Indoor Visible Light Fingerprint Location Method Based on Marine Predator Algorithm-Optimized Least Squares Support Vector Machine

Abstract

To increase the accuracy of indoor visible light positioning, a novel indoor visible light localization technique based on the marine predator algorithm-optimized least squares support vector machine (MPA-LSSVM) is suggested. The light signals of each reference point are recorded in the first place and a fingerprint database is created. Introduced thereafter is the marine predator algorithm, which, through iterative optimization of the hyperparameters of the least squares support vector machine, aims to establish an optimal localization model using finely-tuned hyperparameters. This culminated in the development of a positioning model, successfully attaining the objective of enhancing accuracy in positioning while minimizing time expenditure. In an indoor-positioning scene (size: 1 m × 1 m × 1 m), the average positioning error of the proposed positioning method is 0.041 m, and the proportion of test points with positioning errors less than 0.1 m is 96.7%.

1. Introduction

Visible light communication (VLC) relates to wireless optical communication, which is a technology that uses light emitted by light-emitting diodes (LEDs) to transmit data [1,2,3]. Compared to indoor positioning technologies such as RFID [4], WLAN [5], Bluetooth [6], ZigBee [7], and ultra-wideband [8], VLC has many advantages, such as high security, fast transmission rate, no electro-magnetic radiation, etc. In addition, VLC has the ability to simultaneously illuminate and communicate. With the continuous development of VLC, visible light positioning (VLP), as an emerging technology, has attracted extensive attention and in-depth research from scholars [9,10]. VLP has wide applicability and low cost in various application scenarios due to its strong resistance to electromagnetic signal interference and freedom from electromagnetic radiation, and it is easy to realize large-scale deployment.

In recent years, researchers have conducted extensive studies on enhancing the performance of VLP systems. Depending on the type of sensor used at the receiver side, these methods are mainly categorized into two groups: imaging-based and non-imaging-based. Among the imaging methods, traditional approaches cover proximity [11], trilateral localization [12,13,14], and fingerprint localization. Hong et al. [15] proposed and validated an angle-of-arrival (AOA)-based VLP system, the average positioning error was reduced by 55.6% and 57.2%, respectively. Li [16] proposed a hybrid APTI algorithm that significantly reduces the target localization error at the center of the room and overcomes the limitation when the number of LEDs is small. Hsu et al. [17] proposed an RSS VLP system that utilizes data preprocessing and convolutional neural networks (CNNs) to reduce the under-illuminated areas of the system and achieve improved positioning accuracy.

In order to further improve the positioning accuracy and reduce the time cost, this paper proposes an indoor visible light positioning method based on marine predator algorithm-optimized least squares support vector machine (MPA-LSSVM). Using four LEDs as transmitters and a light meter as receiver, light intensity signals are collected from preset points in the localization area to create a localization structure. The specific localization process is divided into two stages, in the offline stage, the value of the received light intensity and the coordinate point of the location of the illuminance meter are used as the features to construct the fingerprint database, and then the marine predator algorithm (MPA) is introduced to iteratively search for the optimization of the hyperparameters of the least squares support vector machines (LSSVM) to establish the localization model with the optimal hyper-parameters; in the online stage, the light intensity signal collected at the preset test point is inputted into the localization model as the fingerprint data to calculate the coordinates of the test point to finally realize the localization. The collected light intensity signal is input into the localization model as fingerprint data to calculate the coordinates of the test point and finally realize the localization. The experimental results show that the use of this localization method can improve the positioning accuracy and enhance the stability of the system, with wide applicability.

2. Method

2.1. Indoor Visible Light Localization Model

In this paper, the selected localization place is a square space of 1 m × 1 m × 1 m, and the model of the experimental system is shown in Figure 1. A total of four LED lights are placed on the ceiling of the space in four places, A, B, C and D, which are selected to be used as the transmitting end. The illuminometer is located at point E on the floor as the receiving end.

2.2. Channel Model

In an indoor visible light localization system, the propagation of visible light conforms to the Lambertian radiation model, and when there is no obstruction between the transmitting end and the receiving end, it is called a line-of-sight (LoS) link, and under this condition, the DC gain can be expressed as follows:

$$H_{\mathrm{LOS}}=\left\{\begin{array}{l}{\displaystyle \frac{A(m+1)}{2\pi d^2}}{\cos }^m(\theta )T_s(\phi )g(\phi )\cos (\phi ),0\le \phi \le {\phi }_c\\ 0,\phi >{\phi }_c\end{array}\right.$$

(1)

The Lambertian order of the LED is calculated as follows:

$$m={\displaystyle \frac{\ln 2}{\ln (\cos {\varphi }_{1/2})}}$$

(2)

The half power angle of the LED is ${\varphi }_{1/2}$, the radiation angle of the light source LED at the emitting end is $\theta$, the angle of incidence of the illuminator is $\phi$, the field-of-view range angle of the illuminometer is ${\phi }_c$, the effective detection area of the illuminometer is $A$, the straight line distance from the LED to the illuminometer is $d$, the gain of optical filtering in the link is $T_s(\phi )$, the optical concentration gain in the link is $g(\phi )$. When the emitted optical power of the LED is $P_t$, and the received power $P_r$ of the receiver can be expressed as

$$P_r=H_{\mathrm{LOS}}\cdot P_t$$

(3)

2.3. LSSVM

LSSVM can be obtained by improving SVM using the least squares method, LSSVM is more concise and less time-consuming than SVM. LSSVM performs very well in linear regression, can avoid overfitting problems, and has a good generalization ability, so it is suitable for regression prediction.

The constraints of the LSSVM are equational constraints in the following form:

$$\begin{array}{c}\underset{\omega ,b,e}{\min } J\left(\mathit{\omega },\mathit{e}\right)={\displaystyle \frac{1}{2}}{\mathit{\omega }}^T\mathit{\omega }+{\displaystyle \frac{1}{2}}\gamma {\displaystyle {\displaystyle \sum }_{k=1}^N}{\mathit{e}}_{\mathit{k}}^2\\ s.t.{\mathit{y}}_{\mathit{k}}\left[{\mathit{\omega }}^T\phi \left({\mathit{x}}_{\mathit{k}}\right)+b\right]=1-{\mathit{e}}_{\mathit{k}}\\ \gamma >0,k=1,2,\dots ,N\end{array}$$

(4)

where the weight coefficients of the LSSVM are given as $\mathit{\omega }$, $b$ is the threshold, ${\mathit{e}}_{\mathit{k}}$ is the deviation vector, $\gamma$ is the penalty factor, ${\mathit{x}}_{\mathit{k}}$ is the eigenvector, ${\mathit{y}}_{\mathit{k}}$ is for category tags, and $\phi$ is a kernel function that allows linear computation on inputs.

The original LSSVM problem can be transformed by the Lagrange multiplier method into a problem of finding the extreme value of a single parameter, i.e., finding the extreme value of $\mathit{\alpha }$, written as follows:

$$\begin{array}{l}L\left(\mathit{\omega },b,\mathit{e};\mathit{\alpha }\right)=J\left(\mathit{\omega },\mathit{e}\right)-\\ {\displaystyle \sum _{k=1}^N{\mathit{\alpha }}_{\mathit{k}}\left\{{\mathit{y}}_{\mathit{k}}\left[{\mathit{\omega }}^T\phi ({\mathit{x}}_{\mathit{k}}+b)-1+{\mathit{e}}_{\mathit{k}}\right]\right\}}\end{array}$$

(5)

where $\mathit{\alpha }$ is the Lagrangian daily vector and ${\mathit{\alpha }}_{\mathit{k}}$ is the Lagrangian daily number. Taking the derivatives of $\mathit{\omega }$, $b$, ${\mathit{\alpha }}_{\mathit{k}}$, and ${\mathit{e}}_{\mathit{k}}$, respectively, and making their values 0, we obtain the following:

$$\left\{\begin{array}{l}{\displaystyle \frac{\partial L}{\partial \mathit{\omega }}}=0\to \mathit{\omega }={\displaystyle \sum _{\mathit{k}=1}^N{\mathit{\alpha }}_{\mathit{k}}{\mathit{y}}_{\mathit{k}}\phi ({\mathit{x}}_{\mathit{k}})}\\ {\displaystyle \frac{\partial L}{\partial b}}=0\to {\displaystyle \sum _{\mathit{k}=1}^N{\mathit{\alpha }}_{\mathit{k}}{\mathit{y}}_{\mathit{k}}=0}\\ {\displaystyle \frac{\partial L}{\partial {\mathit{\alpha }}_{\mathit{k}}}}=0\to {\mathit{y}}_{\mathit{k}}[{\mathit{\omega }}^T\phi ({\mathit{x}}_{\mathit{k}}+b)]=1-{\mathit{e}}_{\mathit{k}}\\ {\displaystyle \frac{\partial L}{\partial {\mathit{e}}_{\mathit{k}}}}=0\to {\mathit{\alpha }}_{\mathit{k}}=\gamma {\mathit{e}}_{\mathit{k}}\end{array}\right.$$

(6)

Solving the system of equations, we obtain the following:

$$\mathit{y}\left(\mathit{x}\right)=\sum _{k=1}^N{\mathit{\alpha }}_{\mathit{k}}{\mathit{y}}_{\mathit{k}}K\left(\mathit{x},{\mathit{x}}_{\mathit{k}}\right)+b$$

(7)

This is the expression for the LSSVM pre-diction, where $K\left(\mathit{x},{\mathit{x}}_{\mathit{k}}\right)$ is the kernel function. The kernel function chosen in this paper is the radial basis kernel function because of its excellent performance in terms of its generalization ability and wide convergence domain. The expression of the radial basis kernel function is as follows:

$$K\left({\mathit{x}}_{\mathit{i}},{\mathit{x}}_{\mathit{j}}\right)=\exp \left(-x_i-x_j^2/2{\sigma }^2\right),$$

(8)

where ${\sigma }^2$ is the kernel function parameter. In LSSVM, the kernel function parameter ${\sigma }^2$ and the penalty factor $\gamma$ are the key hyperparameters, which determine the model’s ability to differentiate between data samples, as well as its generalization ability and so on. In order to have the best performance of LSSVM, an optimization algorithm is needed to optimize LSSVM to find the optimal hyperparameter values.

2.4. MPA

In this paper, we cite the MPA [18,19] to find the optimal penalty factor and kernel function parameters of the optimal LSSVM. MPA is a group intelligence algorithm that was proposed in 2020, that was mainly inspired by the predator’s predatory strategy—Levy’s motion and Brownian motion in the ocean. In the context of the continuous change of the prey’s position, we consider the predator as the optimal solution and the prey as the current solution, continuously comparing the fitness values of the predator and the prey, performing eugenics to continuously update the predator’s position, and finally obtaining the best position, i.e., the optimal solution. The MPA algorithm is slightly different from other heuristic algorithms; it is divided into three phases according to the number of iterations, and each phase uses a different strategy to calculate the step size and move the prey position, which has the advantages of strong optimization searching ability and fewer required parameters, etc., and the mathematical description of its optimization process is as follows:

(1)

Initialization phase. To prepare for the optimization phase, the MPA initializes the position of the prey within the search space, a process that is completely randomized by the following formula:

$$X_0=X_{min}+rand(X_{ma\mathit{x}}-X_{min}),$$

(9)

where $X_{min}$, $X_{ma\mathit{x}}$ is the search space and $rand$ is a random number within (0, 1).

(2)

Optimization phase. MPA is divided into three stages: high speed ratio ($t<{\displaystyle \frac{1}{3}}T$), equal speed ratio (${\displaystyle \frac{1}{3}}T<t<{\displaystyle \frac{2}{3}}T$), and low speed ratio ($t>{\displaystyle \frac{2}{3}}T$), where t is the current number of iterations and T is the maximum number of iterations. For each phase, MPA defines different search rules to complete the optimization process.

At the beginning of the iteration, the prey adopts a Brownian motion, and the predator remains stationary, which is the high speed ratio phase. In the pre-iteration, the algorithm has a long step length and is able to have high exploration capability, i.e., global search capability.

In the middle of the iteration, the prey adopts Levi’s motion and focuses on the exploitation task, and the predator adopts Brown’s motion and focuses on the search work and gradually shifts from the exploration strategy to the exploitation strategy, but exploration and exploitation are equally important in this phase. The isochronous ratio stage is at this point.

At the end of the iteration, the predator is based on Levi’s motion and mainly uses the exploitation strategy. This is the low-speed ratio phase.

(3)

FADS effect. The fish aggregation device effect parameter (FADS) temporarily alters the foraging behavior of marine predators. Consideration of this effect enables the MPA to avoid the problem of becoming stuck in local extremes during the optimization process.

(4)

Marine memory. Marine predators can remember regions rich in sources of prey misses. Therefore, after performing the optimization phase of the algorithm and updating the prey matrix and predator matrix, the fitness of each solution in the current iteration is compared with its equivalent in the previous iteration, and if it is more fit, the current solution replaces the previous solution, resulting in the optimal solution.

2.5. Positioning Methods

The indoor visible light fingerprint localization method based on MPA-LSSVM proposed in this paper is divided into the following two main phases: In the offline phase, the fingerprint database is first constructed, where the classified labels are the positional coordinates of the reference points, and the features are the values of the light intensities received by a number of reference points selected in the localization area. Then, the MPA is introduced to iteratively find the optimal and establish the localization model for the two hyperparameters of the LSSVM; in the online stage, the light intensity signal at the preset test point is used as the fingerprint data, inputted into the localization model, and the coordinates of the to-be-measured point are computed and outputted to ultimately realize the localization.

The MPA-LSSVM fingerprint localization modeling process is as follows:

(1)

Perform (0, 1) normalization of the signal strength received by the illuminance meter. The specific formula is as follows:

$$x_i^{\prime }={\displaystyle \frac{x_i-x_{min}}{x_{max}-x_{min}}},$$

(10)

where $x_i$ is the collected fingerprint data; $x_{max}$ and $x_{min}$ are the minimum and maximum values in the sample, respectively; and $x_i^{\prime }$ is the value after normalization.

(2)

Determine the parameters of the MPA algorithm, including the number of prey $n$, the maximum number of iterations $Max\_Iter$, the FADS, and the initial position of the prey $X_0$. Let the optimal position be $X_{best}$.

(3)

Define the fitness function. The fitness function chosen in this paper is as follows:

$$f\left(x\right)={\displaystyle \frac{1}{2n}}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2,$$

(11)

where $n$ is the number of samples, $y_i$ is the true output of the training data $x_i$, and ${\widehat{y}}_i$ is the predicted value of the model for $x_i$. The closer the value converges to 0 the closer the predicted value is to the true value, indicating that the solution obtained is closer to the optimal solution.

(4)

Iterative optimization is performed in each of the three different phases to update the predator’s position iteratively. Calculate the fitness value of the prey position and store the marine memory, integrate the effect of FADS on the fitness value, calculate the optimal predator position based on the prey position and behavior, and finally determine the current optimal position $X_{best}$, and from this, obtain [${\gamma }_{best},{\sigma }_{best}^2$].

(5)

The iteration termination condition is determined. When the iteration proceeds to the maximum number of times or when the predator’s fitness value reaches the preset accuracy, the iteration terminates and outputs the optimal parameter set [${\gamma }_{b\mathit{e}st},{\sigma }_{b\mathit{e}st}^2$], otherwise return to step 4.

(6)

The computed global optimal parameters of the MPA are substituted into the LSSVM to complete the model building for fingerprint localization.

The flowchart for building the MPA-LSSVM fingerprint localization model is shown in Figure 2.

3. Results

3.1. Experimental Platforms

In this paper, relevant experiments are conducted to validate the effectiveness of the proposed method and to evaluate the model performance. The parameters of the LED bulbs used in the transmitter side of the experiment are shown in

Table 1. The technical parameters of LED lights.

Parameter	Value
Voltage/V	220
Power/W	3
Initial light effect/(Lm/W)	70
Luminous flux/Lm	250

. The technical parameters of the illumination used at the receiving end are shown in

Table 2. The technical parameters of illumination.

Illumination	Parameter
Measuring range/Lux	1–200,000
Working voltage/V	4.5
Illumination accuracy	±3% rdg

.

Figure 3 shows the experimental platform constructed in this paper, the size of the experimental platform is 1 m × 1 m × 1 m, and the four LED lights A, B, C, and D are suspended at the top, with the position coordinates of (0.75, 0.25, 1), (0.25, 0.25, 1), (0.25, 0.75, 1), (0.75, 0.75, 1), and (0.75, 0.75, 1), in units of ‘m’, respectively. The illuminance meter is used as a signal receiver and is placed in the positioning area at the bottom of the platform.

In this paper, the fingerprint database is constructed by selecting a total of 441 reference points of 21 × 21 on the receiving plane of 1 m × 1 m at the bottom of the localization place, and the positions of the reference points are denoted as (0.75, 0.25, 1), (0.25, 0.25, 1), (0.25, 0.75, 1), and (0.75, 0.75, 1). The feature vectors of the fingerprint database are composed by collecting the light intensity information received from LED lights at different positions on each reference point, forming a piece of fingerprint data and used to construct a fingerprint database.

We define the error function as follows:

$$E=\sqrt{{\left(x-\widehat{x}\right)}^2+{\left(y-\widehat{y}\right)}^2},$$

(12)

where $\left(x,y\right)$ are the real coordinates of the localization point and $\left(\widehat{x},\widehat{y}\right)$ are the estimated coordinates obtained by MPA-LSSVM modeling.

3.2. Experimental Results

In this paper, 441 sets of training fingerprint samples are selected to train the model, and 121 sets of test data are selected to test the model. The MPA algorithm parameters are set as follows: $n$ = 20, $Max\_It\mathit{e}r$ = 50, FADS = 0.2. The histogram of positioning error is shown in Figure 4, and the positioning error in 0~0.02 m accounts for the largest proportion of 33.9%; points with positioning errors within 0.1 m accounted for 96.7% of the total number of points tested; and the average positioning error for all test points was 0.041 m, which can fully satisfy the positioning requirements under the environmental conditions of 1 m × 1 m × 1 m.

3.3. Algorithm Comparison

The localization error of this method is analyzed in comparison with that of the LSSVM algorithm (not optimized by the marine predator algorithm). The comparison of the localization errors of MPA-LSSVM and LSSVM algorithms is shown in

Table 3. The comparison of positioning errors between MPA-LSSVM and LSSVM.

Localization Algorithm	Max Location Error/m	Average Localization Error/m
MPA-LSSVM	0.1213	0.041
LSSVM	0.2289	0.094

. Compared to the LSSVM algorithm, the MPA-LSSVM algorithm reduced the maximum localization error by 53% and the average localization error by 56.4%.

Next, the commonly used particle swarm optimization (PSO) and genetic algorithms (GA) were experimented with in the context of the data in this paper, and the results were compared with the experimental results of the algorithms in this paper. The same 441 sets of training fingerprint samples from the fingerprint library were selected to train the PSO-LSSVM model and GA-LSSVM model, respectively. The population size and maximum number of iterations of the particle swarm algorithm and genetic algorithm are consistent with MPA, where the acceleration coefficients $c_1$ and $c_2$ of the particle swarm algorithm were set to two and the inertia weights were set to one. The genetic algorithm’s probability of variation is set to 0.02 and the crossover probability is set to 0.7.

These models were tested by selecting 121 sets of test data, respectively, and all experiments were repeated 10 times to take the optimal results and compare them. The cumulative probability distribution of localization errors for the three algorithms is shown in Figure 5.

Positioning point errors for 90% of the MPA, GA, and PSO algorithms are 0.0315 m, 0.0427 m, and 0.1012 m respectively.

The localization error of each of the three algorithms and the number of iterations are shown in

Table 4. The positioning error and iteration times of three algorithms.

Location Algorithm	Max Localization Error/m	Average Localization Error/m	Iteration Times
MPA-LSSVM	0.1213	0.041	21
GA-LSSVM	0.1391	0.057	37
PSO-LSSVM	0.1702	0.085	45

. The maximum localization error, the average localization error, and the number of iterations of the MPA-LSSVM are optimal for all three. The maximum localization error of MPA-LSSVM is reduced by 12.80% compared to GA-LSSVM and 28.73% compared to PSO-LSSVM, the average localization error is reduced by 28.07% compared to GA-LSSVM and 51.76% compared to PSO-LSSVM, and the number of iterations is the lowest of all three, with the least time cost, which fully demonstrates that the MPA-LSSVM localization model has a better performance.

The other three scenarios are discussed next, which include the following:

One LED (lamp A) is on;

Two LEDs (lamp A and lamp B or lamp A and lamp C) are on;

Three LEDs (lamp A, lamp B, and lamp C) are on.

Positioning experiments are carried out in these three cases, and the parameter settings as well as the positioning reference point settings were consistent with those in the previous paper, and each experiment was repeated 10 times, and the optimal results were taken for comparison. The average positioning errors for each case and for 90 percent of the positioning points are given in

Table 5. The average positioning error for three cases and 90% of the positioning points.

The Experimental Environment		Average Localization Error/m	90% of the Positioning Points
One LED	A	0.049	0.039
Two LEDs	A, B	0.046	0.037
	A, C	0.043	0.033
Three LEDs	A, B, C	0.042	0.031

.

The experimental results show that the MPA-LSSVM is able to complete accurate localization in the case of different numbers of LEDs, indicating that it has a good generalization performance.

4. Conclusions

In this paper, an indoor visible light fingerprint localization method based on MPA-LSSVM is proposed. A fingerprint database is constructed by using an illuminometer to receive light intensity data from LEDs, and a marine predator algorithm is introduced to optimize the hyperparameters of the least squares support vector machine to construct a localization model with the optimal hyper-parameters to achieve localization and reduce the time overhead. Experiments were conducted in an indoor environment of 1 m × 1 m × 1 m, and the results showed that the average error of the proposed method was 0.041 m, and the localization error of 96.7% of the test points did not exceed 0.1 m. Compared with several other algorithms, the MPA-LSSVM-based localization method has a higher localization accuracy as well as fewer iterations, which achieves high-precision localization and can meet the needs of most localization services. However, the methodology of this study still has some limitations: The experimental platform is relatively small; therefore, follow-up study should consider gradually expanding the experimental platform. Additionally, the study only discusses the situation of localization in two-dimensional planes; therefore, future studies should consider the situation of localization in three-dimensional space. Finally, the background of this paper is the LoS link; in follow-up studies, it should be considered to include the not-line-of-sight (NLoS) situation.