# An Unsupervised Learning Technique to Optimize Radio Maps for Indoor Localization

^{*}

## Abstract

**:**

^{2}, resulted in median accuracies of up to 2.07 m, or a relative improvement of 28.6% with only 15 min of unlabeled training data.

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. Experimental Configuration

^{2}(41 m by 27 m) and is visualized in Figure 2. The inner structure of the building is made of thick concrete walls (gray) and the meeting rooms, offices, and kitchen have plaster walls (amber), wooden doors (brown), and some glass walls (blue).

#### 3.2. Radio Map

- Free-space model [19]: the free-space path loss (FSPL) is the attenuation of radio energy between a sender and receiver antenna in idealized conditions, i.e., the antenna polarizations are perfectly matched, the environment is unobstructed free-space and the antennas are in each others far-field. The FSPL is calculated as follows:$$FSPL=20{log}_{10}\left(d\right)+20{log}_{10}\left(f\right)-27.55$$$FSPL$ [dB] denotes the free-space path loss, d [m] is the distance between the sender and receiver antenna and f [MHz] is the operating frequency, if this is set to 2400 MHz, then the model reduces to:$$FSPL=40.05+20{log}_{10}\left(d\right)$$
- IEEE 802.11 TGn model [20]: the IEEE 802.11 TGn model is a two-slope path loss model, which is suitable for path-loss predictions in office environments. The TGn is calculated as follows:$$TGNL=\left\{\begin{array}{cc}P{L}_{0}+10{n}_{1}{log}_{10}\left(d\right)\hfill & d\le {d}_{br}\hfill \\ P{L}_{0}+10{n}_{2}{log}_{10}\left(d\right)-32\hfill & d>{d}_{br}\hfill \end{array}\right.$$$TGNL$ [dB] denotes the path loss predicted by the TGn model, $P{L}_{0}$ [dB] is the reference path loss and is equal to 40.05 dB, $n1$ and $n2$ are the path loss exponents for the first and second part of the two-slope model and are equal to 2 and 5.2, and ${d}_{br}$ [m] is the breakpoint distance and is equal to 10 m. For $d\le {d}_{br}$, the TGn model equals to the free-space model.
- WHIPP model [21]: the WHIPP model is a theoretical model for indoor environments that includes wall and interaction losses. This model does not use a ray tracing algorithm, but is based on a heuristic algorithm where the dominant path is searched, i.e., the path along which the path loss is the lowest. Here, the path loss values are modeled as:$$WL=\underset{\mathrm{distance}\phantom{\rule{4.pt}{0ex}}\mathrm{loss}}{\underbrace{P{L}_{0}+10\gamma {log}_{10}\left(\frac{d}{{d}_{0}}\right)}}+\underset{\mathrm{cumulated}\phantom{\rule{4.pt}{0ex}}\mathrm{wall}\phantom{\rule{4.pt}{0ex}}\mathrm{loss}}{\underbrace{\sum _{i}{L}_{{W}_{i}}}}+\underset{\mathrm{interaction}\phantom{\rule{4.pt}{0ex}}\mathrm{loss}}{\underbrace{\sum _{j}{L}_{{B}_{j}}}}+{X}_{\sigma}$$$WL$ [dB] denotes the path loss predicted by the WHIPP path loss model, $P{L}_{0}$ [dB] is the path loss at a reference distance ${d}_{0}$ [m], $\gamma $ [-] is the path loss exponent, d [m] is the distance along the path between transmitter and receiver. These two terms represent the path loss due to the traveled distance. The cumulated wall loss represents the sum of all wall losses ${L}_{{W}_{i}}$ when a signal propagates through a wall ${W}_{i}$. The interaction loss represents the cumulated losses ${L}_{{B}_{j}}$ caused by all propagation direction changes ${B}_{j}$ along the path between sender and receiver, and ${X}_{\sigma}$ [dB] is a log-normally distributed variable with zero mean and standard deviation $\sigma $, corresponding to the large-scale shadow fading.

#### 3.3. Self-Calibration

## 4. Unsupervised Learning

#### 4.1. Motivation

**overall deviation**: the overall deviation represents the variation for the whole building and is used as an indication of radio map quality. A value of zero would mean that the measured path losses are exactly equal to the theoretically predicted values at all locations, for all access points.$$RS{S}_{diff}^{i,j}=RS{S}_{meas,sc}^{i,j}-RS{S}_{ref,pl}^{i,j}$$$${\mu}_{diff}^{i}=\frac{1}{{N}_{GP}}\sum _{j}^{{N}_{GP}}RS{S}_{diff}^{i,j}$$$$de{v}_{overall}=\sqrt{\frac{1}{{N}_{AP}\xb7{N}_{GP}}\sum _{i}^{{N}_{AP}}\sum _{j}^{{N}_{GP}}{\left(RS{S}_{diff}^{i,j}-{\mu}_{diff}^{i}\right)}^{2}}$$**room deviation**: the room deviation models the difference between the radio map and the measurements, averaged over a whole room.$$DIF{F}_{room}^{i,k}=\frac{1}{{N}_{GP}^{k}}\sum _{j}^{{N}_{GP}^{k}}RS{S}_{diff}^{i,j}$$$${\mu}_{room}^{i}=\frac{1}{{N}_{rooms}}\sum _{k}^{{N}_{rooms}}DIF{F}_{room}^{i,k}$$$$de{v}_{room}=\sqrt{\frac{1}{{N}_{AP}\xb7{N}_{rooms}}\sum _{i}^{{N}_{AP}}\sum _{k}^{{N}_{rooms}}{\left(DIF{F}_{room}^{i,k}-{\mu}_{room}^{i}\right)}^{2}}$$**local deviation**: the local deviation represents the variation within a room on top of the room deviation, i.e., the differences between measured path loss values and the theoretical path loss values from the radio map are similar within a room but not exactly the same for all locations in this room.$$DIF{F}_{local}^{i,j}=RS{S}_{meas,sc}^{i,j}-RS{S}_{ref,pl}^{i,j}-DIF{F}_{room}^{i,{k}_{j}}$$$${\mu}_{local}^{i}=\frac{1}{{N}_{GP}}\sum _{j}^{{N}_{GP}}DIF{F}_{local}^{i,j}$$$$de{v}_{local}=\sqrt{\frac{1}{{N}_{AP}\xb7{N}_{GP}}\sum _{i}^{{N}_{AP}}\sum _{j}^{{N}_{GP}}{\left(DIF{F}_{local}^{i,j}-{\mu}_{local}^{i}\right)}^{2}}$$

#### 4.2. Route Mapping Filter

#### 4.3. Radio Map Update Step

## 5. Simulation

#### 5.1. Settings

^{2}. The access point configurations are subsets of the access points from Figure 2: a dense scenario with 35 access points (Figure 5a), a normal scenario with 15 access points (Figure 5b), and a sparse scenario with 9 access points (Figure 5c). The WHIPP path loss model serves as basis to simulate real measurements because this model resembles a real-world scenario more closely [21], as shown in Section 4.1.

#### 5.2. Results

#### 5.2.1. Influence of Room and Local Deviation

#### 5.2.2. Influence of Additional Noise

## 6. Experimental Validation

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flow graph of the proposed technique to construct and optimize a model-based radio map. ${N}_{IT}$ is the current training iteration.

**Figure 2.**Floorplan of the office building with indication of walls, doors, elevators, access points (blue dots), and static validation locations (red squares) where a mobile node broadcasted packets at 5 Hz.

**Figure 3.**Tripod with battery powered mobile node and ceiling mounted fixed access points in corridor.

**Figure 4.**Average difference between model-based radio map and measurements, grouped per room, for one access point (green dot), before (

**a**–

**c**) and after the unsupervised learning (

**d**–

**f**).

**Figure 5.**Location of the access points for the simulated scenarios with 35, 15, and 9 fixed access points: dense (

**a**), normal (

**b**), and sparse (

**c**) configuration. The relative improvement in median accuracy after unsupervised learning with 1 h of unlabeled training data, evaluated on 1000 uniformly spread locations for the three scenario’s (

**d**–

**f**). The median accuracy before (

**g**–

**i**) and after learning (

**j**–

**l**) for the three scenario’s. The room deviation (x-axis) and local deviation (y-axis) vary from 0 dB to 16 dB in steps of 2 dB.

**Figure 6.**Accuracy before and after unsupervised learning for a varying level of additional noise with the normal access point configuration.

**Figure 8.**Cumulative distribution function of the localization accuracy before (dashed line) and after training (solid line), for the three access point configurations and the WHIPP path loss model.

**Table 1.**Experimentally measured differences and deviations compared to the theoretical path loss models after self-calibration.

Path Loss Model | Difference [dB] | Deviation [dB] | ||||
---|---|---|---|---|---|---|

min | max | avg | Overall | Room | Local | |

Free-space | −30.3 | 19.7 | −0.4 | 10.9 | 9.7 | 3.5 |

IEEE 802.11 TGn | −37.5 | 19.1 | −0.7 | 9.6 | 8.8 | 3.5 |

WHIPP | −22.0 | 24.0 | 0.8 | 7.6 | 5.7 | 3.7 |

**Table 2.**Accuracy of experimental validation test set per access point (AP) configuration and path loss (PL) model. The first and second value are the accuracy before and after training and the third value is the relative improvement.

#APs | PL Model | Accuracy [m] | |||
---|---|---|---|---|---|

μ | σ | 50th | 75th | ||

9 (sparse configuration) | Free-space | 5.04 → 5.11 (−1.3%) | 3.93 → 3.98 (−1.3%) | 4.12 → 3.93 (4.8%) | 6.50 → 6.35 (2.2%) |

TGn | 4.35 → 4.23 (2.9%) | 3.73 → 3.72 (0.3%) | 3.14 → 3.07 (2.1%) | 5.72 → 5.13 (10.4%) | |

WHIPP | 4.66 → 3.77 (19.0%) | 3.24 → 2.49 (23.3%) | 3.94 → 3.03 (23.3%) | 5.97 → 4.83 (19.1%) | |

15 (normal configuration) | Free-space | 4.28 → 3.97 (7.4%) | 3.43 → 2.88 (16.1%) | 3.49 → 3.40 (2.4%) | 5.03 → 4.99 (0.8%) |

TGn | 4.22 → 3.96 (6.0%) | 3.48 → 3.18 (8.7%) | 3.42 → 3.31 (3.2%) | 5.42 → 4.71 (13.0%) | |

WHIPP | 4.33 → 3.50 (19.1%) | 2.98 → 2.38 (20.0%) | 3.50 → 3.02 (13.7%) | 6.03 → 4.44 (26.4%) | |

35 (dense configuration) | Free-space | 3.13 → 3.22 (−2.9%) | 3.09 → 2.62 (15.5%) | 2.40 → 2.30 (4.1%) | 3.61 → 3.98 (−10.4%) |

TGn | 3.65 → 2.92 (20.1%) | 3.18 → 2.10 (33.9%) | 2.75 → 2.43 (11.7%) | 4.51 → 3.65 (19.1%) | |

WHIPP | 3.23 → 2.66 (17.6%) | 2.14 → 1.74 (18.7%) | 2.90 → 2.07 (28.6%) | 4.31 → 3.52 (18.4%) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Trogh, J.; Joseph, W.; Martens, L.; Plets, D.
An Unsupervised Learning Technique to Optimize Radio Maps for Indoor Localization. *Sensors* **2019**, *19*, 752.
https://doi.org/10.3390/s19040752

**AMA Style**

Trogh J, Joseph W, Martens L, Plets D.
An Unsupervised Learning Technique to Optimize Radio Maps for Indoor Localization. *Sensors*. 2019; 19(4):752.
https://doi.org/10.3390/s19040752

**Chicago/Turabian Style**

Trogh, Jens, Wout Joseph, Luc Martens, and David Plets.
2019. "An Unsupervised Learning Technique to Optimize Radio Maps for Indoor Localization" *Sensors* 19, no. 4: 752.
https://doi.org/10.3390/s19040752