Author Affiliations
School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, Inner Mongolia, Chinashow less
Fig. 1. Indoor visible light positioning model
Fig. 2. ELM network structure
Fig. 3. Genetic algorithm flow chart
Fig. 4. GA-ELM algorithm flow chart
Fig. 5. Indoor three-dimensional localization distribution map
Fig. 6. Actual coordinates versus system predicted coordinates when receiver is at different altitudes. (a) 0.2 m; (b) 0.4 m; (c) 0.6 m; (d) 0.8 m
Fig. 7. Three-dimensional localization error of system when receiver is at different altitudes. (a) 0.2 m; (b) 0.4 m; (c) 0.6 m; (d) 0.8 m
Fig. 8. Localization error cumulative distribution of the system when receiver is at different altitudes
Fig. 9. Experimental scene and receiving end equipment. (a) Experimental scene; (b) receiving end equipment
Fig. 10. Two-dimensional localization results of GA-ELM
Fig. 11. Localization error histogram
Fig. 12. Cumulative distribution of localization error of GA-ELM and ELM algorithms
Fig. 13. Cumulative distribution of localization error of four algorithms
The number of LED | Max localization error /cm | Average localization error /cm | Localization time /s |
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3 | 99.490 | 10.3500 | 0.0315 | 4 | 3.912 | 0.9418 | 0.0413 | 6 | 4.640 | 0.9500 | 0.0874 |
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Table 1. Simulation results for selecting the number of LED
Parameter | Value |
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Light source emission power /W | 10 | Receiver field of view ψc /(°) | 90 | Filter gain Ts(ψ) | 1 | Concentrator gain g(ψ) | 10 | Effective receiving area of receiver /cm2 | 1 | Angle of half-power ϕ1/2/(°) | 30 | Number of neurons | 225 | Population size | 2 | Chromosome length | 1300 | Maximum number of iteration | 200 | Crossover probability | 0.7 | Mutation probability | 0.01 |
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Table 2. Simulation parameters
Data set | Average localization error /cm | Localization time /s |
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11×11 | 74.6800 | 0.00215 | 21×21 | 0.9214 | 0.04235 | 41×41 | 0.9138 | 0.10940 |
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Table 3. Simulation results for different training data sets
No. | Maximum localization error /cm |
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GA-ELM | ELM |
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1 | 4.10 | 9.76 | 2 | 5.51 | 22.21 | 3 | 4.68 | 13.25 | 4 | 5.27 | 10.63 | 5 | 5.10 | 12.42 | 6 | 4.50 | 12.22 | 7 | 4.32 | 11.88 | 8 | 5.78 | 16.29 | 9 | 3.72 | 15.13 | 10 | 5.82 | 13.60 | Average value /cm | 4.88 | 13.34 | Standard deviation /cm | 0.72 | 3.55 |
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Table 4. Maximum localization error for random 10 estimation results
Localization algorithm | Max localization error /cm | Average localization error /cm |
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GA-ELM | 3.9192 | 0.9214 | GA-BP | 15.33 | 3.72 | SVM | 19.51 | 3.74 | BP | 60.18 | 21.04 |
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Table 5. Comparison of localization errors of different algorithms
Localization algorithm | Average localization time /s |
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GA-ELM | 0.04235 | GA-BP | 0.09237 | SVM | 0.09165 | BP | 0.09301 |
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Table 6. Comparison of localization timeliness of different algorithms