1. As shown in Figure 1, each sub-light source takes a pseudo-random sequence with the same length of 31 as the emission sequence, where the hexagon represents the chip, and each chip has a corresponding number. The first chip of sub-light 1 is the first bit of the sequence, and the first chip of sub-light 2 is the fourth bit of the sequence; thus, the delay of the emission sequence of the two sub-light sources $h_1$ is 3.

All sub-lights in the array use the same pseudo-random sequence of length P as the emission sequence. Adjacent sub-lights are assigned a pseudo-random sequence of cyclic shifts in chiral order. The delay of the sequence can start from any of the sub-lights, and the delay of the emission sequence between adjacent sub-lights is $h_j$, $h_{j+1}$, $h_{j+2}$,…, $h_n$,…, $h_{j-2}$, $h_{j-1}$, $1\le j\le n$, $j\in N$. We set the following prerequisites:

$$(K-1)P<\sum _{i=j}^n{h}_i+\sum _{i=1}^{j-1}{h}_i\le KP, K<{\displaystyle \frac{n}{2}}, K\in N.$$

(1)

It can be seen based on the above set conditions that

$$h_n=KP-(h_j+h_{j+1}+\dots +h_{n-1}+\dots +h_{j-2}+h_{j-1}).$$

(2)

The chirality of the pseudo-light array is reversed after specular reflection, as shown in Figure 2.

The delay of the emission sequence between adjacent sub-light sources with opposite chirality is $P-h_j$, $P-h_{j+1}$, $P-h_{j+2}$,…, $P-h_n$,…, $P-h_{j-2}$, $P-h_{j-1}$. The sum of the delays of all emission sequences in the array of real lights is $KP$, while the sum of the delays of all emission sequences in the array of pseudo-lights is $(n-K)P$. Therefore, the authenticity of the array of light sources can be discerned by calculating the sum of the emission sequence delays between adjacent sub-lights. Based on this premise, a sequence of $h_j$, $h_{j+1}$, $h_{j+2}$,…, $h_n$,…, $h_{j-2}$, $h_{j-1}$ forms a positive integer $H_r$ as the ID of the light array. Different light source arrays are distinguished by using different $H_r$, and there must be no cyclic shift relationship between different sequences $H_r$. Taking Figure 1 as an example, the delay of the emission sequence between the sub-light sources is 3, 7, 1, …, 4, respectively, so (3, 7, 1, …, 4) is the ID of the array of this light source.

After setting the light source emission sequence on the transmitter as required above, the emission sequence of the light source can be received through the complementary metal oxide semiconductor (CMOS) image sensor at the receiving end. According to the ID number, ranging from the smallest to the largest and right-hand rules, the sub-light sources in the light source array are arranged in an orderly manner. According to the order of the chirality of the right side, starting from any sub-light source, the sequence cross-correlation operation is used to calculate the emission sequence delay between adjacent sub-light sources, and the delay of the emission sequence is recorded as $h_j^{\prime }$, $h_{j+1}^{\prime }$, $h_{j+2}^{\prime }$,…, $h_n^{\prime }$,…, $h_{j-2}^{\prime }$, $h_{j-1}^{\prime }$. Then, we add the total delay and identify the authenticity of the light source array according to Formula (3).

$$\sum _{i=j}^n{h}_i^{\prime }+\sum _{i=1}^{j-1}{h}_i^{\prime }=\left\{\begin{array}{c}KP, \mathrm{true} \mathrm{light}.\hfill \\ \mathrm{others}, \mathrm{pseudo}\text{-}\mathrm{light}.\hfill \end{array}\right.$$

(3)

At the same time, the sequence $H_r^{\prime }$, composed of $h_j^{\prime }$, $h_{j+1}^{\prime }$, $h_{j+2}^{\prime }$,…, $h_n^{\prime }$,…, $h_{j-2}^{\prime }$, $h_{j-1}^{\prime }$, can be compared with the database containing the IDs of the light sources to determine the ID of the light array.

The algorithm can use a light array with three sub-lights to complete the light source authentication process. Therefore, considering the calculation burden of the algorithm and the design cost of the light source, we use a light source array consisting of three sub-sources in the following simulations.

3. Simulation of the Number of Light Array IDs

All sub-lights in the array use the same pseudo-random sequence of length P as the emission sequence. Adjacent sub-lights are assigned pseudo-random sequences of cyclic shifts in chiral order. The sequence delay is calculated starting from any sub-light source; the sequence delay summation is $KP$; and the cyclic shift relationship between the IDs of the light array cannot be presented. Based on the above, this section simulates the number of light source IDs under different values of coefficient K, different numbers of light sources n, and different sequence lengths P. The simulation results are shown in

Table 1. The number of light source IDs under different coefficients K, numbers of light sources n, and sequence lengths P.

P	K = 1	K = 1	K = 1	K = 2	K = 2	K = 2
	$\mathit{n}$ = 3	$\mathit{n}$ = 4	$\mathit{n}$ = 5	$\mathit{n}$ = 3	$\mathit{n}$ = 4	$\mathit{n}$ = 5
7	5	5	3	0	0	143
15	31	91	201	0	0	4751
31	145	1015	5481	0	0	104,371
63	631	9455	111,569	0	0	1,938,275

.

From Table 1, it is clear that the number of IDs increases exponentially with the increase in the coefficient K, the number of light sources n, and the sequence length P. The coefficient K and the number of light sources n should satisfy $K<{\displaystyle \frac{n}{2}}$. Therefore, when the above conditions are not met, the light source ID cannot be generated.

According to Table 1, when the number of lights n and the coefficient K are determined, the greater the sequence length P value, the more IDs of the light source can be provided. When the coefficient K is 1 and the sequence length P is 7, the number of available IDs decreases as the number of light sources n increases due to the relatively short sequence length. In addition to the above case, the number of light source IDs increases with the increase in the number of light sources n when the coefficient K and the sequence length P are unchanged. Moreover, in other cases where the sequence length P is fixed, any increase between the coefficient K and the number of light sources n increases the number of light source IDs exponentially.

On the basis of the authentication and ID identification of the light source array, in order to further distinguish the sub-light source, it is necessary to ensure that the cyclic relationship cannot be presented within the delay sequence of a light source ID. For example, when the sequence delay is (1, 4, 1, 4, 1, 4) or (5, 5, 5), it cannot be used to determine the initial light source for the start delay. In this way, the number of light source IDs will be reduced.

According to the rolling shutter characteristics, the light spot received by the image sensor is a stripe between light and dark, corresponding to the emission sequence of the light source. The intensity of the light will affect the positioning accuracy and authentication. The authentication algorithm needs to recognize the sequence of stripes emitted by the light source. In the case of sufficient lighting, it is usually possible to identify the stripes. When the light stripe is flashing and bright, it is written as “1”, and, when a dark stripe is visible, it is recorded as “0”. The selection of the length of the light source emission sequence must meet the following conditions.

(1)

Ensure that the spot appears with light and dark streaks on the imaging plane.

The stripe width calculation is as follows:

$$N_{pixel}={\displaystyle \frac{F_s}{f_{T}x}}.$$

(4)

$F_s$ is the receiver scan frequency, and $f_{Tx}$ is the light source transmission frequency. If the resolution of the mobile phone is $a\times b$ and the frame rate is q, the receiver scan frequency is $F_s=a\times b$. From Formula (4), it can be seen that, when $F_s>f_{Tx}$, the width of the stripe will be greater than 1 pixel, and the bright stripes and dark stripes will not overlap, so that the striped light and dark spots can be obtained. Then, the emission sequence of the light source can be obtained. Therefore, the light source transmitting frequency $f_{Tx}$ should first satisfy $f_{Tx}<a\times b$.

(2)

Ensure that the flicker frequency of the light source does not produce dazzling and does not affect the lighting.

Flicker is not noticed by the eyes when the flicker frequency is greater than 200 Hz. Therefore, the light source transmitting frequency $f_{Tx}$ should satisfy $200<f_{Tx}<a\times b$.

(3)

Ensure that the 0 run in the sequence does not cause the lighting to be interrupted.

The length of an m sequence of $n_p(n_p\in N)$ levels is $2^{n_p}-1$, and the sequence with a continuous “0” length does not exceed $n_p-1$. The visual persistence of the eyes is 0.1 s to 0.4 s; to ensure that the sequence of long consecutive zero periods is not detected by the eyes, $(n_p-1)t_p<0.1$ should be satisfied.

(4)

Ensure that the positioning refresh is timely.

The positioning refresh rate is G, and the time required to obtain the emission sequence is

$$t_p={\displaystyle \frac{G}{2^{n_p}-1}}.$$

(5)

The corresponding emission frequency is

$$f_{T}x={\displaystyle \frac{1}{t_p}}={\displaystyle \frac{2^{n_p}-1}{G}}.$$

(6)

The length of the sequence that satisfies all of the above requirements is shown in Formula (7):

$$\left\{\begin{array}{c}200\times G<(2^{n_p}-1)<a\times q,0<n_p\le 20.\hfill \\ (10n_p-10)\times G<(2^{n_p}-1)<a\times q,n_p>20.\hfill \end{array}\right.$$

(7)

Once the refresh rate, receiver resolution, and frame rate are determined, the length of the light source’s emission sequence can be determined by using Formula (7). In practice, smartphones have a resolution of mostly 1080 p (1920 × 1080) and a frame rate of 30 fps. The ideal value of the refresh rate for a global positioning system (GPS) is 1 ms. The emission sequence length is $(2^{n_p}-1)\le 31$ after taking Formula (7).

An m sequence of length 31 generates 145 light source array IDs. See Appendix A for details of the IDs (

Table A1. The 145 light source array IDs generated by an m-sequence of length 31.

The Sequence Length	The Sequence of Light Array IDs
P = 31	(2, 1, 28)	(3, 1, 27)	(3, 2, 26)	(4, 1, 26)	(4, 2, 25)
	(4, 3, 24)	(5, 1, 25)	(5, 2, 24)	(5, 3, 23)	(5, 4, 22)
	(6, 1, 24)	(6, 2, 23)	(6, 3, 22)	(6, 4, 21)	(6, 5, 20)
	(7, 1, 23)	(7, 2, 22)	(7, 3, 21)	(7, 4, 20)	(7, 5, 19)
	(7, 6, 18)	(8, 1, 22)	(8, 2, 21)	(8, 3, 20)	(8, 4, 19)
	(8, 5, 18)	(8, 6, 17)	(8, 7, 16)	(9, 1, 21)	(9, 2, 20)
	(9, 3, 19)	(9, 4, 18)	(9, 5, 17)	(9, 6, 16)	(9, 7, 15)
	(9, 8, 14)	(10, 1, 20)	(10, 2, 19)	(10, 3, 18)	(10, 4, 17)
	(10, 5, 16)	(10, 6, 15)	(10, 7, 14)	(10, 8, 13)	(10, 9, 12)
	(11, 1, 19)	(11, 2, 18)	(11, 3, 17)	(11, 4, 16)	(11, 5, 15)
	(11, 6, 14)	(11, 7, 13)	(11, 8, 12)	(11, 9, 11)	(11, 10, 10)
	(12, 1, 18)	(12, 2, 17)	(12, 3, 16)	(12, 4, 15)	(12, 5, 14)
	(12, 6, 13)	(12, 7, 12)	(12, 8, 11)	(12, 9, 10)	(13, 1, 17)
	(13, 2, 16)	(13, 3, 15)	(13, 4, 14)	(13, 5, 13)	(13, 6, 12)
	(13, 7, 11)	(13, 8, 10)	(13, 9, 9)	(14, 1, 16)	(14, 2, 15)
	(14, 3, 14)	(14, 4, 13)	(14, 5, 12)	(14, 6, 11)	(14, 7, 10)
	(14, 8, 9)	(15, 1, 15)	(15, 2, 14)	(15, 3, 13)	(15, 4, 12)
	(15, 5, 11)	(15, 6, 10)	(15, 7, 9)	(15, 8, 8)	(16, 1, 14)
	(16, 2, 13)	(16, 3, 12)	(16, 4, 11)	(16, 5, 10)	(16, 6, 9)
	(16, 7, 8)	(17, 1, 13)	(17, 2, 12)	(17, 3, 11)	(17, 4, 10)
	(17, 5, 9)	(17, 6, 8)	(17, 7, 7)	(18, 1, 12)	(18, 2, 11)
	(18, 3, 10)	(18, 4, 9)	(18, 5, 8)	(18, 6, 7)	(19, 1, 11)
	(19, 2, 10)	(19, 3, 9)	(19, 4, 8)	(19, 5, 7)	(19, 6, 6)
	(20, 1, 10)	(20, 2, 9)	(20, 3, 8)	(20, 4, 7)	(20, 5, 6)
	(21, 1, 9)	(21, 2, 8)	(21, 3, 7)	(21, 4, 6)	(21, 5, 5)
	(22, 1, 8)	(22, 2, 7)	(22, 3, 6)	(22, 4, 5)	(23, 1, 7)
	(23, 2, 6)	(23, 3, 5)	(23, 4, 4)	(24, 1, 6)	(24, 2, 5)
	(24, 3, 4)	(25, 1, 5)	(25, 2, 4)	(25, 3, 3)	(26, 1, 4)
	(26, 2, 3)	(27, 1, 3)	(27, 2, 2)	(28, 1, 2)	(29, 1, 1)

). The longer the emission sequence, the greater the number of available light source IDs. Conversely, the shorter the emission sequence, the faster the emission sequence can be read. Therefore, in practice, the appropriate length of the emission sequence can be selected according to the specific needs.

4. Algorithm Characterization

This section provides the simulation analysis of the algorithm proposed in this paper from three perspectives. Firstly, the effects of the imaging deviation and focal length on the accuracy of the algorithm are simulated and analyzed. Secondly, we simulate the effective range of the algorithm. Thirdly, compared with other similar algorithms, we verify the advantages of the proposed algorithm in terms of the positioning success rate. The simulation parameters are shown in

Table 2. The parameters applied to determine the correct rate of the delayed addition algorithm.

Parameter	Value
Coordinates of light source array (m)	(10, 10, 3), (10.1, 10.17, 3), (10.2, 10, 3)
Position range (m)	$20\times 20$
Receiver height (m)	1
Light emission sequence	$(1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0)$

.

4.1. Falsification Accuracy Analysis

Due to being affected by the image processing algorithm, lens stains, image distortion, positioning algorithm, and other factors, the coordinates of sub-light source imaging in the image will deviate within a certain range. This deviation causes the distribution of the light source array to change, which could lead to an error in the chirality of the light source. As shown in Figure 3, the algorithm should calculate the chirality in the order of “sub-light source 1, sub-light source 2, and sub-light source 3”. If the imaging coordinates of sub-light source 1 deviate, and its imaging coordinates are considered to be at light source 1a, the judgment algorithm calculates the chirality in the order of “sub-light source 1a, sub-light source 2, and sub-light source 3”. In the case shown in Figure 3a, the algorithm will produce a result that is opposite to the real situation, resulting in a false judgment regarding the authenticity of the light source array. However, the chirality does not change in Figure 3b. Deviations in the imaging coordinates of the sub-light source can cause errors in the authentication algorithm. Therefore, it is necessary to estimate the accuracy of the algorithm.

The focus and other information used in the experiment is derived from common mobile phone models on the market, including the OPPO Reno (ultra-wide angle focus 16 mm), OnePlus 9Pro (focus 23 mm), Xiaomi Mi 10Pro (focus 25 mm), Xiaomi Mi 9 (focus 26 mm), Huawei P50Pro (focus 27 mm), and so on.

When the light source emission sequence is obtained at the receiving end, there will be some errors due to noise. The bit error rate used in this paper is $3.8\times {10}^{-3}$, which is obtained via the hardware verification of CMOS image sensors. In an environment with mirror interference, the receiver position is randomly selected within a 20 m × 20 m range. When the receiver points to the light source array, the relationship between the image coordinate deviation of the light source, the focal distance of the camera, and the accuracy of the authentication algorithm is as shown in Figure 4. The abscissa $\sigma$ is the standard deviation of the coordinate distribution of the light source imaging, and the ordinate $P_e$ is the probability of an error when the algorithm determines the chirality.

As can be seen from Figure 4, the greater the imaging deviation, the greater the probability of the sub-light source imaging coordinate deviating from the real imaging coordinate, and the greater the probability of errors in identifying the real and pseudo-light source. It can also be seen that the larger the focal length, the lower the error probability of the pseudo-detection algorithm. This is mainly because the larger the focal length, the larger the image of the light source array on the imaging plane and the easier it is to identify the stripes photographed. Therefore, a lower error probability for the pseudo-detection algorithm is achieved.

4.2. Algorithm Range Simulation

This section provides a simulation analysis of the scope of the algorithm. We use the bit error rate of the light emission sequence, obtained experimentally from previous research, when it is read at the receiving end.

The experimental parameters are shown in Table 2. In addition, the standard deviation is 5 pixels, and the focal length is 0.027 m. When the receiver lens is pointed at the center of the light array, the error rate at different positions of the receiver is as shown in Figure 5. The triangle in the figure represents the center point of the light source array. The horizontal coordinate indicates the distance between the receiver and the center of the light source array, and the vertical coordinate indicates the algorithm error rate. As can be seen from Figure 5, the bit error rate has a minor effect on the algorithm. When the receiver is within a 6 m radius of the center of the light source array, the probability of error detection in the algorithm is about 2%. At this time, the error probability of the algorithm is extremely low, meeting the requirements of normal room size authentication.

4.3. 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 × 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 × 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, 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 $W\le 10$. 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.

5. Conclusions

In this paper, on the basis of a chiral light source array, in order to increase the number of light source IDs, a light source authentication algorithm based on the delay and sum of the light source emission sequence is proposed from the perspective of the emission sequence.

Firstly, we describe the principles of the algorithm in detail and give a method for the determination of the ID of the light source array under the algorithm. Secondly, the number of light source IDs is analyzed, and the usable length of the emission sequence is derived. Finally, from the perspective of light source array imaging, we analyze the algorithm to identify the cause of the errors associated with the real and pseudo-light sources. The algorithm proposed in this paper is simulated and analyzed from the three perspectives of the authentication accuracy rate, scope of action, and success rate in localization. This algorithm improves the sequence utilization and the positioning success rate and increases the number of available IDs for light sources. Compared with the authentication algorithm based on the vector product, which is suitable for small indoor environments, the algorithm proposed in this paper is suitable for environments with large indoor areas and a large number of light sources. It should be noted that our proposed algorithm is only suitable for a single-reflection problem. This algorithm does not consider dual-reflection scenarios.