## 3 Results
### 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  
Figure 4: The histogram of positioning error.  
Figure 3: The experimental platform.  
of the localization errors of MPA-LSSVM and LSSVM algorithms is shown in Table 3. 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 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.  
Figure 5: The cumulative distribution of positioning errors.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Localization Algorithm** & **Max Location Error/m** & **Average Localization Error/m** \\ \hline MPA-LSSVM & 0.1213 & 0.041 \\ LSSVM & 0.2289 & 0.094 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The comparison of positioning errors between MPA-LSSVM and LSSVM.  
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 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.