# An Information-Based Approach to Precision Analysis of Indoor WLAN Localization Using Location Fingerprint

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. System Description

#### 3.1. System Overview

#### 3.2. Fundamental Limit of Localization Precision

#### 3.2.1. Localization Precision vs. Signal Distributions

#### Analysis with Gaussian signal distribution

#### Analysis with Rayleigh signal distribution

#### 3.2.2. Impact of the AP Number

**Figure 3.**CDFs of errors with different AP numbers in the LOS environment. (

**a**) Under the Gaussian signal distribution; (

**b**) under the Rayleigh signal distribution.

**Figure 4.**CDFs of errors with different AP numbers in the non-LOS (NLOS) environment. (

**a**) Under the Gaussian signal distribution; (

**b**) under the Rayleigh signal distribution.

#### 3.2.3. Impact of Noise Variance

**Figure 5.**CDFs of errors with different variance of noise in the LOS environment. (

**a**) Under the Gaussian signal distribution; (

**b**) under the Rayleigh signal distribution.

**Figure 6.**CDFs of errors with different variances of noise in the NLOS environment. (

**a**) Under the Gaussian signal distribution; (

**b**) under the Rayleigh signal distribution.

#### 3.2.4. Fundamental Limit with a Mixed Signal Distribution

#### 3.3. AP Placement Optimization

## 4. Simulation Results

Parameters | Values |
---|---|

Platform | MATLAB 7.0 |

Carrier frequency | 2.4 GHz |

$P\left(\right)open="("\; close=")">{d}_{0}$ | −28 dBm |

β | 2.2 |

Number of candidate AP locations | 144 (LOS), 176 (NLOS) |

Number of RPs | 144 (LOS), 176 (NLOS) |

Number of test points | 100 |

Dimensions of the target environment | $12\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\times 12\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ (LOS), $36\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\times 21\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ (NLOS) |

k | 3 |

${T}_{0}$ | 200 |

N | 500 |

α | 0.95 |

${T}_{\mathrm{S}}$ | 0.1 |

${P}_{w}$ | 10 |

#### 4.1. Regular LOS Environment

**Figure 9.**CDFs of errors in the regular LOS environment. (

**a**) With one AP; (

**b**) with two APs; (

**c**) with three APs; (

**d**) with four APs.

#### 4.2. Irregular NLOS Environment

**Figure 11.**CDFs of errors in the irregular NLOS environment. (

**a**) With one AP; (

**b**) with two APs; (

**c**) with three APs; (

**d**) with four APs.

#### 4.3. Computation Overhead

## 5. Discussion

**Figure 14.**Placement of the optimal AP locations. (

**a**) With three APs; (

**b**) with four APs; (

**c**) with five APs; (

**d**) with six APs; (

**e**) with seven APs; (

**f**) with eight APs; (

**g**) with nine APs; (

**h**) with 10 APs.

**Figure 15.**CDFs of errors under different signal distributions. (

**a**) With three APs; (

**b**) with four APs; (

**c**) with five APs; (

**d**) with six APs; (

**e**) with seven APs; (

**f**) with eight APs; (

**g**) with nine APs; (

**h**) With 10 APs.

## 6. Case Study

**Figure 17.**Experimental platform of WLAN RSS recording. (

**a**) Deployment of D-link DAP-2310 APs; (

**b**) interface of WLAN RSS.

#### 6.1. CDFs of Errors with Different AP Numbers

**Figure 18.**CDFs of errors with different AP numbers. (

**a**) Under the Gaussian signal distribution; (

**b**) under the Rayleigh signal distribution; (

**c**) under the mixed signal distribution.

#### 6.2. CDFs of Errors by Using Different AP Optimization Approaches

**Figure 19.**CDFs of errors by using different AP optimization approaches. (

**a**) With three APs; (

**b**) with four APs; (

**c**) with five APs; (

**d**) with six APs.

#### 6.3. Positioning Errors under Different Signal Distributions

AP Number | Gaussian Signal Distribution | Rayleigh Signal Distribution | Mixed Signal Distribution |
---|---|---|---|

2 | 3.884 m | 5.360 m | 3.225 m |

3 | 2.911 m | 2.974 m | 2.701 m |

4 | 2.494 m | 2.210 m | 2.210 m |

5 | 2.255 m | 1.966 m | 1.966 m |

6 | 2.032 m | 1.884 m | 1.954 m |

7 | 1.8998 m | 1.819 m | 1.819 m |

#### 6.4. Time Overhead by Using Different AP Optimization Approaches

#### 6.5. Extension to a Multi-Floor Environment

#### 6.5.1. CDFs of Errors by Using Different AP Optimization Approaches

**Figure 22.**CDFs of errors by using different AP optimization approaches. (

**a**) With three APs; (

**b**) with four APs; (

**c**) with five APs; (

**d**) with six APs.

#### 6.5.2. Positioning Errors under Different Signal Distributions

AP Number | Gaussian Signal Distribution | Rayleigh Signal Distribution | Mixed Signal Distribution |
---|---|---|---|

3 | 5.07 m | 3.65 m | 3.65 m |

4 | 3.55 m | 3.59 m | 3.26 m |

5 | 3.25 m | 3.31 m | 3.19 m |

6 | 3.12 m | 3.32 m | 3.12 m |

7 | 3.08 m | 2.93 m | 2.87 m |

8 | 2.87 m | 3.02 m | 2.78 m |

9 | 2.77 m | 2.77 m | 2.77 m |

AP Number | Gaussian Signal Distribution | Rayleigh Signal Distribution | Mixed Signal Distribution |
---|---|---|---|

3 | ③⑤⑨ | ④⑥⑦ | ④⑥⑦ |

4 | ③④⑤⑦ | ①④⑦⑧ | ④⑤⑥⑦ |

5 | ③④⑥⑦⑧ | ①③⑥⑧⑨ | ②④⑥⑦⑧ |

6 | ②③④⑥⑧⑨ | ①③⑤⑥⑦⑧ | ②③④⑥⑦⑧ |

7 | ②③⑤⑥⑦⑧⑨ | ③④⑤⑥⑦⑧⑨ | ①②③④⑥⑦⑧ |

8 | ①②③④⑤⑥⑦⑧ | ①③④⑤⑥⑦⑧⑨ | ①②③④⑥⑦⑧⑨ |

9 | ①②③④⑤⑥⑦⑧⑨ | ①②③④⑤⑥⑦⑧⑨ | ①②③④⑤⑥⑦⑧⑨ |

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Zhou, M.; Qiu, F.; Tian, Z.; Wu, H.; Zhang, Q.; He, W.
An Information-Based Approach to Precision Analysis of Indoor WLAN Localization Using Location Fingerprint. *Entropy* **2015**, *17*, 8031-8055.
https://doi.org/10.3390/e17127859

**AMA Style**

Zhou M, Qiu F, Tian Z, Wu H, Zhang Q, He W.
An Information-Based Approach to Precision Analysis of Indoor WLAN Localization Using Location Fingerprint. *Entropy*. 2015; 17(12):8031-8055.
https://doi.org/10.3390/e17127859

**Chicago/Turabian Style**

Zhou, Mu, Feng Qiu, Zengshan Tian, Haibo Wu, Qiao Zhang, and Wei He.
2015. "An Information-Based Approach to Precision Analysis of Indoor WLAN Localization Using Location Fingerprint" *Entropy* 17, no. 12: 8031-8055.
https://doi.org/10.3390/e17127859