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- 1. RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing and Its Implementation on Mobile Devices by Anthea Wain Sy Au A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto c Copyright ⃝ 2010 by Anthea Wain Sy Au
- 2. Abstract RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing and Its Implementation on Mobile Devices Anthea Wain Sy Au Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2010 As the demand of indoor Location-Based Services (LBSs) increases, there is a growing interest in developing an accurate indoor positioning and tracking system on mobile devices. The core location determination problem can be reformulated as a sparse natured problem and thus can be solved by applying the Compressive Sensing (CS) theory. This thesis proposes a compact received signal strength (RSS) based real-time indoor positioning and tracking systems using CS theory that can be implemented on personal digital assistants (PDAs) and smartphones, which are both limited in processing power and memory compared to laptops. The proposed tracking system, together with a simple navigation module is implemented on Windows Mobile-operated smart devices and their performance in diﬀerent experimental sites are evaluated. Experimental results show that the proposed system is a lightweight real-time algorithm that performs better than other traditional ﬁngerprinting methods in terms of accuracy under constraints of limited processing and memory resources. ii
- 3. Acknowledgements I would like to express my sincere gratitude to my supervisor, Professor Shahrokh Valaee, whose knowledge, guidance and support have make this work possible. I would also like to thank Professor Moshe Eizenman, who gives valuable opinions to improve this work. I owe my special thanks to Chen Feng, whom I have been working with regarding to this project. In addition, I would like to thank my colleagues at the Wireless and Internet Research Laboratory (WirLab). I am grateful for the Natural Sciences and Engineering Research Council of Canada (NSERC) for its generous ﬁnancial support. Finally, I would give my regard to my parents and my sister for their strong moral supports and encouragement. iii
- 4. Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 RSS-based WLAN Positioning Systems . . . . . . . . . . . . . . . . . . . 3 1.2.1 Location-Sensing Techniques . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Existing Positioning Systems . . . . . . . . . . . . . . . . . . . . . 4 1.3 Problem Statement and Objectives . . . . . . . . . . . . . . . . . . . . . 4 1.4 Technical Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Background and Related Works 2.1 12 Signal Propagation Modeling . . . . . . . . . . . . . . . . . . . . 13 2.1.2 Location Fingerprinting . . . . . . . . . . . . . . . . . . . . . . . 14 Fingerprinting-Based Positioning Methods . . . . . . . . . . . . . . . . . 16 2.2.1 K-Nearest Neighbour Method (KNN) . . . . . . . . . . . . . . . . 16 2.2.2 Probabilistic Approach . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.3 2.3 12 2.1.1 2.2 Indoor RSS-based WLAN Positioning Techniques . . . . . . . . . . . . . Region of Interest and Access Points Selections . . . . . . . . . . 19 Indoor Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 21 Kalman ﬁlter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
- 5. 2.3.2 Particle ﬁlter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.3 Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Pedestrian Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Aﬃnity Propagation Algorithm For Clustering . . . . . . . . . . . . . . . 24 2.6 Compressive Sensing Theory . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.7 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 Compressive Sensing Based Positioning System 28 3.1 Indoor Positioning System Overview . . . . . . . . . . . . . . . . . . . . 28 3.2 Oﬄine Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.1 Fingerprint Collections . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2.2 Clusters Generation by Aﬃnity Propagation . . . . . . . . . . . . 31 3.2.3 Interaction between the database server and the mobile device during oﬄine phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . Online Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.1 Coarse Localization Stage: Cluster Matching . . . . . . . . . . . . 35 3.3.2 Fine Localization Stage: Compressive Sensing Recovery . . . . . . 38 3.3.3 3.3 33 Interaction between the database server and the mobile device during online phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 43 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 Indoor Tracking System 46 4.1 General Bayesian Tracking Model . . . . . . . . . . . . . . . . . . . . . . 47 4.2 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 Overview of Proposed Indoor Tracking System . . . . . . . . . . . . . . . 49 4.3.1 Modiﬁed Coarse Localization Stage . . . . . . . . . . . . . . . . . 50 4.3.2 Map-Adaptive Kalman Filter . . . . . . . . . . . . . . . . . . . . 55 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4 v
- 6. 5 Simple Navigation System 59 5.1 Overview of Navigation System . . . . . . . . . . . . . . . . . . . . . . . 59 5.2 Map Database Generation at Initial Setup . . . . . . . . . . . . . . . . . 60 5.2.1 Layout Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.2.2 Map Features Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . 61 Path Routing Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3.1 Path Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Tracking Update Analysis Module . . . . . . . . . . . . . . . . . . . . . . 64 5.4.1 Analysis Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.4.2 Voice Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.3 5.4 5.5 6 Software Implementation on Mobile Devices 69 6.1 Software Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.2 Devices in Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.3 Software Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.3.1 Software’s Functionalities . . . . . . . . . . . . . . . . . . . . . . 72 6.3.2 Resources Folder . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.3.3 Libraries’ Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . 74 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.4 7 Experimental Results 7.1 77 77 7.1.1 Experimental Sites . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.1.2 Performance Benchmarks . . . . . . . . . . . . . . . . . . . . . . . 81 7.1.3 7.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Positioning Results on Bahen Fourth Floor . . . . . . . . . . . . . . . . . 82 7.2.1 82 RSS Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
- 7. 7.2.2 Online Phase: Coarse Localization Analysis . . . . . . . . . . . . 87 7.2.4 Online Phase: Fine Localization Analysis . . . . . . . . . . . . . . 90 7.2.5 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . 92 Tracking Results on CNIB Second Floor . . . . . . . . . . . . . . . . . . 95 7.3.1 RSS Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 7.3.2 CS-based Positioning Results . . . . . . . . . . . . . . . . . . . . 96 7.3.3 Modiﬁed Coarse Localization Analysis . . . . . . . . . . . . . . . 99 7.3.4 Map Adaptive Kalman Filter Analysis . . . . . . . . . . . . . . . 100 7.3.5 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . 102 7.3.6 Navigation and Real Time Implementations . . . . . . . . . . . . 104 7.3.7 7.4 85 7.2.3 7.3 Oﬄine Phase: Clustering Results by Aﬃnity Propagation . . . . . Subject Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 8 Conclusion 8.1 109 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Bibliography 113 vii
- 8. List of Tables 1.1 Existing RSS-based WLAN Position Systems [1] . . . . . . . . . . . . . . 5 1.2 Comparison of a PDA and a laptop . . . . . . . . . . . . . . . . . . . . . 8 6.1 Devices Speciﬁcations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.1 Comparison of experimental sites . . . . . . . . . . . . . . . . . . . . . . 78 7.2 Traces Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.3 Actual parameters γ (o) used for experiments on Bahen fourth ﬂoor. . . . 87 7.4 A set of optimal parameters for the CS-based position system applied on Bahen fourth ﬂoor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Position error statistics for diﬀerent methods on Bahen fourth ﬂoor. (For validation set) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 94 A set of optimal parameters for the CS-based position system applied on CNIB second ﬂoor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 94 Position error statistics for diﬀerent methods on Bahen fourth ﬂoor. (For stationary user testing set) . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 93 99 Positioning error statistics for diﬀerent positioning methods on CNIB second ﬂoor. (For mobile user testing set) . . . . . . . . . . . . . . . . . . . 100 7.9 A set of optimal parameters for the proposed tracking system applied on CNIB second ﬂoor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 viii
- 9. 7.10 Position error statistics for the CS-based positioning system and the two tracking systems on CNIB second ﬂoor. (For mobile user testing set) . . 104 7.11 Summary of the three traces tested by the subjects . . . . . . . . . . . . 107 7.12 Subjects testing results on CNIB second ﬂoor . . . . . . . . . . . . . . . 107 ix
- 10. List of Figures 1.1 The problem setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Kernel-based method [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1 Block diagram of the proposed indoor localization system. . . . . . . . . 29 3.2 Interaction between the database server and the mobile device during ofﬂine phase. 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Interaction between the database server and the mobile device during online phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1 Block diagram of the proposed indoor tracking system. . . . . . . . . . . 50 4.2 Coarse localization stage for the proposed tracking system. . . . . . . . . 51 4.3 Map-Adoptive Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1 Navigation System Overview . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2 Dijkstra Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3 Tracking update analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4 A point in close range to a line segment . . . . . . . . . . . . . . . . . . . 65 5.5 Determining the direction of turn based on the two line segments ℓi and ℓi+1 67 6.1 The overview of the software design. Arrows shows the dependency of the libraries and blue colored boxes are the developed modules for the software. 72 6.2 An example screenshot of Detect AP operation. . . . . . . . . . . . . . . x 73
- 11. 7.1 Example histograms of RSS distributions of the same access point over 50 time samples for diﬀerent devices pointing North at the same reference point on Bahen fourth ﬂoor. . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 84 An example of RSS measurements over time and their averages with respect to the number of time samples of the same access point for diﬀerent devices at the same reference point on Bahen fourth ﬂoor. . . . . . . . . 7.3 An example of averaged RSS of the same access point in spatial domain for diﬀerent orientations and diﬀerent devices on Bahen fourth ﬂoor. . . . 7.4 84 85 Number of clusters generated by the aﬃnity propagation algorithm depending on the value of parameter γ (o) for four orientations on Bahen fourth ﬂoor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 86 The clustering results on the four ﬁngerprint databases collected by PDA1 on Bahen fourth ﬂoor. Each circle is a RP collected in the database and each color represents one cluster. . . . . . . . . . . . . . . . . . . . . . . 7.6 The ARMSE versus number of used APs, when diﬀerent number of generated clusters are used for the coarse localization on Bahen fourth ﬂoor . 7.7 89 The cumulative error distributions using diﬀerent cluster matching schemes on Bahen fourth ﬂoor. (8 APs are used) . . . . . . . . . . . . . . . . . . 7.9 89 The cumulative error distributions using diﬀerent number of clusters for the coarse localization on Bahen fourth ﬂoor. (8 APs are used) . . . . . . 7.8 88 90 The ARMSE versus number of used APs, using diﬀerent AP schemes for ﬁne localization on Bahen fourth ﬂoor. . . . . . . . . . . . . . . . . . . . 92 7.10 Eﬀect of the threshold λ1 on ARMSE on Bahen fourth ﬂoor. (8 APs are used) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7.11 The cumulative error distributions using diﬀerent positioning systems on Bahen fourth ﬂoor. (8 APs are used) . . . . . . . . . . . . . . . . . . . . xi 94
- 12. 7.12 Comparison of mean computation time using diﬀerent positioning systems in Bahen fourth ﬂoor. (8 APs are used) . . . . . . . . . . . . . . . . . . . 95 7.13 Example histograms of RSS distributions of the same access point over 50 time samples (40 time samples for Smartphone) for diﬀerent devices at the same reference point in CNIB second ﬂoor. . . . . . . . . . . . . . . . 97 7.14 An example of RSS distributions across time and their averages with respect to the number of time samples of the same access point for diﬀerent devices at the same reference point in CNIB second ﬂoor. . . . . . . . . . 97 7.15 An example of RSS distributions of the same access point in spatial domain for diﬀerent orientations and diﬀerent devices in CNIB second ﬂoor. (only a part of the ﬁngerprints are shown) . . . . . . . . . . . . . . . . . . . . 98 7.16 The clustering results on the four ﬁngerprint databases collected by PDA2 on CNIB second ﬂoor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.17 The cumulative error distributions for diﬀerent positioning systems on CNIB second ﬂoor. (10 APs are used) . . . . . . . . . . . . . . . . . . . . 99 7.18 Eﬀect of the walking distance β on ARMSE in CNIB second ﬂoor. (10 APs are used) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.19 The cumulative error distributions using diﬀerent Kalman ﬁlter parameters in CNIB second ﬂoor. (10 APs are used) . . . . . . . . . . . . . . . . 101 7.20 The cumulative error distributions for diﬀerent Kalman ﬁlter update schemes in CNIB second ﬂoor. (10 APs are used) . . . . . . . . . . . . . . . . . . 102 7.21 The cumulative error distributions using the CS-based positioning system and the three tracking systems in CNIB second ﬂoor. (10 APs are used) . 103 7.22 Example trace results. The black line is the actual trace, the green dots are the CS-based positioning results and the purple line is the results of the proposed tracking system. . . . . . . . . . . . . . . . . . . . . . . . . 104 xii
- 13. 7.23 The deﬁnition of the connected graph and the map features on CNIB second ﬂoor. The blue lines and blue circles represent the edges and nodes of the connected graph. The red squares represents the destinations. The diamonds represents the map features and the pink circles represents the locations of the 15 deployed access points . . . . . . . . . . . . . . . . . . 105 7.24 Example screenshot of the software that shows the actual track that the user is walking. The line shows the routed path generated by the navigation module. The squares denote the user’s locations and the circle denotes the destination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 xiii
- 14. Chapter 1 Introduction 1.1 Motivation With the wide deployment of the mobile wireless systems and networks, the locationbased services (LBSs) are made possible on mobile devices, such as laptops, smartphones and personal digital assistants (PDAs). There are a lot of applications that rely on the locations of these mobile devices, such as navigation, people and assets tracking, locationbased security and coordination of emergency and maintenance responses to accidents, interruptions of essential services and disasters, etc [3–5]. In order to deliver reliable LBSs, real-time and accurate user’s locations must be obtained. Hence, there is a growing interest in developing eﬀective positioning and tracking systems. For the outdoor environment, Global Positioning System (GPS) and cellular network based systems [3,6,7] are commonly used as the techniques to provide navigation services. However, these techniques cannot be used directly in indoors, as the signals are usually too weak to be used for localization purposes. Thus, wireless indoor positioning has become an increasingly popular research topic in recent years. There are several methods that are built on top of the GPS-capable phones to provide indoor localization [8]. One example is the Assisted GPS (A-GPS), which requires a 1
- 15. Chapter 1. Introduction 2 connection to a network location server in order to obtain the estimated location with an average of 5-50m accuracy [8]. Another one is the Calibree proposed in [9], which utilizes the detected signal strength from GSM cell towers to determine relative positions of mobile phones and their absolute locations can be determined if some of the phones are equipped with GPS receivers. In addition, indoor localization can also be implemented on GSM mobile phones [10] and CDMA mobile phones [11] through the use of wide signal-strength ﬁngerprints. The median errors of these cellular-based system are around 4-5m. Although these methods are able to provide moderately accurate position estimate in indoors, their accuracies may not be enough to provide reliable LBSs and also they are only applicable to mobile phones. Besides the use of GPS and cellular network, diﬀerent types of wireless technologies and sensors are also employed for the indoor positioning. In particular, positioning systems using ultra-wide band (UWB) signals, infrared, radio frequency (RF), proximity sensors and ultrasound systems [1, 8, 12] are able to localize users with high accuracies. However, these systems require the installation of additional infrastructures and sensors, which lead to high budget and labour cost and preventing them from having large-scale deployments. Due to the wide deployment of wireless local area network (WLAN), which is specifically referred to as the IEEE 802.11b/g standard in this thesis, there are many indoor positioning systems that make use of WLAN for estimating user’s position. Time of arrival (TOA) [13] and time diﬀerence of arrival (TDOA) [1,14] are two techniques that can be used for localization, but they require extra conﬁguration and setup to provide valid measurements. Thus, received signal strength (RSS) is the feature metric used for the WLAN positioning systems, as it can be obtained directly from existing WLAN access points (APs) by any device that is equipped with a WLAN network adapter. This thesis presents an accurate RSS-based WLAN positioning and tracking system that can be implemented on mobile devices with limited resources. The aﬃnity propa-
- 16. Chapter 1. Introduction 3 gation algorithm for clustering data points [15] and the compressive sensing theory for recovery of the sparse and incoherently sampled signals [16] are two concepts applied on the proposed system. 1.2 RSS-based WLAN Positioning Systems The WLAN IEEE 802.11b/g is a standard used for providing wireless internet access for indoor areas. It is operated at 2.4 GHz Industrial, Scientiﬁc and Medical (ISM) band within a range of 50-100 m. As mentioned earlier, the RSS can be easily obtained by using any WLAN-integrated device, thus it is used by most of the WLAN positioning systems. 1.2.1 Location-Sensing Techniques There are three major techniques to obtain the location estimate from the RSS [8, 17]. They are listed as follows: 1. Triangulation: The RSS can be translated into distance from the particular AP according to a theoretical or empirical signal propagation model. Then, with distance measurements from at least 3 APs with known positions, lateration can be performed to estimate the locations. This approach does not give accurate estimate, as the indoor radio propagation channel is highly unpredictable and thus the use of the propagation model is not reliable. 2. Proximity: This method ﬁnds the strongest RSS from a speciﬁc AP and determines the location to be the region covered by this AP. This method only gives a very rough position estimate but it is easy to be implemented. 3. Scene Analysis: This method ﬁrst collects RSS readings at known positions, which are referred to as ﬁngerprints, in the area of interest. Then, it estimates the loca-
- 17. Chapter 1. Introduction 4 tions by comparing the online measurements with the ﬁngerprints through pattern recognition techniques. This method is used by most WLAN positioning systems, as it is able to compute accurate location estimates. This is the approach used by the positioning and tracking system proposed in this thesis. 1.2.2 Existing Positioning Systems Table 1.1 summarizes some of the existing WLAN positioning systems that can be accessible to the public. It shows that the use of ﬁngerprinting achieves the best accuracy in indoor areas. Although the Ekahau [18] attains the best accuracy, it uses the the probabilistic method to compute the estimated positions and thus requires a more comprehensive survey of RSS readings in the region of interest. In addition, its position calculation is computed at the server as the complexity of the probabilistic method is too high to be performed on the mobile devices. This raises additional issues when using this systems. First, the devices must be connected to the same network as the server to obtain position estimates. Second, positions obtained from the server must be encrypted before it is transmitted to the mobile devices, in order to protect the privacy of the users. The aim of this thesis is to design an indoor positioning and tracking system that can provide accurate position estimate with relatively low computational complexity, so that it can be computed on mobile devices. This solution may have a database server to keep track of the ﬁngerprints database collected, but once downloaded to the devices, they are no longer required to be connected to the server to obtain position estimates. This system is more ﬂexible and has no privacy concerns to the users. 1.3 Problem Statement and Objectives A typical WLAN indoor tracking scenario as illustrated in Fig. 1.1 consists of 1) a mobile device equipped with a WLAN adapter, which is carried by a user and collects
- 18. 5 Chapter 1. Introduction Microsoft Research Ekahau [18] RADAR [19, 20] Inter Place Lab and Skyhook’s WPS [21] Range Building/local area Building/local area Position Mobile device Server (Ekahau Posi- Mobile device Calculation Metropolitan area tioning Engine) Position Fingerprinting + Fingerprinting + Map-based pinpoint- Method KNN + Viterbi-like probabilistic ing (obtain APs data algorithm by war driving) and triangulation Accuracy 3-5m 1-3m 20+ m Table 1.1: Existing RSS-based WLAN Position Systems [1] RSS from detectable access points for localization; 2) access points (APs), which can be commonly found in most buildings and their exact positions are not necessarily known to the localization systems, as they may belong to diﬀerent network groups and possibly 3) a database server, which stores the ﬁngerprints collected by the mobile device. The WLAN-enabled device can extract information, such as MAC address, SSID and received signal strength (RSS) about these APs by receiving messages broadcasted from them. This thesis focuses on the WLAN localization and tracking problem using RSS as the measurement metric. The mobile device carried by the user collects the RSS from L diﬀerent APs whose unique MAC addresses are used for identiﬁcation. Then, the system determines the current position based on this RSS measurements and previously collected ﬁngerprint database. The goal of this thesis is to propose a real-time WLAN positioning and tracking system that can give accurate position estimate and can be implemented on mobile devices, so that LBSs can be applied. In the context of this thesis, the mobile devices refer to the handheld devices, such as personal digital assistants (PDAs) and smartphones, which
- 19. 6 Chapter 1. Introduction Reference Point WLAN Access Point User equipped with mobile device Database Server 000 Figure 1.1: The problem setup have degraded WLAN antennas, limited power, memory and computation capabilities, thus a light-weight algorithm is required to allow these devices to have real-time and accurate performance. The localization problem is deﬁned as follow. First, the device collects online RSS readings from available APs periodically at a time interval ∆t, which is limited by the device’s network card and hardware performances. These online RSS readings can be denoted as r(t) = [r1 (t), r2 (t), . . . , rL (t)], t = 0, 1, 2, ..., where rl (t) refer to the RSS reading collected from AP l at time t. Then, the proposed positioning and tracking system uses r(t) to compute the position estimate, denoted as p(t) = [ˆ(t), y (t)]T , where ˆ x ˆ (ˆ(t), y (t)) are the Cartesian coordinates of the estimated position at time t. x ˆ 1.4 Technical Challenges The unpredictable variation of RSS in the indoor environment is the major technical challenge for the RSS-based WLAN positioning systems. There are four main reasons that lead to the variation of RSS. First, due to the structures of the indoor environment and the presence of diﬀerent obstacles, such as walls and doors, etc, the WLAN signals experience severe multi-path and fading and the RSS varies over time even at the same location. Secondly, since the WLAN uses the licensed-free frequency band of 2.4GHz, the interference on this band can be very large. Example sources of interference are the
- 20. Chapter 1. Introduction 7 cordless phones, BlueTooth devices and microwave. Moreover, the presence of human bodies also aﬀects the RSS by absorbing the signals [22], as human bodies contain large amount of water, which has the same resonance frequency as the WLAN. Finally, the orientation of the measuring devices also aﬀects the RSS, as orientation of antenna aﬀects the antenna gain and the signal is not isotropic in real indoor environment. All of the above reasons make it infeasible to ﬁnd a good radio propagation model to describe the RSS-position relationship. Thus, a ﬁngerprinting method is often used instead to characterize the RSS-position relationship. This method computes the position estimate by matching the online RSS readings to the ﬁngerprints collected during training phase. This pattern matching process is a non-trivial problem as there are derivations between the online RSS readings to the ﬁngerprint RSS readings due to the time-varying characteristics of the indoor radio propagation channel. In addition, the movement of objects, including the movement of the user who carries the mobile device, also aﬀects the RSS readings. This type of variation of RSS is needed to be addressed by the ﬁngerprinting-based positioning systems, in order to provide accurate position estimate. Another challenge relates to the computational capabilities of the mobile devices. Table 1.2 compares the processor speed and memory equipped by a PDA, which is used in this thesis to evaluate the performance of the proposed positioning system and a labtop with average performance. It shows that the PDA has very limited computation speed and memory when comparing to the labtop. Thus, some of the positioning systems that can be implemented on the laptop may not be able to be used by the PDA. The computational complexity and the use of memory must be taken into consideration when designing the positioning and tracking systems in this thesis.
- 21. 8 Chapter 1. Introduction Devices Processor Speed RAM HP iPAQ hx4700 624 MHz 64 MB Dell Inspiron 15 Laptop 2.2 GHz 4 GB Table 1.2: Comparison of a PDA and a laptop 1.5 Scope In this thesis, a two stage indoor RSS-based WLAN positioning and tracking system is proposed and implemented on two mobile devices. Such system is able to address the challenges mentioned in the previous section. The structure of this thesis is organized as follows. First, Chapter 2 reviews the existing RSS-based WLAN positioning techniques. It also describes two ﬁngerprinting based methods: K-nearest neighbour (KNN) and kernelbased probabilistic methods which are used in later chapter as performance benchmarks to the proposed positioning system. In addition, it presents diﬀerent ways to improve these positioning methods, such as the determination of region of interest, selection of APs and the use of ﬁlters with inputs of previous estimate and pedestrian motion models. Some overview of navigation systems design is also included. Finally, the two concepts used in this thesis for developing the proposed system are presented. It describes how the aﬃnity propagation algorithm is operated to generate clusters. Then, the compressive sensing theory is brieﬂy summarized. The compressive sensing based positioning system is introduced in Chapter 3. This chapter presents how such system is operated to estimate the user’s position. It ﬁrst describes how the clustering process is done on the collected ﬁngerprint database by applying the aﬃnity propagation algorithm during oﬄine phase. Then, it discusses the two stage online phase where the actual positioning is operated. First, the coarse localization stage reduces the area of interest by choosing a few clusters of RPs, whose RSS readings
- 22. Chapter 1. Introduction 9 from the database are best-matched to the online RSS readings. Then, the ﬁne localization stage converts the localization problem into sparse signal recovery problem, so that CS theory can be applied. The interactions between the mobile device and the server are also explained in the chapter. In Chapter 4, the CS-based positioning system is extended into a tracking system. The proposed tracking system has a modiﬁed coarse localization stage, which the previous estimate is used to select the nearby RPs, in addition to the clusters of RPs selected according to the online RSS readings. The tracking system uses the Kalman ﬁlter to smooth the estimate update. Since the user is more likely to make turns at intersection regions and hence may violate the liner motion model, the Kalman ﬁlter is reset at these regions to enhance the performance of such tracking system. Chapter 5 describes a simple navigation system, which consists of a path routing module to generate the path that leads the user to the destination and a tracking update analysis module that checks whether the user follows the path and gives appropriate guidance accordingly. It also explains how the map information is extracted to be used by the navigation system. This navigation system, together with the proposed positioning and tracking system are implemented as a software that can be installed on any smartphone or PDA that uses the Windows Mobile platform. The design of the software is presented in Chapter 6. Chapter 7 includes all the experimental results conducted in two experimental sites. The experiments done on the fourth ﬂoor of Bahen Centre focused on the evaluation of the proposed positioning system, whereas the performance of the proposed tracking system was evaluated using the data collected on the second ﬂoor of Canadian Nation Institute for the Blind (CNIB). Finally, Chapter 8 presents the concluding remarks and gives directions for the future work.
- 23. Chapter 1. Introduction 1.6 10 Contributions This thesis proposes and implements a two stages indoor RSS-based WLAN positioning, tracking and navigation system using compressive sensing, clustering and ﬁltering techniques. Here are the list of contribution, including the chapters presenting them and publications referring to them: 1. Compressive sensing based positioning system: This positioning system applies the aﬃnity propagation algorithm on the collected ﬁngerprint database to generate clusters of RPs, which have similar RSS values and are geographically close to each other. Then, such system uses the coarse localization stage to choose the relevant clusters of RPs, based on the online RSS measurement. Finally, the localization problem is translated into a sparse signal problem, so that the estimated position can be computed by solving a ℓ1 norm minimization problem according to the compressive sensing theory. (Chapter 3 and [23, 24]) 2. Tracking system: The CS-based positioning system can be easily extended to include the previous position estimate and the map information to improve its performance. The tracking system has a modiﬁed coarse localization stage. In addition to the clusters of RPs selected based on the online RSS measurements, RPs which are physically close to the previous position estimate are also chosen and the common RPs found in both sets are used in the ﬁne localization stage. The computed estimate is then post-processed by the Kalman ﬁlter. This ﬁlter is reset when the estimate is at the intersection regions, as the user may make turns and violate the liner motion model used by the Kalman ﬁlter. (Chapter 4) 3. Navigation system: A simple navigation system, which uses the map database to generate path to destination using Dijkstra algorithm and gives guidance, is developed. It also determines whether the user follows the path and gives appropriate instructions at proper times. (Chapter 5).
- 24. Chapter 1. Introduction 11 4. Software implementation and performance evaluation: A software is developed to implement the proposed positioning and tracking system, as well as a simple navigation system. It is written in C# and can be installed on any smartphone or PDA that uses Windows Mobile as its operating system. This software can give real-time position updates and also navigation guidance to the user. The performance evaluations of the proposed positioning and tracking system are done for two diﬀerent experimental sites: Bahen centre and CNIB. Experimental results show that these systems are able to provide good position estimate of the user and can be implemented on the PDAs with limited resources, to give real-time performance. (Chapter 6 and 7 and [23, 24]). This project is a joint work with Chen Feng, a visiting PhD student from the Beijing Jiaotong University, at the Wireless and Internet Research Laboratory (WirLab), supervised by Professor Shahrokh Valaee. We work closely together to implement the indoor tracking and navigation system on the handheld devices. Chen focuses more on the compressive sensing based positioning system, while I focus more on the tracking and navigation system, as well as the software implementation.
- 25. Chapter 2 Background and Related Works In this section, a brief overview of RSS-based WLAN positioning and tracking techniques is given. The two ﬁngerprinting-based methods, namely KNN and Kernel-based are summarized in Sections 2.2.1 and 2.2.2, as they are implemented in Chapter 7 to compare the performance of the proposed positioning system. In addition, some works about pedestrian navigation are summarized. There are two additional concepts used by this thesis to develop the proposed positioning and tracking system using the ﬁngerprinting approach. Section 2.5 describes the operation of the aﬃnity propagation algorithm, which generates clusters of similar data points. Section 2.6 summarizes the compressive sensing theory which can be applied on the localization problem to estimate the user’s location. 2.1 Indoor RSS-based WLAN Positioning Techniques The key problem for the indoor RSS-based positioning systems is to identify the RSSposition relationship, so that the user’s location can be estimated based on the RSS collected at that location. There are two approaches in dealing with this relationship [25]: the uses of signal propagation models [26, 27] and the location ﬁngerprinting methods [2, 19, 28]. 12
- 26. 13 Chapter 2. Background and Related Works 2.1.1 Signal Propagation Modeling This technique uses the RSS readings collected by the mobile device to estimate the distances of the device from at least three APs, whose locations are known, based on a signal radio propagation model. Then triangulation is used to obtain the device’s position [8]. The accuracy of this technique depends heavily on ﬁnding a good model that can best describe the behavior of the radio propagation channel. However, the indoor radio propagation channel is highly unpredictable and time-varying, due to severe multipath in indoor environment; shadowing eﬀect arising from reﬂection, refraction and scattering caused by obstacles and walls; and interference with other devices operated at the same frequency (2.4GHz) as the IEEE 802.11b/g WLAN standard, such as cordless phones, microwaves and BlueTooth devices. There are two models that are often used for the indoor radio propagation channel: • Combined model of path loss and shadowing [29] This model combines the simpliﬁed path-loss model with the eﬀect of shadowing, which is assumed to be a log-normal random process. The received power pr which is d meters away from a speciﬁc AP is given by: pr [dBm] = p0 [dBm] + 10 log10 K − 10γ log10 d − ηdB d0 (2.1) where K is a constant depending on the antenna characteristics and channel attenuation, p0 is the signal power at a reference distance d0 for the antenna far ﬁeld, γ is the path-loss exponent, which varies for diﬀerent surrounding environments 2 (2 ≤ γ ≤ 6 for indoor environment) and ηdB ∼ N (0, ση ) is a Gaussian random variable. • Wall Attenuation Factor model [19] This model includes the eﬀects of obstacles or walls between the transmitter and
- 27. Chapter 2. Background and Related Works receiver. The received power can be obtained by: nW · W AF nW < C d pr [dBm] = p0 [dBm] − 10γ log10 − d0 C · W AF nW ≥ C 14 (2.2) where nW is the number of obstacles or walls between the transmitter and receiver, C is a threshold up to which no signiﬁcant attenuation can be observed and W AF is the wall attenuation factor. The two empirical models require the calibration of the parameters, such as the path loss exponent, which vary depending on diﬀerent environments. This often requires a comprehensive survey of the RSS distributions over the environment, which is a time consuming process. In addition, the models assume the RSS is distributed isotropically from the transmitter. This is often not the case for indoor environments due to the presence of obstacles. The orientation of the antenna of the mobile device also aﬀects the RSS [22], but it is not reﬂected in the two models. Finally, the locations of the APs may not be known in the real scenario, as these APs may be installed and owned by diﬀerent vendors. All of these make the models inadequate to describe the RSS-position relationship in real situation and lead to errors in estimating the user’s location. 2.1.2 Location Fingerprinting A location ﬁngerprinting method is often used instead of the radio propagation model, as it can give better estimates of the user’s locations for indoor environments. This method is divided into two phases: oﬄine and online phases. During the oﬄine phase, which is also referred to as the training phase, the RSS readings from diﬀerent APs are collected by the WLAN-integrated mobile device at known positions, which are referred to as the reference points (RPs) to create a ﬁngerprint database, also known as the radio map. Since the orientation of the device’s antenna aﬀects the RSS readings, a more comprehensive ﬁngerprint database can be built by collecting RSS readings for diﬀerent
- 28. Chapter 2. Background and Related Works 15 orientations at the same RP. The actual positioning takes place in the online phase. The mobile device, which is carried by the user collects RSS readings from diﬀerent APs at an unknown position. Then, these RSS online measurements are compared to the ﬁngerprint database to estimate the user’s location by using diﬀerent methods described in the next section. The accuracy of the estimated position of the user depends highly on the number of RPs collected in the ﬁngerprint database. If there are more RPs, then the radio map has a ﬁner resolution and thus allows a better estimation [28]. In addition, since the RSS varies over time, collecting more time samples of RSS readings at the same RP also improves the position estimation. Thus, this ﬁngerprint database collection is a time consuming and labour-intensive process. [30] uses the spatial correlation of adjacent RPs to generate the database by interpolation from a small number of RPs and this method is able to reduce the labour eﬀort and time required for the oﬄine phase. Another disadvantage of this ﬁngerprinting approach is the maintenance of such databases. Since the RSS propagation environment varies with time, the accuracy of using the database degenerates over time, as the current RSS readings slowly deviate from the readings in the database. The database may even be rendered useless, if the environment changes signiﬁcantly. This requires the ﬁngerprint database to be rebuilt periodically, in order to ensure the accuracy of the positioning system. [31] presents a novel method to update the radio map using the online RSS readings, which can eﬃciently update the ﬁngerprint database without the labour and time overhead cost as required by rebuilding such database from scratch. As shown in [32], the RSS readings collected by diﬀerent network cards are diﬀerent, which can vary up to -25dBm. This indicates that the same ﬁngerprint database cannot be used by diﬀerent mobile devices, which are equipped with diﬀerent WLAN network cards. That means that the ﬁngerprint collection process must be done on each device and lead to very high labour and time costs. Another method is to use the signal strength
- 29. Chapter 2. Background and Related Works 16 diﬀerence (SSD) between APs instead of the RSS as the ﬁngerprint [33]. Although there are limitations to the location ﬁngerprinting, it is a simple and eﬀective method to be used by indoor positioning systems. This thesis also uses this approach to estimate the user’s location. 2.2 Fingerprinting-Based Positioning Methods There are two approaches to estimate the user’s location based on the online RSS measurements and the ﬁngerprint database [34, 35]. The deterministic approach only uses the average of the RSS time samples from each RP to estimate the location, whereas the probabilistic approach incorporates all the RSS time samples for the computation. For the following section, assume the collected ﬁngerprint database is denoted as a set {(pi , ψ i (1), . . . , ψ i (T ))|i = 1, . . . , N }, where pi is the Cartesian coordinates for RP i, ψ i (t) = [ψi,1 (t), . . . , ψi,L (t)]T is the RSS readings vector for RP i at time t with ψi,j (t) denoted as the RSS reading from AP j for RP i at time t. T is the total number of collected time samples, N is the total number of RPs and L is the total number of APs. The online RSS measurement vector can be denoted as r = [r1 , ...rL ]T . 2.2.1 K-Nearest Neighbour Method (KNN) The K-nearest neighbour (KNN) method is a deterministic approach that uses the average of the RSS time samples of RPs from the ﬁngerprint database to estimate the user’s location [19]. It ﬁrst examines the Euclidean distance of the online RSS measurement vector to the RPs in the database, namely: ¯ Di = ∥r − ψ i ∥ ¯ where ψ i = 1 T ∑T τ =1 (2.3) ψi,1 (τ ) is the average RSS vector for RP i. Then, the distances are sorted in ascending order and the ﬁrst K RPs that have the smallest distances are
- 30. 17 Chapter 2. Background and Related Works obtained to estimate the location p: ˆ K 1 ∑ p p= ˆ K i=1 i (2.4) The calculated distances can be used as weights to estimate the location and it is referred to as the weighted-KNN. The estimated location can be found by ∑K 1 pi i=1 p = ∑K Di1 ˆ (2.5) i=1 Di 2.2.2 Probabilistic Approach The location estimation problem can be solved by using probabilistic models [2, 36, 37, 37, 38]. The core concept is to ﬁnd the posterior distribution of the location, which is the conditional probability p(pi |r) [37]. This conditional probability can be estimated by using the Maximum A Posteriori (MAP) estimator, which is derived from Bayes rule. That is: pM AP = arg max f (pi |r) = arg max ˆ pi pi f (r|pi )f (pi ) N ∑ (2.6) f (r|pi )f (pi ) i=1 where f (pi |r) and f (r|pi ) are the conditional probability density functions. Note that the denominator of (2.6) can be safely ignored as it remains the same regardless of the choice of pi . In general, there is no prior knowledge of the device’s location and thus the prior density f (pi ) is assumed to be uniform, which transforms this MAP estimation into a Maximum Likelihood (ML) estimation: pM L = arg max f (r|pi ) ˆ (2.7) pi The estimation can be further improved by including the likelihood densities as the weight for the K RPs with the highest likelihood densities, namely: pM L+weight = ˆ K ∑ wi p i (2.8) i=1 f (r|pi ) wi = ∑K j=1 f (r|pi ) (2.9)
- 31. Chapter 2. Background and Related Works 18 There are several methods to estimate the likelihood density functions f (r|pi ), i = 1, . . . , N from the ﬁngerprint database. Two of the common methods are reviewed here. Both of them assume that the RSS from diﬀerent APs are uncorrelated and independent, ∏ so that the density function can be simpliﬁed to f (r|pi ) = L f (rk |pi ). k=1 Histogram The likelihood density functions can be estimated by the histogram method. This method requires two parameters to generate a histogram for the RSS time samples collected for each of the AP at each of the RP [37]. The ﬁrst parameter is the number of bins, which are a set of non-overlapping intervals that cover the whole possible range of the RSS values. The second is the origin of the bins, which is necessary to determine the boundaries of the bins. Then, the likelihood density estimate for a particular RSS value can be obtained as the relative frequency of the bin, which contains that particular RSS value [37]. There are several drawbacks for this method. First, the likelihood density estimate depends heavily on the choice of the origin and the bin width and thus careful experimental calibration of these parameters is required [37]. Second, a large amount of RSS samples for each RP is required to generate a reliable histogram that produces good location estimate. Kernel-Based Instead of using the histogram, the kernel-based method uses the kernel density estimator to estimate the density functions [2,37]. The density function can be estimated as follows: T ∑ ˆ(r|p ) = 1 f K(r; ψ i ) i T t=1 (2.10) where K(r; ψ i ) denotes the kernel function. A common choice of the kernel function is the Gaussian kernel. By assuming that the RSS from diﬀerent APs are uncorrelated and
- 32. Chapter 2. Background and Related Works 19 independent, the Gaussian kernel function is deﬁned as: ) ( 1 ∥r − ψ i (t)∥2 K(r; ψ i ) = √ exp − ∗ ∗ 2(σi )2 ( 2πσi )L (2.11) ∗ where σi is the kernel bandwidth. The determination of this kernel bandwidth is evalu- ated in [2]. Since this method takes all the RSS time samples collected at each RP into account for estimating the likelihood densities, the computation time is much larger than the KNN method. In this thesis, the kernel-based method is also implemented to compare its performance to the proposed positioning system. The operation of the method using the Gaussian kernel is summarized in Fig. 2.1 [38]. 2.2.3 Region of Interest and Access Points Selections Before applying the above methods on the whole ﬁngerprint database to estimate the user’s location, two pre-processing steps can be introduced to conﬁne the localization problem into a subset of relevant RPs and a subset of APs, which can distinguish the RPs easily. The region of interest determination step is able to mitigate the eﬀect of the deviations between the online readings and the radio map due to the time-varying characteristic of the indoor radio channel [39]. In addition, the purpose of AP selection step is to remove extra APs that may lead to biased estimations and redundant computations, which is often the case as APs are widely deployed in indoor buildings [38]. Both steps are often carried out together as the reliability of the APs varies for diﬀerent RPs [36, 38, 39]. The joint clustering technique proposed in [39] selects the strongest m APs to generate the probability distribution for each RPs and groups the RPs, which have the same q strongest APs list, as a cluster during oﬄine phase. The argument of using strongest APs is that they provide the highest probability of coverage over time [39]. However, they may not be a good choice, as the variation of the APs may also lead to error in estimation [28]. [40] presents another AP selection criterion that is
- 33. 20 Chapter 2. Background and Related Works Given: Radio Map: {(pi , ψ i (1), . . . , ψ i (T ))|i = 1, . . . , N } Number of APs: L Number of time samples: T Inputs: Online RSS measurement vector: r Outputs: Position estimate: p ˆ Kernel-based Method: ∗ Optimal bandwidth: σi ( 4 ) 1 −1 ∗ σi = L+2 L+4 σi T L+4 ˆ ∑ 1 l where, σi = L L (ˆi )2 ˆ2 l=1 σ (ˆi )2 = σl 1 T −1 ∑T t=1 (ψi,l (t) ¯ − ψi,l )2 , ¯ ψi,l = 1 T ∑T t=1 ψi,j (t) Weight calculation: ) ( ∑ 2 1 i wi = T (√2πσ∗ )L T exp − ∥r−ψ∗(t)∥ t=1 2(σ )2 i i Estimation: p= ˆ ∑N i=1 wi pi ∑N i=1 wi Figure 2.1: Kernel-based method [2]. based on AP’s discrimination power in terms of entropy calculations. Several more AP selection schemes and the use of spatial ﬁltering for region of interest determination can be found in [2]. This thesis uses the aﬃnity propagation algorithm to generate cluster of RPs with similar RSS readings during oﬄine phase. Then, a coarse localization stage is introduced in online phase to identify in which cluster of RPs should the user be located. In addition,
- 34. Chapter 2. Background and Related Works 21 diﬀerent AP selection schemes are also explored for the proposed positioning system. 2.3 Indoor Tracking Most of the indoor tracking methods use past position estimates and pedestrian motion dynamics to reﬁne the current position estimate determined by the above positioning methods. In addition, the dynamic motion model can also be used in conjunction with the current position estimate to predict the future possible locations. The pedestrian motion dynamics can be modeled by a general Bayesian tracking model and a ﬁlter is then derived to reﬁne the position estimates [41]. There are two ﬁlters that are used commonly to improve the accuracy of positioning systems [41]: Kalman ﬁlter and Particle ﬁlter. 2.3.1 Kalman ﬁlter By assuming the Gaussian tracking noise model and linear motion dynamics, the general ﬁlter becomes a Kalman ﬁlter, whose optimal solution is a minimum mean square error (MMSE) estimate. Although the assumption of Gaussian RSS-position relationship is not often the case [22], the application of the Kalman ﬁlter as the post-processing step is able to improve the accuracy of the positioning systems [41–44]. The parameters of the Kalman ﬁlter are needed to be found experimentally. [45] provides some guidelines on how to set the parameters for each update steps based on the map information. 2.3.2 Particle ﬁlter The particle ﬁlter is a sequential Monte Carlo method that generates random samples, known as particles, according to a motion models and estimates their probability densities [46, 47]. Unlike the Kalman ﬁlter, the particle ﬁlter can be applied on non-Gaussian and non-linear models. In addition, map information can be used to further improve the
- 35. Chapter 2. Background and Related Works 22 performance of the particle ﬁlter by assigning zero weights to the invalid particles, such as those across the wall [48,49]. Backtracking based on the map information is also proposed in [50]. Moreover, information obtained from accelerometers and inertial measurement units (IMU) can also be used to reﬁne the motion models and let the ﬁlter to generate particles that are more relevant and hence improve the tracking accuracy [51, 52]. However, the major drawback of the particle ﬁlter is its high computation complexity. For example, 1600 particles are needed for each ﬁlter update for a 40m×40m experimental area to achieve the best performance [49]. This large computation workload can not be handled by the mobile devices to give real-time updates to the user. Hence, this thesis chooses the Kalman ﬁlter to post-process the estimates instead of the particle ﬁlter, which may severely hinder the operations of the mobile devices. 2.3.3 Other Methods Besides the use of the above ﬁlters, several other methods are also used for the indoor tracking. The Horus positioning system [36] smooths out the resulting location estimate by simply averaging the last W location estimates obtained by the discrete-space estimator. Liao et al. proposed a method to predict the user’s orientation, which is then used for the next position estimate to improve the accuracy, from the previously computed location estimates [53]. A Viterbi-like algorithm, which is developed to enhance the RADAR system [20] and is also implemented by [54], makes use of historical data based on the KNN method to determine the location estimates. Finally, a nonparametric information ﬁlter based on the kernel-based probabilistic method is proposed in [55]. This ﬁlter, whose computational complexity is lower than particle ﬁlter, is able to deal with tracking scenarios where Kalman ﬁlter is inapplicable.
- 36. Chapter 2. Background and Related Works 2.4 23 Pedestrian Navigation Indoor navigation for pedestrian is diﬀerent from the vehicular navigation using GPS, which becomes an essential tool to the driver. Gilli`ron and Merminod [56] describes e how to implement the personal navigation system for indoor applications. It is crucial to extract information from the indoor maps as topological models and node/link models, so that they can be used for implementation of route guidance. They also implement map matching algorithms, so that the system can self-correct the user’s locations due to bad estimates based on the topological elements from the map databases, traveled distances and direction changes. [48] also describes how the map information can be used for indoor location-aware systems. There are diﬀerent ways to present the guidance information graphically to the users based on diﬀerent output devices and they are explored in [57]. The experience of using the indoor navigation systems can be enhanced in a smart environment, which is equipped with diﬀerent kinds of sensors that can convey additional information to users [58]. There are more restrictions for the navigation systems when they are targeted to visually impaired users. [59] describes the path planning and following algorithms speciﬁcally designed for visually impaired. In summary, such systems generate obstacle-free paths; provide more detailed information about the surrounding area and give the guidance in relation to special objects, such as walls, doors and rails, etc. In addition to the commonly used Dijkstra algorithm to generate the routes [56], a cactus tree-based algorithm is also used to generate a high-level guidance. A more detailed development of an indoor routing algorithm for the blind and its comparison to the one for the sighted can be found in [60]. This thesis develops a simple navigation system, which uses the proposed tracking system to provide updates of user’s locations. Such system is implemented as a software on PDAs and smartphones and is given to the visually impaired people to test its usefulness in helping them to get familiar with the indoor environment.
- 37. Chapter 2. Background and Related Works 2.5 24 Aﬃnity Propagation Algorithm For Clustering In this thesis, the aﬃnity propagation algorithm described in [15] is used to cluster the RPs with similar RSS readings, so that the proposed positioning and tracking system is able to conﬁne the localization problem into a smaller region. Unlike the traditional K-means clustering method, which may lead to bad clustering results due to bad choice of randomly selected K initial exemplars [61], the aﬃnity propagation algorithm is able to generate good clustering results without predetermining the initial exemplars. This algorithm allows all the data points to have equal chance to become exemplars and is easy to be implemented, thus it is chosen in this thesis to cluster the RPs. The aﬃnity propagation algorithm generates a set of exemplars and corresponding clusters by recursively transmitting real-valued messages between data points with an input measure of similarity between pairs of data points [15]. The pairwise similarity s(i, j) indicates the suitability of data point j to be the exemplar of data point i. Another input measure is the preference, which is also the self similarity for data point k, p(k) = s(k, k). This value deﬁnes the a priori possibility that data point k to become an exemplar. If all the data points are equally possible to be exemplars, then their preferences can be set to a common value. High preference values will lead to large number of clusters generated by the algorithm. In practice, the preference values are commonly assigned as the minimum or median similarity to generate moderate number of clusters. The core operations of the algorithm is the transmission of two kinds of real-valued messages: responsibility message, r(i, j) and availability message, a(i, j). The responsibility message, r(i, j), is sent from data point i to candidate exemplar j to reﬂect the suitability of data point j to serve as the exemplar for data point i taking into considerations the other potential exemplars. It is updated according to r(i, j) = s(i, j) − ′ max {a(i, j ′ ) + s(i, j ′ )} ′ j s.t.j ̸=j (2.12)
- 38. 25 Chapter 2. Background and Related Works The availability message, a(i, j) is sent from candidate exemplar j to data point i to reﬂect how appropriate that data point i should choose data point j as its exemplar, taking into account the responsibility messages from other data points that data point j should be an exemplar. Its update rule is: a(i, j) = min 0, r(j, j) + ∑ max{0, r(i′ , j)} i′ s.t.i′ ̸={i,j} (2.13) Two additional messages: self-responsibility, r(i, i) and self-availability, a(i, i) are also calculated for each data point i. These messages reﬂect accumulated evidence that i is an exemplar. The formulas to update these two messages are stated below: r(i, i) = p(i) − ′ max {a(i, j ′ ) + s(i, j ′ )} ′ a(j, j) = ∑ j s.t.j ̸=j max{0, r(i′ , j)} (2.14) (2.15) i′ s.t.i′ ̸=j The exemplars can then be identiﬁed by combining the two messages. For data point i, ﬁnd j ′ = arg max{a(i, j) + r(i, j)} (2.16) j If j ′ = i, then data point i is an exemplar; otherwise, data point j ′ is the exemplar for data point i. The messages are passed recursively between pairs of data points by following the above updating rules (2.12) to (2.15) until a good set of exemplars and corresponding clusters gradually emerges. 2.6 Compressive Sensing Theory This thesis describes how the localization problem can be re-formulated into a sparse signal recovery problem, so that the compressive sensing theory discussed in [16, 62, 63] can be applied to estimate the user’s location. Compressive sensing theory allows compressible signals to be recovered by fewer samples than traditional methods, which according to the Nyquist sampling theory requires
- 39. Chapter 2. Background and Related Works 26 the sampling rate to be at least twice the maximum bandwidth. This is possible when signals of interest are sparse and are sampled incoherently. The compressive sensing problem can be formulated as follow [16, 63]: Consider a discrete-time signal x as a N × 1 vector in RN . Such signal can be represented as a linear combination of a set of basis {ψ i }N . Constructing a N × N basis i=1 matrix Ψ = [ψ 1 , ψ 2 , ...ψ N ], the signal x can be expressed as x= N ∑ si ψi = Ψs (2.17) i=1 where s is a N × 1 vector and is an equivalent representation of x in the diﬀerent basis Ψ. A signal is K-sparse when it can be represented as a linear combination of K ≪ N basis vectors. This means that there is only K nonzero entries for vector s. The overall compressive sensing problem can be expressed as y = Φx = ΦΨs = Θs (2.18) where Φ is a M × N , M < N measurement sensing matrix for sensing the signal x, Θ = ΦΨ is an M × N matrix, and y is a M × 1 observation vector collected as a result of this sensing process. This problem can be referred to as incoherent sampling if the largest correlation between the sensing matrix Φ and the representation basis Ψ, √ µ(Φ, Ψ) = N · max | < ϕi , ψ j > | is small. 1≤i,j≤N Compressive sensing theory requires both the sparsity and incoherent sampling, so that the signal can be recovered exactly with high probability. If M ≥ cKlog(N/K) ≪ N , where c is a small constant, the signal can be reconstructed by solving the following l1 norm minimization problem: s = arg min ∥s∥1 such that Θs = y ˆ (2.19) s∈RN This is a convex optimization problem that can be easily converted into a linear program, known as basis pursuit, through primal-dual method [62, 64]. Additional algorithms
- 40. Chapter 2. Background and Related Works 27 to solve this optimization problem can also be found in [64]. In this thesis, the ℓ1 minimization problem is solved by using the basis pursuit linear program provided in the matlab toolbox, ℓ1 -MAGIC, developed by Cand`s [65]. e 2.7 Chapter Summary This chapter gives a brief overview of diﬀerent methods developed for the RSS-based WLAN indoor positioning systems. It also discusses how the reduction of the region of interest and selection of access points can enhance the accuracy of these systems. Two ﬁngerprinting methods, KNN and kernel-based probabilistic techniques are described in details, as they are served as the performance benchmarks for the proposed positioning system. Moreover, several indoor tracking techniques that are able to improve the accuracy through the use of previous estimates and pedestrian motion models are also discussed. The developments of indoor navigation systems are also included to provide some insight on how the location information produced by the positioning and tracking systems can be used. Finally, the aﬃnity propagation algorithm for clustering data points and the compressive sensing theory for sparse and incoherent sampled signals are discussed, these concepts are used by the proposed positioning and tracking systems.
- 41. Chapter 3 Compressive Sensing Based Positioning System Due to the unpredictable nature of the RSS distribution at indoor environment, most of the indoor RSS-based WLAN positioning systems use the ﬁngerprinting approach to acquire the explicit RSS and position relationship, in order to compute a more accurate estimation of user’s position. The compressive sensing based positioning system proposed in this chapter is also a ﬁngerprinting method. Unlike the traditional ﬁngerprinting systems, the proposed system reformulates the localization problem into a sparse-natured problem and thus the compressive sensing concept can be applied to ﬁnd the estimated positions. A coarse localization stage is also introduced to constraint the region of interest into smaller relevant area, which eﬀectively reduces the computation time and minimizes the maximum errors attained. 3.1 Indoor Positioning System Overview As depicted in Fig. 3.1, the compressive sensing based positioning system consists of two phases: oﬄine phase where the training is done to generate the ﬁngerprint database and the aﬃnity propagation algorithm is applied to generate clusters; online phase where 28
- 42. Chapter 3. Compressive Sensing Based Positioning System 29 RSS readings are obtained for the actual localization to take place. The online phase consists of two stages. First, the coarse localization stage is carried out to reduce the area of interest into a smaller region by choosing clusters of RPs based on online RSS readings. Then, in ﬁne localization stage, the localization problem is reformulated into a sparse signal recovery problem, which allows the application of compressive sensing theory to estimate the device’s position. The following sections describe the individual blocks as shown in Fig. 3.1 in details. Offline Phase Fingerprinting RSS Collections in 4 orientations Clustering Affinity Propagation Online Phase online RSS readings Fine Localization Compressive Sensing Coarse Localization cluster matching AP selection Orthogonalization L1-norm minimization Estimated Location Figure 3.1: Block diagram of the proposed indoor localization system. 3.2 Oﬄine Phase Oﬄine phase is the training period that allows the positioning system to collect RSS data at the area of interest and preprocess them to enable the system to estimate the mobile device’s position in the online phase. This training must be done wherever the positioning system is ﬁrst deployed. The time required for the training depends on the
- 43. Chapter 3. Compressive Sensing Based Positioning System 30 size of the survey site. Moreover, the database may need to be rebuilt if the surrounding environment of the area of interest changes signiﬁcantly. According to Fig. 3.1, two operations are performed in the oﬄine phase for the proposed system and they are described in the following subsections. 3.2.1 Fingerprint Collections The ﬁrst operation of the oﬄine phase is the ﬁngerprinting. During ﬁngerprinting, RSS readings from diﬀerent APs are collected by a WLAN-enabled mobile device at desired known positions, referred to as the reference points (RPs), which are often the grid points pre-deﬁned on the map. RSS readings are sampled at a regular time interval, in order to obtain their distributions over time. Since the orientation of the antenna inside the device aﬀects the RSS readings, the device is pointed to a speciﬁc orientation when collecting RSS readings at each RP. In this thesis, RSS readings are collected at four common directions, namely North, East, South and West as represented mathematically by the set O = {0◦ , 90◦ , 180◦ , 270◦ }. The raw set of RSS time samples collected from AP i at RP j and orientation o is (o) denoted as {ψi,j (τ ), τ = 1, ..., q, q > 1}, where q is the total number of time samples collected. Then, the average of these raw time samples are computed and stored in a database, known as the radio map on the server. Such radio map database gives the spatial and RSS relationship in the given (o) ψ 1,1 (o) ψ 2,1 Ψ(o) = . . . (o) ψL,1 environment and can be represented as Ψ(o) : (o) (o) ψ1,2 · · · ψ1,N (o) (o) ψ2,2 · · · ψ2,N (3.1) . . .. . . . . . (o) (o) ψL,2 · · · ψL,N where o ∈ O = {0◦ , 90◦ , 180◦ , 270◦ } and ψi,j = (o) 1 q ∑q τ =1 (o) ψi,j (τ ) is the average of RSS readings over time from AP i at RP j at a speciﬁc orientation o, for i = 1, 2, . . . , L and j = 1, 2, . . . , N . L is the total number of APs detected throughout the whole region of
- 44. Chapter 3. Compressive Sensing Based Positioning System 31 interest and N is the total number of RPs. The columns of Ψ(o) represent the average RSS readings at each RP, which can be referred to as the radio map vector and is denoted as (o) (o) ψ j = [ψ1,j (o) ψ2,j ··· (o) ψL,j ]T , j = 1, 2, . . . , N (3.2) Besides the average RSS reading matrix Ψ(o) , the database server also stores the variance of these time samples, which are useful in determining which APs should be selected for localization. The variance vector for each RP is deﬁned as (o) (o) ∆j = [∆1,j (o) where ∆i,j = 1 q−1 ∑q (o) τ =1 (ψi,j (τ ) (o) ∆2,j ··· (o) ∆L,j ]T , j = 1, 2, . . . , N (3.3) (o) − ψi,j )2 is the unbiased variance of RSS readings from AP i at RP j for orientation o. For each RP j, its position represented as Cartesian coordinates (xj , yj ), together with its average and variance of the RSS readings from diﬀerent APs at diﬀerent orientations (o) (o) form a set of (xj , yj ; ψ j ; ∆j ), o ∈ O, which is stored in the ﬁngerprint database. The database is then preprocessed as described in the next subsection before being used for the computation of position estimation during online phase. Note that if there is no RSS readings collected from an AP at a RP and an orientation, the corresponding value in the ﬁngerprint database is set to a small value to imply its invalidity. 3.2.2 Clusters Generation by Aﬃnity Propagation Due to the time varying characteristics of the indoor propagation channel, RSS readings collected during online phase may deviate from those stored in the radio map database. As a result, these deviation may lead to error estimation of position. In addition, the computation time for ﬁnding position updates increases proportionally to the number of RPs. Therefore, a coarse localization stage is introduced at the online phase to conﬁne the localization problem into a smaller region, namely a subset of RPs that have similar RSS readings to the online measurement, before the ﬁne localization is performed. This
- 45. Chapter 3. Compressive Sensing Based Positioning System 32 stage can eﬀectively reduce the computation time due to the reduction of number of relevant RPs, as well as the errors introduced by the potential outliers. The RPs collected in the oﬄine phase are required to be divided into subsets, so that a coarse localization stage can take place during the online phase. The RPs whose RSS readings are similar and physically close to each other should belong to the same group. This group division process, which is referred to as the clustering process in the proposed system is done during the oﬄine phase after the ﬁngerprints collection is ﬁnished. Since the RSS readings for the same RP vary for the four orientations, the clustering process is performed on each of the four radio map databases separately. The aﬃnity propagation algorithm described in Section 2.5 is used to generate the desirable clusters, as this algorithm allows all the RPs to have equal chances to be exemplars and is easily to be implemented. It requires two input parameters, namely the similarity between pairs of RPs and the preference values. At orientation o, the similarity between RP i and RP j is deﬁned as (o) (o) s(i, j)(o) = −∥ψ i − ψ j ∥2 , ∀i, j ̸= i ∈ {1, 2, ..., N }, o ∈ O (3.4) Since all of the RPs are equally desirable to be exemplars, their preferences are set to a common value. In order to generate a moderate number of clusters, the common preference for orientation o is deﬁned as p(o) = γ (o) · median{s(i, j)(o) , ∀i, j ̸= i ∈ {1, 2, ..., N }}, o ∈ O (3.5) where γ (o) is a real number which is experimentally determined, such that a desired number of clusters is generated. For each orientation, o ∈ O, the aﬃnity propagation algorithm takes the above deﬁnitions of similarity (3.4) and preference (3.5) as inputs and then it recursively updates the responsibility messages and availability messages according to (2.12) to (2.15) until a good set of exemplars and the corresponding clusters emerges [15]. This set of generated exemplars is denoted as H(o) and the corresponding cluster member set with RP
- 46. Chapter 3. Compressive Sensing Based Positioning System 33 (o) j as the exemplar is represented as Cj , j ∈ H(o) . In general, the RPs that are within the same cluster should be physically in close proximity, as the neighboring RPs should attain similar RSS readings. However, due to the varying characteristics of RSS readings (such as the shadowing eﬀects), there exist RPs that are physically far away from their assigned clusters. These RPs, referred to as outliers, are manually assigned back to the clusters that are physically closeby to reduce the potential errors in position estimations. 3.2.3 Interaction between the database server and the mobile device during oﬄine phase Fig. 3.2 illustrates how the proposed positioning system is set up on the mobile device and the server during oﬄine phase to obtain and process the training data required for the localization. The mobile device collects RSS time samples from detectable APs at speciﬁc positions (RPs) and transmits these data to the server. After the ﬁngerprint collection is done by the device, the server creates the radio map database and generates clusters for each orientation by applying the aﬃnity propagation algorithm. This algorithm is run on the server as it is an iterative process that consumes a large amount of memory and processing power that may not be supported by the mobile device. At the end of the oﬄine phase, the server obtains the coordinates of the RPs, radio map matrices, variance of RSS readings and also clusters information for each orientation. These data are then used in the online phase for the computation of position estimations. 3.3 Online Phase During the online phase, the device, carried by a mobile user and pointed to an unknown orientation, collects online RSS readings from detectable APs, which are then used together with the ﬁngerprint database to estimate the device’s location. The online RSS
- 47. Chapter 3. Compressive Sensing Based Positioning System Mobile Device 34 Server Collect RSS time samples from APs at RP j for 4 orientations Compute the average and variance of RSS readings over time, _j (o), _ j(o) ∆ ψ Send RP j’ s information: _j (o), _j (o) & coordinates (x_j, y_j) SEND Collect fingerprint for RP j in 4 orientations ∆ Use the device to collect N RPs ψ Create overall radio map matrix: (o) = [ _ 1(o), _ 2(o),…, _N (o)] ψ ψ ψ Ψ Apply affinity propagation on each radio map to generate sets of exemplars H(o) and their corresponding members C_j (o) Outlier adjustment for each radio map Figure 3.2: Interaction between the database server and the mobile device during oﬄine phase. measurement vector at time t is denoted as r(t) = [r1 (t), r2 (t), · · · , rL (t)]T (3.6) where {rk (t), k = 1, ..., L} is the online RSS readings from AP k at time t. Since the positioning system does not take into account the previous estimate, the time dependency notation (t) is dropped in this chapter for simplicity purpose, i.e. the online RSS reading is denoted as r instead of r(t). As shown in Fig. 3.1, the collected measurement vector is the input to the proposed positioning system. First, it is used in the coarse localization stage to reduce the area of interest. Then it is also used in the ﬁne localization stage to obtain the ﬁnal estimated position. The details of these two stages are described in the following sections.
- 48. Chapter 3. Compressive Sensing Based Positioning System 3.3.1 35 Coarse Localization Stage: Cluster Matching As mentioned earlier, the goal of the coarse localization stage is to reduce the region of interest from the whole ﬁngerprint database to a subset of it. Thus, it can reduce the computation time for the ﬁne localization stage, as fewer RPs are considered. It can also conﬁne the maximum localization error to be the size of this subset, whereas this error can be much larger when no coarse localization stage is implemented. The coarse localization is done by selecting the clusters, as deﬁned in the oﬄine phase, whose RSS radio map vectors best-match with the online RSS measurement vector r. Since the target device can be physically located at the boundaries of the deﬁned clusters, a few best-matched clusters, instead of only one cluster, are selected to eliminate the inaccuracy due to the edge problem. The cluster matching process can be interpreted as ﬁnding a set of best-matched exemplars SRSS with their corresponding cluster members set CRSS , such that they have the highest similarities with the online reading. It is crucial to have a good similarity function between the online reading r and an exemplar j ∈ H(o) , ∀o ∈ O, denoted as SM atch (r, j)(o) , so that the clusters for which the online measurement vector r should belong to can be correctly identiﬁed. The worst case scenario, where wrong sets of clusters are chosen for the online measurement vector r, should be avoided, as this results in a wrong localization region and thus introduces large localization error. This may happen, as the online RSS readings may deviate from the ﬁngerprint database due to the time varying indoor radio propagation channel. In order to reduce the occurrences of such scenarios, several matching schemes are considered in this thesis. These schemes provide diﬀerent ways to deﬁne the appropriate similarity function SM atch (r, j)(o) . 1. Exemplar based cluster matching This is the most basic scheme, which uses the same deﬁnition as (3.4) for the clustering in oﬄine phase. The similarity computes the Euclidean distance of the
- 49. Chapter 3. Compressive Sensing Based Positioning System 36 online measurement vector r to the individual exemplar’s RSS radio map vector from each cluster: (o) SM atch (r, j)(o) = −∥r − ψ j ∥2 , ∀j ∈ H(o) , ∀o ∈ O (3.7) 2. Average based cluster matching Instead of using the exemplar RSS radio map vector, the average of the RSS radio map vectors of all the cluster members, which gives a more comprehensive and representative readings of the whole cluster, is used to compute the Euclidean distance against the online measurement vector r: SM atch (r, j)(o) = −∥r − ∑ 1 (o) |Cj | (o) k∈Cj (o) ψ k ∥2 , ∀j ∈ H(o) , ∀o ∈ O (3.8) 3. Weighted Average cluster matching This scheme takes into account the stability of the RSS readings from a speciﬁc AP at diﬀerent RPs. Diﬀerent weights are added to the similarity function for each AP of each cluster at each orientation, so that it gives more weight to the stable RSS readings. The stability of an AP at a RP can be determined as the inverse of the variance of the RSS readings collected from that AP at that RP calculated in the oﬄine phase, thus APs with smaller variances are more reliable and have larger weights. The similarity function is deﬁned as: (o) SM atch (r, j)(o) = −∥Wj · (r − (o) Wj 1 ∑ (o) |Cj | (o) k∈Cj (o) ψ k )∥2 , ∀j ∈ H(o) , ∀o ∈ O √ (o) w1,j 0 ··· 0 √ (o) 0 w2,j 0 0 = . .. . . 0 0 . √ (o) 0 ··· 0 wL,j (3.9) (3.10)
- 50. Chapter 3. Compressive Sensing Based Positioning System (o) where Wj 37 (o) is the diagonal weight matrix and wl,j , l = 1, 2, . . . , L is the weight of AP l for cluster j at orientation o. This weight is proportional to the inverse of the variance of the AP for the speciﬁc cluster, namely (o) wl,j ∝ 1 ¯ (o) ∆ l,j ¯ (o) ∆l,j = 1 (3.11) ∑ (o) |Cj | (o) k∈Cj Then these weights are normalized, so that (o) ∆l,k ∑L k=1 (3.12) (o) wl,j = 1. 4. Strongest APs matching In this scheme, the online measurement vector is ﬁrst pre-ﬁltered to determine L′ APs that have the strongest RSS readings. Then, the similarity can be calculated using any of the above schemes by only considering the RSS readings from these selected APs. Since the APs that have stronger RSS readings tend to be more stable as the device is with high probability within their coverage area, whereas the APs with weaker signals tend to vary in time, the scheme is able to provide good matching similarity deﬁnition by only considering the reliable APs. All the above cluster matching schemes attempt to reduce the possibility of choosing the wrong clusters used by the ﬁne localization and thus improving the system’s stability and accuracy. The performances of these schemes are evaluated in details in Chapter 7. By evaluating the similarity function described above, the set of best matched exemplars SRSS with their corresponding cluster members set CRSS can be found as: SRSS = {(j, o)| SM atch (r, j)(o) > α, j ∈ H(o) , o ∈ O} (o) CRSS = {(k, o)| k ∈ Cj , (j, o) ∈ SRSS } (3.13) (3.14) where α is a predeﬁned threshold value to determine whether a cluster should be included into SRSS . Since only a few set of clusters are desired to be included in SRSS , α is set to
- 51. 38 Chapter 3. Compressive Sensing Based Positioning System be a high percentage, α1 , of the maximum similarity diﬀerence, that is α = α1 · max j∈H(o) ,o∈O { } SM atch (r, j)(o) + (1 − α1 ) · min j∈H(o) ,o∈O { SM atch (r, j)(o) } (3.15) Finally, the region of interest of the localization problem can be reduced to the set of ˜ ˜ ˜ CRSS . The modiﬁed radio map matrix ΨL×N , N = |CRSS | can be obtained as (o) ˜ Ψ = [ψ j , ∀(k, o) ∈ CRSS ]. (3.16) This matrix will then be used by the following ﬁne localization stage. Note it is possible that this matrix may contain the radio map vectors from the same RP but at diﬀerent orientations, as all clusters from diﬀerent orientations are considered for cluster matching. 3.3.2 Fine Localization Stage: Compressive Sensing Recovery The ﬁngerprint-based localization problem can be reformulated as a sparse signal recovery problem, as the position of the mobile user is unique in the discrete spatial domain. By assuming that the mobile user is located exactly at RP j and facing at orientation o, such that (j, o) ∈ CRSS , the user’s location can be represented relative to these RPs instead of the actual location. The mathematical representation is a 1-sparse vector, denoted as θ N ×1 , whose elements are all equal to zero except the n-th element, so that θ(n) = 1, ˜ where n is the corresponding index of the RP at which the mobile user is located, that is θ = [0, ..., 0, 1 , 0, ..., 0]T (3.17) nth element Then, the online RSS measurement r obtained by the mobile device can be expressed as: ˜ y = Φr = ΦΨθ + ε (3.18) ˜ where Ψ is the modiﬁed radio map matrix as deﬁned in (3.16) and ϵ is an unknown measurement noise. The matrix ΦM ×L is an AP selection operator applied on the online
- 52. 39 Chapter 3. Compressive Sensing Based Positioning System RSS measurement vector r to obtain vector y, where M < L is the desired number of APs to be selected. Based on this sparse signal recovery formulation, the following parts explain how the location of the mobile user can be recovered by using the compressive sensing theory. A. Access Points Selection Since most modern buildings are equipped with a large number of APs to ensure good quality of wireless services, the total number of detectable APs in these buildings, L is often much greater than that required for positioning. These extra APs lead to excessive computations and possibly biased estimations if some of the APs are not reliable. Inclusion of RSS readings from unstable APs may introduce error to the estimations, as online RSS values may deviate from the readings in the oﬄine database. Therefore, an access point selection step is introduced to select a subset of reliable and stable APs from the available ones to be used for the actual positioning, in order to eliminate the errors due to large number of APs. Denote the set of all available APs found within all the RPs by L with |L| = L. Then the AP selection step is to determine a subset of APs, M ⊆ L, such that |M| = M ≤ L. The AP selection process is carried out by applying the AP selection operator Φ on the online measurement vector r as deﬁned in (3.18). Each row of Φ, is a 1 × L vector th that selects the desired lm AP, where lm ∈ M, by assigning ϕ(lm ) = 1 and zero to the rest of the elements, namely: ϕm = [0, ..., 0, 1 , 0, ..., 0], lm ∈ M, ∀m = 1, 2, . . . , M (3.19) lm −th element In this thesis, three AP selection schemes are used based on APs stabilities and diﬀerentiability in spatial domain. Their performances are evaluated in a later chapter. 1. Strongest APs [39]
- 53. Chapter 3. Compressive Sensing Based Positioning System 40 This scheme selects the set of M APs with the strongest RSS readings from the online RSS measurement vector. These APs with strong RSS readings are more reliable than the ones with weak RSS readings, as they provide a high probability of coverage over time. The set of APs can be obtained by sorting the elements of the online measurement vector r in descending order and selecting indices of the ﬁrst M values that correspond to the APs with highest RSS readings. Since the online RSS readings are diﬀerent for each run, the AP selection operator Φ is created dynamically on the device for each update during the online phase. 2. Fisher Criterion [38, 66] This scheme selects the APs which discriminate themselves the best within RPs. The discrimination ability for each AP i, i ∈ {1, 2, . . . , L} can be quantiﬁed through the Fisher criterion. The metric for AP i, denoted as ξi is deﬁned as ∑ ξi = (o) (j,o)∈CRSS (ψi,j ∑ (j,o)∈CRSS ¯ where ψi = 1 ˜ N ∑ (j,o)∈CRSS ¯ − ψi )2 (o) (3.20) ∆i,j (o) ψi,j . The APs with highest ξi are chosen to construct the AP selection operator Φ for the actual localization. This metric accounts for two factors: the denominator ensures that RSS values should not vary too much over time, thus implies that the oﬄine and online values are similar and the numerator evaluates the discrimination ability of each AP by considering the strength of variations of mean RSS across RPs. Since this metric calculations are done across the RPs j at orientation o chosen in the coarse localization stage, (j, o) ∈ CRSS , the AP selection operator Φ is created dynamically on the device for each update during the online phase. 3. Random Combination Unlike the above two schemes, which select the appropriate APs based on diﬀerent criteria and create the AP selection operator Φ dynamically for each update, the
- 54. Chapter 3. Compressive Sensing Based Positioning System 41 random combination scheme does not take into account the performance of the APs and thus have less computation complexity during online phase and also does not require large number of RSS time samples for the variance calculation in the oﬄine phase as required by the Fisher criterion. The AP selection operator Φ is deﬁned as a randomly generated i.i.d. Gaussian M × L matrix. Thus, according to (3.18), y = Φr, y is a set of M linear combinations of online RSS values from L APs. Since the same matrix can be reused for each update, it can be generated and stored ﬁrst during the training period and retrieved for use directly in the online phase, saving the time to dynamically generate the matrix as required by the other two schemes. B. Orthogonalization and Signal Recovery using ℓ1 -minimization Compressive sensing theory requires both sparsity and incoherence of the signal, so that it can be recovered accurately. Although the localization problem as deﬁned in (3.18) ˜ satisﬁes the sparsity requirement, Φ and Ψ are in general coherent in the spatial domain. Thus, an orthogonalization procedure is applied to induce the incoherence property as required by the CS theory [67, 68]. The orthogonalization process is done by applying an orthogonalization operator, T, on the vector y, such that z = Ty. The operator is deﬁned as T = QR† (3.21) ˜ where R = ΦΨ, and Q = orth(RT )T , where R† is a pseudo-inverse of matrix R and orth(R) is an orthogonal basis for the range of R. By applying this operator on y, (3.18) becomes: z = Ty = QR† y = QR† Rθ + QR† ε = Qθ + ε′ (3.22)
- 55. Chapter 3. Compressive Sensing Based Positioning System 42 ˜ where ε′ = Tε. If M is in the order of log N , the minimum bound required by the CS theory, θ can be well-recovered from z with very high probability, by solving the following ℓ1 -minimization problem [67, 68]. ˆ θ = arg min ∥θ∥1 , s.t. z = Qθ + ε′ . (3.23) ˜ θ∈RN The computation complexity of the ℓ1 -minimization algorithm grows proportional to the dimension of vector θ, which is the number of potential RPs. Therefore, the coarse localization stage, which reduces the area of interest from all the N RPs into a subset ˜ of N < N RPs, reduces the computational time and resources required for solving the ℓ1 -minimization problem, and thus allows this procedure to be carried out by resourcelimited mobile devices. C. Interpretation of Actual Position The above procedure is able to recover the exact position, if the mobile user is located at one of the RPs facing one of the orientations in the set of O, which is the assumption made earlier in order to formulate the localization problem into a 1-sparse natured problem. However, in real situation, the mobile user may not be located at an RP facing a certain ˆ orientation. Thus, in actual implementation, the recovered position vector θ is not a 1-sparse vector, rather a vector with a few non-zero coeﬃcients. A post-processing step ˆ is conducted to interpret this recovered location vector θ into an actual location and compensate the error induced by the grid assumption. The procedure chooses the set of ˆ all indices of the dominant elements in θ, which are above a certain threshold λ, denoted as R ˆ R = {n|θ(n) > λ} (3.24) ˆ λ = λ1 max(θ) (3.25) where λ1 is a parameter within a range (0, 1) and is adjusted experimentally. Then, the estimated location of the mobile user can be calculated as a weighted average of these
- 56. Chapter 3. Compressive Sensing Based Positioning System 43 ˆ potential candidate points, using the normalized value in θ as the corresponding weight for each potential RP, that is p = (ˆ, y ) = ˆ x ˆ ∑ ηn · (xn , yn ) (3.26) n∈R ∑ ˆ ˆ where ηn = θ(n)/ n∈R θ(i) and (xn , yn ) is the cartesian coordinates of RP n. 3.3.3 Interaction between the database server and the mobile device during online phase The roles of the mobile device and the server during the online phase are illustrated in Fig. 3.2. First, the device collects the online RSS readings from all the detectable APs, namely r. Then the device requests the map and the representative RSS readings for each cluster from the server, in order to perform coarse localization. After the best-matched clusters are found, the device communicates with the server to obtain the relevant radio ˜ map matrix Ψ for the following ﬁne localization. The device carries out steps of AP selection, orthogonalization and ℓ1 -minimization to obtain the recovered location vector ˆ θ. Finally, the device asks the server for the potential candidate RP’s coordinates and ˆ computes the estimated position according to θ. 3.4 Chapter Summary In this chapter, the proposed compressive sensing based positioning system is described in details. The system involves two phases. The oﬄine phase is the training period that collects RSS values from detectable access points at reference points to create the ﬁngerprint database. It also runs the aﬃnity propagation algorithm to create diﬀerent clusters of RPs with similar RSS reading patterns and within physical proximity. The actual localization takes place in the online phase, which consists of two stages. First, the mobile device collects the online RSS readings, which are used to ﬁnd the subset of
- 57. Chapter 3. Compressive Sensing Based Positioning System Mobile Device Coarse Localization (cluster matching) Server Collect online RSS readings r , 44 It contains: Ψ (o), ∆_j (o), H(o), C_j(o) - list of RPs coordinates - map REQUEST Request and obtain map and RSS values of exemplars. SEND Retrieve map and RSS readings of exemplars Find best matched cluster exemplars, S SEND S Use the received matched cluster exemplars S to obtain the matched cluster members C and generate a smaller radio map matrix Ψ Obtain Ψ ͂ , ∆_j(o) SEND Send Ψ ͂ , ∆_j(o) ͂ AP selection Orthogonalization Fine Localization (CS-theory) l1-norm minimization Interpret device’s location using relevant RPs coordinates. REQUEST RPs’ coordinates Retrieve relevant RPs’ coordinates SEND RPs’ coordinates Figure 3.3: Interaction between the database server and the mobile device during online phase. relevant RPs by the coarse localization stage through cluster matching process. Several cluster matching schemes are discussed in an attempt to reduce the eﬀect of outliers and derivations in RSS readings between oﬄine and online phases. This stage reduces the area of interest from the whole database into a smaller region, thus reducing the computation time for the latter stage, and also minimizes the eﬀect of outliers and RSS time varying derivations. Then, a ﬁne localization stage is applied on this reduced area to ﬁnd the estimated position. It is done by formulating the localization problem into a sparsenatured signal recovery problem, such that the compressive sensing theory can be applied to recover the desired signal. There are several steps to compute the estimated position: access point selection, orthogonalization, ℓ1 -minimization problem and interpretation of recovered location vector into actual location, which are described in the chapter. The chapter also explains diﬀerent roles of the mobile device and the server in the
- 58. Chapter 3. Compressive Sensing Based Positioning System 45 proposed system. The server is mainly served as a database storage, which when requested by the device, sends required information, such as map and RSS readings to the device. It is also responsible for running the aﬃnity propagation algorithm to form clusters during oﬄine phase, as the device does not have enough computation resources to run such clustering scheme. The mobile device collects the RSS readings and obtains information from the server, in order to estimate its location locally.
- 59. Chapter 4 Indoor Tracking System The previous chapter describes a positioning system that can accurately estimate a stationary user’s position. This positioning system is modiﬁed in this chapter in order to track the dynamic mobile user. The proposed indoor tracking system uses the Kalman ﬁlter with map information to smooth out the location estimate and also uses previous position estimate to choose the relevant region of interest in the coarse localization stage. This chapter ﬁrst describes the Kalman ﬁlter and then the proposed indoor tracking system. In this chapter, the tracking problem is deﬁned as follows. The device carried by the mobile user periodically collects the online RSS readings from each APs at a time interval ∆t, which is limited by the device’s network card and hardware performances. The online RSS readings vector is denoted as r(t) = [r1 (t), r2 (t), . . . , rL (t)], t = 0, 1, 2, ..., where rl (t) corresponds to the RSS from AP l at time t. Then, the indoor tracking system uses these RSS readings to estimate the user’s location at time t, which is denoted as p(t) = [ˆ(t), y (t)]T . ˆ x ˆ 46
- 60. Chapter 4. Indoor Tracking System 4.1 47 General Bayesian Tracking Model The tracking problem of a mobile user can be modeled by a general Bayesian tracking model as follows [41] and [47]: x(t) = ft (x(t − 1), w(t)) (4.1) z(t) = ht (x(t), v(t)) (4.2) where x(t) = [x(t), y(t), vx (t), vy (t)] is the state of the user at time t with (x(t), y(t)) as the Cartesian coordinates of the user’s location and vx (t) and vy (t) as the velocities in x and y directions, respectively. Assuming the tracking is a Markov process of order one, the state evolves as a function ft of previous state and w(t), i.i.d. process noise vector only. In addition, the measurement z(t) depends on the current state and the i.i.d. measurement noise vector v(t) through the function ht . The current location of the mobile user, x(t) can then be estimated recursively from the set of measurements up to time t, i.e. z(1 : t) = {z(i), i = 1, ..., t}, in terms of the probability distributive function (pdf), denoted as p(x(t)|z(1 : t)). Assuming that the initial pdf p(x0 |z 0 ) ≡ p(z 0 ) and p(x(t−1)|z(1 : t−1)) are known, the pdf p(x(t)|z(1 : t)) can be obtained by the following prediction and update stages: 1. Prediction Stage: The prior pdf p(x(t)|z(1 : t−1)) can be predicted based on p((x(t)|x(t−1)), which is deﬁned by the state process equation (4.1) and the previous state pdf. ∫ p(x(t)|z(1 : t − 1)) = p((x(t)|x(t − 1))p(x(t − 1)|z(1 : t − 1))dx(t − 1) (4.3) 2. Update Stage: Then, the prior pdf can be updated by the measurement z(t) obtained at time t

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