# Graph-Based Semi-Supervised Learning for Indoor Localization Using Crowdsourced Data

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## Abstract

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## 1. Introduction

## 2. Background and Related Works

## 3. Problem Formulation

## 4. Linear Regression Algorithm against Device Diversity Problem

#### 4.1. Pre-Processing of RSS Values

#### 4.2. Linear Regression Algorithm against Device Diversity Problem

- compute ${\mathbf{a}}_{old}$ and ${\mathbf{b}}_{old}:=$ least squares regression estimator based on ${H}_{old}$
- compute the residuals ${d}_{old}\left(i\right)$ for $i=1,\dots ,c$
- sort the absolute values of these residuals, $|{d}_{old}\left(1\right)|\text{}\le |{d}_{old}\left(2\right)|\le \dots \le \text{}|{d}_{old}\left(c\right)|$
- arrange the absolute values of the residuals in ascending order, let ${H}_{new}$ be a subset consisting of the nearest neighbors corresponding to the first h the absolute values of the residuals in the sequence
- compute ${\mathbf{a}}_{new}$ and ${\mathbf{b}}_{new}:=$ least squares regression estimator based on ${H}_{new}$

#### 4.3. Automatic Device-Transparent Algorithm for Crowdsourcing Indoor Localization System

## 5. AP Localization Using Compressed Sensing Method

- ${\mathbf{y}}_{\ell \times M}$ are the compressive noisy RSS measurements.
- ${\mathsf{\Phi}}_{\ell \times N}$ is the measurement matrix. Each row in this matrix represents the location of one RP, with an element of 1 to indicate the grid point at which the RP is located. Thus, only a few of RSS values are collected on the locations of RPs instead of measuring all the RSS values on the overall grid, which reduces the workload in the offline phase.
- ${\mathsf{\Psi}}_{N\times N}$ is the sparsity basis on which the measured signals have sparse coefficients $\mathsf{\Theta}$. In this matrix, ${\mathsf{\Psi}}_{ij}=RSS\left({d}_{ij}\right)$ indicates the RSS values collected at grid point i from the AP located at grip point j, for all $1\le i\le N$ and $1\le j\le N$. Assume that the transmition power of an AP is ${P}_{t}\left(\mathrm{dBm}\right)$. Then $RSS\left(d\right)$ is calculated based on the empirical indoor propagation model of [20]:$$\begin{array}{c}\hfill RSS\left(d\right)=\left\{\begin{array}{cc}{P}_{t}-40.2-20\mathrm{log}\left(d\right),\hfill & \mathrm{if}\text{}d\le 8\hfill \\ {P}_{t}-58.5-33\mathrm{log}\left(d\right),\hfill & \mathrm{if}\text{}d8\hfill \end{array}\right.\end{array}$$
- $\epsilon $ is the measurement noise.

## 6. RSS Difference-Aware Graph-Based Semi-Supervised Learning RSS Smoothing Method

#### 6.1. Estimation of ${\widehat{R}}_{d}({S}_{i},{S}_{j})$

#### 6.1.1. Offline Training Phase

#### 6.1.2. Online Localization Phase

#### 6.2. Finding the Optimal Solution

#### 6.3. Experimental Results

- Set one of the labelled points as unlabelled.
- Use the rest of the labelled points, 125 unlabelled points and RG-SSL method to estimate the RSS value of the above unlabelled point.

## 7. RSS Difference-Aware Sparse Graph-Based Semi-Supervised Learning Method and Experimental Results

#### 7.1. Sparse Graph Construction for RG-SSL Using CS Method

#### 7.2. Experimental Results

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | linear dichroism |

## References

- Sorour, S.; Lostanlen, Y.; Valaee, S.; Majeed, K. Joint indoor localization an radio map construction wiht limited deployment load. IEEE Trans. Mob. Comput.
**2015**, 14, 1031–1043. [Google Scholar] [CrossRef] - Feng, C.; Valaee, S.; Au, A.W.S.; Tan, Z. Received-signal-strength-based indoor positioning using compressive sensing. IEEE Trans. Mob. Comput.
**2012**, 11, 1983–1993. [Google Scholar] [CrossRef] - Gu, Y.; Lo, A.; Niemegeers, I. A survey of indoor positioning systems for wireless personal network. IEEE Commun. Surv. Tutor.
**2009**, 11, 13–32. [Google Scholar] [CrossRef] - Alarifi, A.; Al-Salman, A.; Alsaleh, M.; Alnafessah, A.; Al-Hadhrami, S.; Al-Ammar, M.A.; Al-Khalifa, H.S. Ultra Wideband Indoor Positioning Technologies: Analysis and Recent Advances. Sensors
**2016**, 16, 707. [Google Scholar] [CrossRef] [PubMed] - Feng, C.; Valaee, S.; Tan, Z. Localization of wireless sensors using compressive sensing for manifold learning. In Proceedings of the 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Tokyo, Japan, 13–16 September 2009; pp. 2715–2719. [Google Scholar]
- Harle, R. A survey of indoor inertial positioning systems for pedestrians. IEEE Commun. Surv. Tutor.
**2013**, 15, 1281–1293. [Google Scholar] [CrossRef] - Bahl, P.; Padmanabhan, V. Radar: An in-building RF-based user location and tracking system. In Proceedings of the 2000 Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Tel Aviv, Israel, 26–30 March 2000; pp. 775–784. [Google Scholar]
- Kushki, A.; Plataniotis, K.N.; Venetsanopoulos, A.N. Kernel-based positioning in wireless local area networks. IEEE Trans. Mob. Comput.
**2007**, 6, 689–705. [Google Scholar] [CrossRef] - Rai, A.; Chintalapudi, K.K.; Padmanabhan, V.N.; Sen, R. Zee: Zero-effort crowdsourcing for indoor localization. In Proceedings of the 18th Annual International conference on Mobile Computing Network, Istanbul, Turkey, 22–26 August 2012; pp. 293–304. [Google Scholar]
- Viel, B.; Asplund, M. Why is fingerprint-based indoor localization still so hard? In Proceedings of the 2014 IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOM Workshops), Budapest, Hungary, 24–28 March 2014; pp. 443–448. [Google Scholar]
- Pan, J.J.; Pan, S.J.; Yin, J.; Ni, L.M.; Yang, Q. Tracking mobile users in wireless networks via semi-supervised colocalization. IEEE Trans. Pattern Anal. Mach. Intell.
**2012**, 34, 587–600. [Google Scholar] [CrossRef] [PubMed] - Au, A.W.S.; Feng, C.; Valaee, S.; Reyes, S.; Sorour, S.; Markowitz, S.N.; Gold, D.; Gordon, K.; Eizenman, M. Indoor tracking and navigation using received signal strength and compressive sensing on a mobile device. IEEE Trans. Mob. Comput.
**2013**, 12, 2050–2062. [Google Scholar] [CrossRef] - Redzic, M.; Brennan, C.; O’Connor, N. SEAMLOC: Seamless indoor localization based on reduced number of calibration points. IEEE Trans. Mob. Comput.
**2014**, 13, 1326–1337. [Google Scholar] - Yang, S.; Dessai, P.; Verma, M.; Gerla, M. FreeLoc: Calibration-free crowdsourced indoor localization. In Proceedings of the 32nd IEEE International Conference on Computer Communications (INFOCOM), Turin, Italy, 14–19 April 2013; pp. 2481–2489. [Google Scholar]
- Wu, C.; Yang, Z.; Liu, Y. Smartphones based crowdsourcing for indoor localization. IEEE Trans. Mob. Comput.
**2015**, 14, 444–457. [Google Scholar] [CrossRef] - Yu, N.; Xiao, C.; Wu, Y.; Feng, R. A Radio-Map Automatic Construction Algorithm Based on Crowdsourcing. Sensors
**2016**, 16, 504. [Google Scholar] [CrossRef] [PubMed] - Kaemarungsi, K. Distribution of wlan received signal strength indication for indoor location determination. In Proceedings of the 1st International Symposium on Wireless Pervasive Computing, Phuket, Thailand, 16–18 January 2006; pp. 2952–2957. [Google Scholar]
- Zheng, V.W.; Pan, S.J.; Yang, Q.; Pan, J.J. Transferring Multi-device Localization Models using Latent Multi-task Learning. In Proceedings of the 23rd national conference on Artificial intelligence, Chicago, IL, USA, 13–17 July 2008; pp. 1427–1432. [Google Scholar]
- Tsui, A.W.; Chuang, Y.H.; Chu, H.H. Unsupervised Learning for Solving RSS Hardware Variance Problem in WiFi Localization. Mob. Netw. Appl.
**2009**, 14, 677–691. [Google Scholar] [CrossRef] - Feng, C.; Valaee, S.; Tan, Z. Multiple Target Localization Using Compressive Sensing. In Proceedings of the 2009 IEEE Global Communications Conference (GLOBECOM), Honolulu, HI, USA, 30 November– 4 December 2009; pp. 1–6. [Google Scholar]
- Liu, X.D.; He, W.; Tian, Z.S. The improvement of RSS-based location fingerprint technology for cellular networks. In Proceedings of the 2012 International Conference on Computer Science and Service System (CSSS), Nanjing, China, 11–13 August 2012; pp. 1267–1270. [Google Scholar]
- Hasani, M.; Lohan, E.-S.; Sydanheimo, L.; Ukkonen, L. Path-loss model of embroidered passive RFID tag on human body for indoor positioning applications. In Proceedings of the 2014 IEEE RFID Technology and Applications Conference (RFID-TA), Tampere, Finland, 8–9 September 2014; pp. 170–174. [Google Scholar]
- Latif, S.; Memon, A.; Chawdhry, B.; Zielinski, R.; Khan, G. Accuracy Assessment of D-Model for Modeling Wall Attenuation in Indoor Environment. In Proceedings of the 2014 Sixth International Conference on Computational Intelligence, Communication Systems and Networks (CICSyN), Tetovo, Macedonia, 27–29 May 2014; pp. 71–76. [Google Scholar]
- Zhang, L.; Shahrokh, V.; Zhang, L.; Xu, Y.; Ma, L. Signal propagation-based outlier reduction technique (SPORT) for crowdsourcing in indoor localization using fingerprint. Proceedings of Personal, Indoor, and Mobile Radio Communications (PIMRC), 2015 IEEE 26th Annual International Symposium on, Hong Kong, China, 30 August–2 September 2015; pp. 2008–2013. [Google Scholar]
- Rahman Sakib, M.S.; Quyum, M.A.; Andersson, K.; Synnes, K.; Korner, U. Improving Wi-Fi based indoor positioning using Particle Filter based on signal strength. In Proceedings of the 2014 IEEE Ninth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Singapore, 21–24 April 2014; pp. 1–6. [Google Scholar]
- Ma, L.; Xu, Y. Received signal strength recovery in green WLAN indoor positioning system using singular value threholding. Sensors
**2015**, 15, 1292–1311. [Google Scholar] [CrossRef] [PubMed] - Rousseeuw, P.J.; Driessen, K.V. Computing LTS Regression for Large Data Sets. Data Min. Knowl. Discov.
**2006**, 12, 29–45. [Google Scholar] [CrossRef] - Candès, E.J. Compressive sampling. In Proceedings of the international congress of mathematicians, Madrid, Spain, 22–30 August 2006; pp. 1433–1452. [Google Scholar]
- Baraniuk, R.G. Compressive sensing. IEEE Signal Proc. Mag.
**2007**, 24, 118–121. [Google Scholar] [CrossRef] - Cande`s, E.J.; Wakin, M.B. An introdution to compressive sampling. IEEE Signal Proc. Mag.
**2008**, 25, 21–30. [Google Scholar] [CrossRef] - Chen, S.S.; Donoho, D.L.; Saunders, M.A. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput.
**1998**, 20, 33–61. [Google Scholar] [CrossRef] - Tropp, J.; Gilbert, A. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit. IEEE Trans. Inf. Theory
**2008**, 53, 4655–4666. [Google Scholar] [CrossRef] - Dai, W.; Milenkovic, O. Subspace pursuit for compressive sensing signal reconstruction. IEEE Signal Proc. Mag.
**2009**, 55, 2230–2249. [Google Scholar] [CrossRef] - Pourahmadi, V.; Valaee, S. Indoor Positioning and distance-aware graph-based semi-supervised learning method. In Proceedings of the 2012 IEEE Global Communications Conference (GLOBECOM), Anaheim, CA, USA, 3–7 December 2012; pp. 315–320. [Google Scholar]
- Cheng, B.; Yang, J.; Yan, S.; Fu, Y.; Huang, T.S. Learning with ℓ
^{1}-Graph for image analysis. IEEE Trans. Image Proc.**2010**, 19, 858–866. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**RSS values of an AP over the corridor area of the fourth floor of the Bahen Building, University of Toronto.

**Figure 10.**Comparison of signal distribution of radio map. (

**a**) Original radio map (

**b**) RG-SSL method (

**c**) G-SSL method (

**d**) SCTW method (

**e**) SPORT method

**Figure 11.**Comparison of signal distribution of test data. (

**a**) Original radio map (

**b**) RG-SSL method (

**c**) G-SSL method (

**d**) SCTW method (

**e**) SPORT method

**Figure 12.**Comparison of localization results. (

**a**) Original radio map (

**b**) RG-SSL method (

**c**) G-SSL method (

**d**) SCTW method (

**e**) SPORT method

**Figure 14.**Comparison of Weighted graph. (

**a**) Weighted graph calculated by heat kernel method; (

**b**) Weighted graph calculated by CS method.

**Figure 15.**Smoothed signal distribution of radio map and localization results using RSG-SSL. (

**a**) Smoothed signal distribution of radio map; (

**b**) Localization results.

Algorithm | Cumulative Probability (Location Error Is 2 m) | Average Error (m) | Maximum Error (m) |
---|---|---|---|

RG-SSL | 63.5% | 2.07 | 4 |

G-SSL | 60% | 2.13 | 4.5 |

SPORT | 60% | 2.15 | 4.5 |

SCTW | 54.3% | 2.24 | 5.5 |

Original data | 42.9% | 2.89 | 10 |

© 2017 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/).

## Share and Cite

**MDPI and ACS Style**

Zhang, L.; Valaee, S.; Xu, Y.; Ma, L.; Vedadi, F. Graph-Based Semi-Supervised Learning for Indoor Localization Using Crowdsourced Data. *Appl. Sci.* **2017**, *7*, 467.
https://doi.org/10.3390/app7050467

**AMA Style**

Zhang L, Valaee S, Xu Y, Ma L, Vedadi F. Graph-Based Semi-Supervised Learning for Indoor Localization Using Crowdsourced Data. *Applied Sciences*. 2017; 7(5):467.
https://doi.org/10.3390/app7050467

**Chicago/Turabian Style**

Zhang, Liye, Shahrokh Valaee, Yubin Xu, Lin Ma, and Farhang Vedadi. 2017. "Graph-Based Semi-Supervised Learning for Indoor Localization Using Crowdsourced Data" *Applied Sciences* 7, no. 5: 467.
https://doi.org/10.3390/app7050467