# Indoor Location Sensing with Invariant Wi-Fi Received Signal Strength Fingerprinting

^{*}

## Abstract

**:**

## 1. Introduction

- A new method is introduced by resorting to invariant RSS statistics as the reference in fingerprinting, together with the effective RSS readings chosen as input data, which make the proposed fingerprinting accurate and robust against random spatiotemporal disturbances.
- The automatic removal of ineffective Wi-Fi signal sources in the process of soliciting effective RSS readings makes the proposed method efficient in fingerprinting with the in-situ reduction in the dimensions of decision space.
- A proposed design guideline is presented as a rule of thumb for estimating the number of Wi-Fi signal sources required to be available for any given number of calibration locations under a certain level of random spatiotemporal disturbances. This will serve as a key guideline for the benefits of the society who wish to employ invariant RSS-based indoor localization using Wi-Fi fingerprinting.
- Our method requires no recalibration once the invariant RSS statistics are set initially, unlike conventional methods which require recalibration after a certain period of time. This contributes better localization success rate with stable performance in time.

## 2. Related Work

## 3. Methodology

#### 3.1. Invariant Wi-Fi RSS Method

**s**

_{i}(t)}

_{j}, at time t at a particular calibration location j due to m Wi-Fi sources, i = 1, …, m, is represented as:

**s**, is used to represent it as a random variable.

**s**

_{i,j}(t), the RSS from the ith Wi-Fi source at the jth calibration location, as:

_{i,j}represents the time-invariant RSS with no spatiotemporal disturbances present,

**α**

_{i,j}(t) the multiplicative signal alteration factor to account for the spatiotemporal disturbances of r

_{i,j}, and

**δ**

_{i,j}the sensor noise. Note that we introduce r

_{i,j}as the ideal time-invariant signal attenuated by the distance from the signal source i to the location j through the invariant channel characteristics, taking only fixed building infrastructure and furniture layout into consideration.

**s**

_{i,j}(t), is then considered as the alteration of r

_{i,j}by

**α**

_{i,j}(t), 0 <

**α**

_{i,j}≤ 1, reflecting the stochastic channel characteristics due to randomly moving people and/or objects as well as randomly orienting smartphone users disturbing the channel during RSS measurement.

**ŝ**

_{i,j}(t), as

**s**

_{i,j}(t) with minimal random spatiotemporal disturbances, i.e.,

**α**

_{i,j}≈ 1. Then, from Equation (2):

**ŝ**

_{i,j}(t) ≈ r

_{i,j}+

**δ**

_{i,j}

**ŝ**

_{i,j}(t) comes mostly from sensor noise,

**δ**

_{i,j}, multiple measurements of

**ŝ**

_{i,j}(t) form a cluster around r

_{i,j}, the statistics of which is governed by that of

**δ**

_{i,j}. Assuming that the statistics of

**δ**

_{i,j}are time-invariant, so is

**ŝ**

_{i,j}(t). For convenience, the statistics of

**ŝ**

_{i,j}(t) are represented as a random variable,

**s**

_{i,j}. Then, at the calibration location j with m available Wi-Fi sources, an m dimensional vector of invariant RSS statistics, {

**s**

_{i}}

_{j}, i = 1, ..., m, is defined. For the pattern classification point of view, {

**s**

_{i}}

_{j}represents the jth reference pattern class in the m dimensional space of Wi-Fi sources. The small blue ellipses in Figure 2 schematically represent three invariant reference pattern classes, {

**s**

_{i}}

_{j}, j = 1, 2, 3, in two-dimensional Wi-Fi source space i = 1, 2. Notice that the red ellipses surrounding the blue ellipses represent spatiotemporally varying RSS statistics.

_{i}(t)}, captured at an unknown location is done by identifying the reference pattern class among {

**s**

_{i}}

_{j}, j = 1, …, n, that maximally support {s

_{i}(t)}. The support of {s

_{i}(t)} by the reference pattern class j is defined here as the number of s

_{i}(t) that fall in

**s**

_{i,j}for i = 1, …, m, or the sum of the likelihood probabilities of s

_{i}(t) to belong to

**s**

_{i,j}, for i = 1,…, m. Note that, in counting the number or summing the likelihood probabilities, only those s

_{i}(t) having a sufficiently high level of statistical confidence as a member of

**s**

_{i,j}are allowed to participate in the sum, while excluding others. That is, s

_{i}(t) ∈

**s**

_{i,j}, for i = 1, …, m, when the following equation is satisfied:

**s**

_{i,j}) and σ(

**s**

_{i,j}) are the mean and the standard deviation of

**s**

_{i,j}.

Algorithm 1. Pseudocode of the localization phase in estimating the user’s location based on real-time spontaneous sensed Wi-Fi RSS vector. |

Input: Spontaneous RSS Vector Measurement {s_{i}(t)}Output: Estimated Location L∈{1,..,n} |

1: m ← Number of Wi-Fi Sources |

2: n ← Number of Calibration Locations |

3: s_{i,j} ← A component of {s_{i}}_{j}, representing Invariant RSS Pattern for the ith Wi-Fi source at Calibration Location j |

4: σ(s_{i,j}) ← Standard Deviation of s_{i,j} |

5: ξσ(s_{i,j}) ← Decision Margin |

6: for j = 1 to n do |

7: for i = 1 to m do |

8: if s_{i}(t) ∈ s_{i,j}, i.e., |s_{i}(t) - Mean of s_{i,j} | < ξσ(s_{i,j}) then |

9: Either sum(j) ← sum(j) + 1 or sum(j) ← sum(j) + Pr(s _{i}(t)| s_{i,j}) |

10: end if |

11: end for |

12: if sum(j) > Maximum (default: Maximum = 0.0) then |

13: Maximum = sum(j) |

14: L ← j |

15: else if sum(j)= Maximum then |

16: L ← 0 |

17: end if |

18: end for |

19: if L = 0 then |

20: Reject and Recapture Signals |

21: end if |

_{i}(t) having a sufficiently high level of statistical confidence as a member of

**s**

_{i,j}, are selected to participate in classification in comparison to the conventional methods that takes all available RSS to participate in the classification. This will cause the proposed method deliver better performance with the low variance, thus, preventing RSS instability effects as encountered by the conventional methods. The other advantage of our proposed method is that by a proper choice of decision margin, a minimal false negative can be achieved with the expense of rejections. The slight rise in rejections is handled by repeating location queries which ultimately produces true positives. Experiments demonstrating the superior performance of our proposed method are detailed in Section 4.

#### 3.2. Design Guideline of Invariant RSS Based Wi-Fi Fingerprinting

#### 3.2.1. Design Guideline Development Procedure

**Step 1: Invariant Reference RSS Generation**

**s**

_{i}(t)}

_{j}with

**α**

_{i,j}≈ 1. We generate the signal propagation values based on the

**ŝ**

_{i,j}(t) as defined in Equation (3). The value of

**ŝ**

_{i,j}(t) is based on r

_{i,j}, where r

_{i,j}is the ideal time-invariant signal attenuated by the distance from the Wi-Fi signal source i to the location j through the invariant channel characteristics, taking only fixed building infrastructure and furniture layout into consideration. In the invariant RSS values generation, we set the following number of Wi-Fi signal sources m and the number of calibration locations n as defined in Table 1 to the same setup area.

**Step 2: Invariant Reference Pattern Classes Formulation**

**s**

_{i}}

_{j}, as mentioned in Figure 1, are set and the invariant reference pattern classes are defined. At each calibration location j, with all available Wi-Fi signal sources, i = 1, 2, ..., m, will produce an m dimensional invariant RSS statistics vector, {

**s**

_{i}}

_{j}. From the invariant RSS statistics, the reference pattern classes are formulated and stored in a database.

**Step 3: Spontaneous RSS Generation**

_{i,j}, due to the moving people and objects that may disrupt the channel and/or the orientation of the smartphone user disturbing or blocking the channel at the time of Wi-Fi sensor measure the RSS. The effect of α

_{i,j}on spontaneous RSS is represented by a multiplication coefficient to invariant reference RSS by executing Equation (2). The explanation of each parameter in the equation are already mentioned in Section 3.1. The level of α

_{i,j}values is selected in 0.1 intervals. At each level of α

_{i,j}, the associated α to each Wi-Fi source is distributed in the uniform random distribution of sigmoid function as:

**Step 4: Effective Invariant RSS Selection**

**Step 5: Class Separation Degree Computation**

_{i,j}= 0.4, and remains 100% when α

_{i,j}is incremented. Although it remains 100% as it is incremented, the numbers of Wi-Fi signals that can discriminate/separate each calibrated location are also getting higher. This shows that higher values of α

_{i,j}will give better location separation options.

#### 3.2.2. Proposed Design Guideline

## 4. Evaluation and Results

#### 4.1. Experimental Setup

^{2}area on a floor of a building. There are 25 Wi-Fi signals available for fingerprinting with 20 calibration locations assigned based on 4 m × 4 m as the initial resolution. The resolution will be increased and decreased during the comparative investigation of different calibration location resolutions (resolution between 1 m × 1 m and 6 m × 6 m). The calibration locations are the point that has been used to collect the readings of the Wi-Fi RSS data. Figure 7a depicts the floor map of the experimental area with all 20 calibration locations (Loc. 1 to Loc. 20). Each calibration location is within equal distance from each other based on the specified resolution and it is being marked on the floor for easy identification. In the training phase, 100 invariant RSS data are collected at each calibration location to form invariant reference class patterns. To collect invariant RSS data with minimal random spatiotemporal disturbances, the data are collected after midnight when no random disturbance such as human is present. Furthermore, a smartphone is placed on a pinnacle of the head of a remotely controlled robot to avoid any blocking effect of the Wi-Fi sensor. The smartphone collects Wi-Fi RSS at a particular calibration location and the RSS data is sent to a server, and the readings are tagged to the location associated with it. Figure 7b illustrates the robot that has been used during data collection. However, during the testing stage in the localization phase, the smartphone could either be held by a human or attached to a robot to obtain a real spontaneous RSS measurement. Meanwhile, for performance comparison, the conventional non-invariant reference class patterns are formed with 100 spontaneous RSS data collected at each calibration location in normal office hours when people may be present in rooms and corridors. A Samsung Galaxy S4 smartphone with Android version 4.4.2 is used in the experiment.

#### 4.2. Comparison of Success Rate and Its Temporal Variation

#### 4.3. Comparison of Success Rate at Different Resolution of Calibration Locations

#### 4.4. Comparison of Performance from Samples Collected over Different Length of Time

#### 4.5. Computational Complexity Analysis

#### 4.6. Application Model Implementation

## 5. Theoretical Analysis

**s**

_{i,j}) in Algorithm 1), γ < λ, around their means, as shown in Figure 13. Note that the above simulation model used for RSS distributions is not realistic but intended to show the performance of proposed method under harsh conditions. However, in our experiments, the sensor noise

**δ**

_{i,j}is found to be bounded by 3 dBm independent of calibration locations. Therefore, the decision margin ξσ(

**s**

_{i,j}) in Algorithm 1 or γσ in Figure 13 is set as 3 dBm in real experiments.

_{1}and P

_{2}(refer to Figure 13). Then, the probability that l and m Wi-Fi sources fall within the right and wrong calibration locations, respectively, can be computed by:

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Medina, C.; Segura, J.C.; De la Torre, A. Ultrasound Indoor Positioning System Based on a Low-Power Wireless Sensor Network Providing Sub-Centimeter Accuracy. Sensors
**2013**, 13, 3501–3526. [Google Scholar] [CrossRef] [PubMed] - Zhuang, Y.; Yang, J.; Li, Y.; Qi, L.; El-Sheimy, N. Smartphone-Based Indoor Localization with Bluetooth Low Energy Beacons. Sensors
**2016**, 16. [Google Scholar] [CrossRef] [PubMed] - Ni, L.M.; Liu, Y.; Lau, Y.C.; Patil, A.P. LANDMARC: Indoor Location Sensing Using Active RFID. Wirel. Netw.
**2004**, 10, 701–710. [Google Scholar] [CrossRef] - Lee, S.; Ha, K.N.; Lee, K.C. A Pyroelectric Infrared Sensor-based Indoor Location-Aware System for the Smart Home. IEEE T. Consum. Electr.
**2006**, 52, 1311–1317. [Google Scholar] [CrossRef] - Gezici, S.; Tian, Z.; Giannakis, G.B.; Kobayashi, H.; Molisch, A.F.; Poor, H.V.; Sahinoglu, Z. Localization via Ultra-Wideband Radios: A Look at Positioning Aspects for Future Sensor Networks. IEEE Signal Proc. Mag.
**2005**, 22, 70–84. [Google Scholar] [CrossRef] - Zhao, Y.; Dong, L.; Wang, J.; Hu, B.; Fu, Y. Implementing Indoor Positioning System via ZigBee Devices. In Proceedings of the 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 26–29 October 2008; pp. 1867–1871.
- Deng, Z.; Wang, G.; Qin, D.; Na, Z.; Cui, Y.; Chen, J. Continuous Indoor Positioning Fusing WiFi, Smartphone Sensors and Landmarks. Sensors
**2016**, 16, 1427. [Google Scholar] [CrossRef] [PubMed] - Curran, K.; Furey, E.; Lunney, T.; Santos, J.; Woods, D.; McCaughey, A. An Evaluation of Indoor Location Determination Technologies. J. Locat. Based Serv.
**2011**, 5, 61–78. [Google Scholar] [CrossRef] - Kaemarungsi, K.; Krishnamurthy, P. Analysis of WLAN’s Received Signal Strength Indication for Indoor Location Fingerprinting. Pervasive Mob. Comput.
**2012**, 8, 292–316. [Google Scholar] [CrossRef] - Bahl, P.; Padmanabhan, V.N. RADAR: An In-building RF-based User Location and Tracking System. In Proceedings of the IEEE 19th International Conference on Computer Communications, Tel Aviv, Israel, 26–30 March 2000; pp. 775–784.
- Eisa, S.; Peixoto, J.; Meneses, F.; Moreira, A. Removing Useless APs and Fingerprints from WiFi Indoor Positioning Radio Maps. In Proceedings of the IEEE 4th International Conference on Indoor Positioning and Indoor Navigation, Belfort-Montbeliard, France, 28–31 October 2013; pp. 1–7.
- Dawes, B.; Chin, K.-W. A Comparison of Deterministic and Probabilistic Methods for Indoor Localization. J. Syst. Softw.
**2011**, 84, 442–451. [Google Scholar] [CrossRef] - Bolliger, P. Robust Indoor Positioning through Adaptive Collaborative Labeling of Location Fingerprints. Ph.D. Thesis, ETH Zurich, Zurich, Switzerland, February 2011. [Google Scholar]
- Kjærgaard, M.B. Indoor Location Fingerprinting with Heterogeneous Clients. Pervasive Mob. Comput.
**2011**, 7, 31–43. [Google Scholar] [CrossRef] - Narzullaev, A.; Park, Y.; Yoo, K.; Yu, J. A Fast and Accurate Calibration Algorithm for Real-Time Locating Systems Based on the Received Signal Strength Indication. AEU Int. J. Electron. Commun.
**2011**, 65, 305–311. [Google Scholar] [CrossRef] - Milioris, D.; Tzagkarakis, G.; Papakonstantinou, A.; Papadopouli, M.; Tsakalides, P. Low-Dimensional Signal-Strength Fingerprint-Based Positioning in Wireless LANs. Ad Hoc Netw.
**2014**, 12, 100–114. [Google Scholar] [CrossRef] - Narzullaev, A.; Park, Y. Novel Calibration Algorithm for Received Signal Strength Based Indoor Real-Time Locating Systems. AEU Int. J. Electron. Commun.
**2013**, 67, 637–644. [Google Scholar] [CrossRef] - Gutierrez, N.; Belmonte, C.; Hanvey, J.; Espejo, R.; Dong, Z. Indoor Localization for Mobile Devices. In Proceedings of the 11th IEEE International Conference on Networking, Sensing and Control, Miami, FL, USA, 7–9 April 2014; pp. 173–178.
- Husen, M.N.; Lee, S. Indoor Human Localization with Orientation Using Wi-Fi Fingerprinting. In Proceedings of the ACM 8th International Conference on Ubiquitous Information Management and Communication, Siem Reap, Cambodia, 9–11 January 2014.
- Martin, E.; Vinyals, O.; Friedland, G.; Bujcsy, R. Precise Indoor Localization using Smart Phones. In Proceedings of the ACM Multimedia, Firenze, Italy, 25–29 October 2010; pp. 787–790.
- Shin, B.-J.; Lee, K.-W.; Choi, S.-H.; Kim, J.-Y.; Lee, W.J.; Kim, H.S. Indoor Wifi Positioning System for Android-Based Smartphone. In Proceedings of the International Conference on Information and Communication Technology Convergence, Jeju Island, Korea, 17–19 November 2010.
- Chen, Q. A Rule-Based Approach to Indoor Localization Based on Wifi Signal Strengths. Ph.D. Thesis, Hong Kong University of Science and Technology, Hong Kong, China, August 2012. [Google Scholar]
- Luo, Y.; Hoeber, O.; Chen, Y. Enhancing Wi-Fi Fingerprinting for Indoor Positioning Using Human-Centric Collaborative Feedback. Hum. Centric Comput. Inf. Sci.
**2013**, 3. [Google Scholar] [CrossRef] [Green Version] - So, J.; Lee, J.-Y.; Yoon, C.-H.; Park, H. An Improved Location Estimation Method for Wifi Fingerprint-Based Indoor Localization. Int. J. Softw. Eng. Appl.
**2013**, 7, 77–86. [Google Scholar] - Chan, E.C.L.; Baciu, G.; Mak, S.C. Orientation-based Wi-Fi Positioning on the Google Nexus One. In Proceedings of the 6th IEEE International Conference on Wireless and Mobile Computing, Networking and Communications, Niagara Falls, ON, Canada, 11–13 October 2010; pp. 392–397.
- Husen, M.N.; Lee, S. Indoor Location Wi-Fi Fingerprinting Using Invariant Received Signal Strength. In Proceedings of the International Conference on Engineering Technology and Entrepreneurship, Kuala Lumpur, Malaysia, 16–18 November 2015.
- Sánchez-Rodríguez, D.; Hernández-Morera, P.; Quinteiro, J.M.; Alonso-González, I. A Low Complexity System Based on Multiple Weighted Decision Trees for Indoor Localization. Sensors
**2015**, 15, 14809–14829. [Google Scholar] [CrossRef] [PubMed] - Husen, M.N.; Lee, S. High Performance Indoor Location Wi-Fi Fingerprinting Using Invariant Received Signal Strength. In Proceedings of the ACM 10th International Conference on Ubiquitous Information Management and Communication, Danang, Vietnam, 4–6 January 2016.

**Figure 1.**Proposed method of the smartphone-based indoor location fingerprinting based on invariant Wi-Fi received signal strength.

**Figure 2.**Schematic representation of three reference pattern classes in 2-dimensional Wi-Fi source space that illustrates the difference between the distribution of invariant reference pattern classes (small blue ellipses) and the spatiotemporal varying RSSs (large red ellipses).

**Figure 4.**The visual representation of setup area to generate invariant reference RSS with 20 Wi-Fi signal sources i = 1, 2, …, m; and seven calibration locations j = 1, 2, …, n; (m = 20, n = 7).

**Figure 5.**An example of the visualization in computing the class separation degree at (n = 7, m = 20). This example showing the computation of the class separation degree at different levels of disturbance: α = 0.1, 0.2, 0.3, 0.4, 0.5, and 0.7.

**Figure 6.**Design guideline for the number of Wi-Fi signal sources (m) and level of disturbance (α) for a given number of calibration locations (n) to achieve certain class separation degree.

**Figure 7.**(

**a**) The initial experiment floor map area with marked calibration locations. Later, the number of calibration locations are increased and decreased according to its resolution; (

**b**) The robot attached with a smartphone Wi-Fi sensor used in sensing invariant Wi-Fi RSS data collection. The collected data are sent through the network and stored in a server.

**Figure 8.**The success rate of the proposed method (green) in comparison with that of the conventional methods (red and blue), where the temporal variation over 18 weeks span is clearly shown. It is verified that the recalibration applied to the conventional methods puts their success rate back to the initial one.

**Figure 9.**A comparative evaluation of the possible resolution of fingerprinting, where the proposed method (green) is able to achieve 90% success rate at 3.7-m resolution while the conventional methods (red and blue) fail even at 6-m resolution.

**Figure 10.**Performance comparison with a different number of samples collected over different time length. The result shows no degradation in our proposed method as the time length is increased in comparison to the conventional methods.

**Figure 11.**Comparison of average execution time for different methods: RADAR with α = 1, Remove Useless APs with α = 0.8, and Invariant RSS proposed with α = 0.3.

**Figure 12.**Smartphone’s indoor localization application information flow for initial human-robot interaction.

**Figure 13.**Schematic representation of different class distributions enlightening class separability, decision margins, correct decision probability, erroneous decision probability, and class boundary.

**Figure 15.**Precision-Recall curve of the proposed approach that shows the classifier performance with 25 Wi-Fi sources.

**Figure 16.**Precision-Recall curve changes due to increasing in the number of Wi-Fi sources from 25 to 50. The arrows demonstrate the respective changes from 25 to 50 Wi-Fi sources at different class separability.

No. of Wi-Fi Signal Sources | No. of Calibration Locations |
---|---|

20 | 7 |

50 | |

80 | |

20 | 15 |

50 | |

80 | |

20 | 20 |

50 | |

80 |

© 2016 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**

Husen, M.N.; Lee, S.
Indoor Location Sensing with Invariant Wi-Fi Received Signal Strength Fingerprinting. *Sensors* **2016**, *16*, 1898.
https://doi.org/10.3390/s16111898

**AMA Style**

Husen MN, Lee S.
Indoor Location Sensing with Invariant Wi-Fi Received Signal Strength Fingerprinting. *Sensors*. 2016; 16(11):1898.
https://doi.org/10.3390/s16111898

**Chicago/Turabian Style**

Husen, Mohd Nizam, and Sukhan Lee.
2016. "Indoor Location Sensing with Invariant Wi-Fi Received Signal Strength Fingerprinting" *Sensors* 16, no. 11: 1898.
https://doi.org/10.3390/s16111898