A Thesis. entitled. Development of Novel Algorithms for Localization in Wireless Sensor Networks. Nuwan Rajika Kumarasiri

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1 A Thesis entitled Development of Novel Algorithms for Localization in Wireless Sensor Networks by Nuwan Rajika Kumarasiri Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Engineering Dr. Vijay Devabhaktuni, Committee Chair Dr. Nghi Tran, Committee Co-Chair Dr. Mansoor Alam, Committee Member Dr. Robert Green, Committee Member Dr. Weiqing Sun, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo December 2014

2 Copyright 2014, Nuwan Rajika Kumarasiri This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

3 An Abstract of Development of Novel Algorithms for Localization in Wireless Sensor Networks by Nuwan Rajika Kumarasiri Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Engineering The University of Toledo December 2014 Highly accurate localization in wireless sensor networks (WSNs) has been considered as one of the most significant challenges in wireless sensor networks. Significant efforts have been made in order to uplift the solutions to this challenging problem as, localization of a signal source in a wireless sensor network is now appealing for a range of real life applications, including emergency services, navigational systems, and civil/military surveillance. For instance, a couple of seconds of delay in identifying a location of an injured victim could create life threatening situations. During the last few years, several techniques have been proposed to provide an accurate estimation of the location of an unknown sensor node. Received-signal-strength (RSS), angle-of-arrival (AOA), time-difference-of-arrival (TDOA) and time-of-arrival (TOA) to name a few. While these techniques are quick to produce fairly accurate location estimation, they suffer effects from non-line-of-site (NLOS) conditions, unavailability of one or more sensors, or the requirement of expensive receivers, all of which would lead to poor or no location estimation at all. Motivated by the above observations, this thesis aims to develop two novel localization algorithms for localization in WSNs. Furthermore, it suggests to use Dempster-Shafter theory as an efficient tool for localization purposes in WSNs. In this thesis two new localization schemes are proposed. One proposed algorithm for localization in WSNs simultaneously exploits received signal strength (RSS) and iii

4 time difference of arrival (TDOA) measurements. The accuracy and convergence reliability of the proposed hybrid scheme is also enhanced by incorporating RSS measurements from Wi-Fi networks via cooperative communications between Wi-Fi and sensor networks. Simulation results show that the proposed hybrid positioning approach significantly outperforms each individual method. The advantages of the proposed scheme, which include providing high location accuracy, fast convergence, low complexity implementation, and low power consumption, make it an attractive localization solution via WSNs. A low cost data fusion technique for node positioning that fuses different parameters obtainable from signal measurements, such as received-signal-strength (RSS), angle, and time observations is proposed next. Such a tool enables additional network-based parameters (e.g. hop-counts, delays, etc.) to be easily incorporated to enhance the accuracy of the classification process. The proposed classifier records an improved accuracy of 83.7% from its initial 38.3% accuracy in locating the cell associated with a sensor node at low computational complexity. iv

5 To my loving wife and parents for their love and support.

6 Acknowledgments First of all, I would like to express my sincere gratitude to my advisors, Dr. Vijay Devabhaktuni and Dr. Nghi Tran for their patience, motivation, enthusiasm, immense knowledge, and continuous support towards the successful completion of my master s degree study and research. Their guidance helped me throughout the time that has been spent in research and writing of this thesis. Beside my advisors, I would like to thank the rest of my thesis committee, Dr. Mansoor Alam, Dr. Robert Green, and Dr. Weiqing Sun for their encouragement and insightful comments. I also want to be thankful to the National Science Foundation (NSF) and Department of Electrical Engineering and Computer Science at the University of Toledo for providing financial support for my graduate education. I am very thankful to Khair Al Shamaileh for his guidance throughout my Master s degree program and Colin Elkin for his time reviewing my thesis and providing valuable feedback. Your support is greatly appreciated. I am also very thankful to my friends and colleagues in the Computer Aided Design and Simulation lab (NE 2042) at the University of Toledo for their stimulating discussions and assistance. You made my stay at the research lab a memorable one. I would especially like to thank my dear wife, Sewwandi, for her love, kindness, and tremendous support given to me at all time. Finally, I would like to thank my family, my parents, my three sisters, and my brother for their continuous support, love, and encouragement throughout every step of mine on this planet. vi

7 Contents Abstract iii Acknowledgments vi Contents vii List of Tables x List of Figures xi List of Abbreviations xiii List of Symbols xiv 1 Introduction Research Objective Publications and Contributions in Thesis Thesis Organization Literature Review Introduction Source Localization Methods Received Signal Strength (RSS) Time of Arrival (TOA) Time Difference of Arrival (TDOA) vii

8 Angle of Arrival (AOA) Hybrid Localization Schemes Comparison between Localization Schemes Source Localization Estimators Nonlinear Estimator Linear Estimator An Improved Hybrid RSS/TDOA Wireless Sensors Localization Technique Utilizing Wi-Fi Networks Overview Proposed Scheme Underline Scenario Problem Formulation Solving the Proposed Hybrid Equations Nonlinear Estimators Newton-Raphson Gauss-Newton Linear Estimators Taylor-series Closed-form Estimator Pseudo Codes and Flow Charts Cramér-Rao Lower Bound for Hybrid Localization Scheme Experimental Results Conclusions Low Cost Data Fusion Technique for Localization in Wireless Sensor Network Overview viii

9 4.2 Geo-locating Internet Hosts Overview of Machine Learning approach Kernel Density Estimators Mathematical Model Learning Based Localization in Wireless Sensor Networks Feature Selection Localization Algorithm and Flowchart Experimental Results Conclusions and Future Work Conclusion and Future work Conclusion Future work References 72 A MATLAB Source Code 85 ix

10 List of Tables 1.1 Publications and contributions in thesis Comparison of different localization methods Comparison of different localization estimators Comparison of Newton-Raphson and Gauss-Newton iterative estimators for near source (2, 3). E = (x ˆx) 2 + (y ŷ) Comparison of Taylor-series and closed-form estimators near source (2, 3). E = (x ˆx) 2 + (y ŷ) MSE for the near source scenario, cσ t =0.1 m, cσ r =0.1 m, and cσ rw (Wi- Fi)=0.125 m. M= MSE for the far source scenario with noise equal to 2 m range estimation error. M= Accuracy of the classifier with different number of features x

11 List of Figures 2-1 Classification of localization algorithms Sensor localization process Localization using RSS, TOA, TDOA or AOA The interaction of three or more circle provides the location estimations in RSS and TOA The interaction of three or more parabola provides the location estimations in TDOA The interaction of two or more line of bearing (LOB) provides the location estimations in AOA Classification of localization estimation schemes Networking structure of the proposed scheme The proposed cooperative algorithm (TS estimator) The proposed cooperative algorithm (Closed-form estimator) Flow chart for iterative localization scheme Estimation of x and y coordinates for unknown sensor location, (2, 3) for hybrid RSS/TDOA scheme Estimation of x and y coordinates for unknown sensor location, (2, 3) for enhanced hybrid RSS/TDOA(Wi-Fi) scheme CDF plot of location errors; 4 receivers. Taylor-series estimator CDF plot of location errors; 4 receivers. Closed-form estimator CDF plot of location errors; 5 receivers. Taylor-series estimator xi

12 3-10 CDF plot of location errors; 5 receivers. Closed-form estimator Schematic representation of the machine learning localization scheme The pseudo code of the proposed classifier for localization in wireless sensor network Flowchart for the machine learning localization algorithm The experimental set up for the classifier based localization scheme Using DS theory as an effective data fusion mechanism xii

13 List of Abbreviations 2-D Two-dimensional 3-D Three-dimensional AOA CDF CRLB DS FIM GPS LOB LOS LS MEMS ML NLS NLOS RSS TDOA TOA TS UWB WLS WSN(s) Angle of Arrival Cumulative Distribution Function Cramér-Rao Lower Bound Dempster-Shafer Fisher Information Matrix Global Positioning System Line of Bearing Line of Sight Least Square Micro-Electro-Mechanical System Maximum-likelihood Non Linear Least Square Non Line of Site Received Signal Strength Time Difference of Arrival Time of Arrival Taylor-series Ultra Wide Band Weighted Least Square Wireless Sensor Network(s) xiii

14 List of Symbols T Transpose Inverse E Expectation operator var Variance Distributed as I Identity matrix Zero matrix of appropriate size â Estimate of a diag(a)..... Diagonal matrix with vector a as main diagonal O(n) The complexity of the algorithm x Vector x c Speed of light, c 3x10 8 ms -1 xiv

15 Chapter 1 Introduction Positioning systems estimate the location of a person or an object either relative to a known position or within a coordinate system. Highly accurate localization in a wireless sensor network (WSN), i.e. finding the position of a sensor node, has been considered as one of the most significant challenges in wireless sensor networks (WSNs) [1, 2, 3]. In the last few decades, various positioning systems have been invented to develop highly-accurate, low-power, low-cost localization schemes due to their appeal for a range of real life applications, including navigational systems [4, 5, 6], civil/military surveillance [7, 8], and emergency services [9, 10, 12, 13]. For an instance, few seconds of delay in identifying location of an injured victim could create life threatening situations. The requirement for accurate and optimal localization schemes have been even motivated by demand with the rapid development of cost-effective Micro-Electro-Mechanical System (MEMS). Furthermore, the problem becomes even more challenging in locations where broadcasted signals take longer and multiple paths thus arrive with lower signal strength at the receiver location. Wireless networks utilize radio waves and/or microwave in order to maintain communication channels between devices/users through deployed network nodes or sensors. Each mote (sensor) in the wireless sensor network is equipped with sensing, computation, or communication capabilities. 1

16 During the last few decades, several techniques have been proposed to provide an accurate estimation of the location of an unknown sensor node (please see [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26] and references therein). For example, by measuring the received-signal-strength (RSS) at three or more known sensor nodes, trilateration can be used to estimate the location of the unknown source [15, 16, 17]. Angle-ofarrival (AOA) is another well-known technique used for localization [18, 19, 20]. Using this method, the angles of arrival (AOAs) of signals are measured at the receivers, and the source location is then estimated using triangulation. Time-difference-of-arrival (TDOA) [21, 22, 23] and time-of-arrival (TOA) [24, 25, 26] fall into the time-based category for localization. Specifically, these methods rely on the measurements of time the signal takes to reach the known sensor nodes from the unknown node. The resulting measurements at three or more receivers generate a hyperbola at which the unknown source may reside. Among these techniques, RSS and TDOA are more popular in WSNs due to the ease of implementation. On the other hand, while AOA in general produces fairly good results even at only two known receivers, it requires expensive antenna arrays at each receiver. For the TOA-based methods, synchronization between the serving receivers and the source side is required, which makes it an obstacle for localization in WSNs. To further improve the localization performance, one can use a hybrid location scheme in which individual approaches can be combined [27, 28, 29]. For example, in [27], the combination of RSS and AOA was proposed. Given that a sensor node is a small and inexpensive device, a combination of simple schemes with low complexity and cost, such as RSS and TDOA can be considered. Due to the distributed nature of sensor nodes in WSNs, considerable efforts have also been dedicated to the idea of cooperative localization, in which a source node is assumed to be able to communicate with not only reference nodes but also other source nodes [33]. Given such cooperative communications, additional location information obtained from some extra reliable 2

17 links can be exploited to improve the overall accuracy. As Wi-Fi access points become increasingly prevalent, their exploitation in localization purposes for WSNs is also natural. For example, in [34], a low cost, easy to implement scheme for indoor mobile localization that utilizes RSS Fingerprint, Wi-Fi, and Bluetooth was proposed. While these localization schemes produce accurate estimation, they are quickly affected by the complexity associated with the dynamic changes in indoor environments. All these localization schemes have one significant limitation in common, which is that they can be easily affected by the non-line-of-sight (NLOS) conditions [83, 84, 85, 86] or multi-path fading [87, 88, 89]. Global positioning system (GPS) [44, 82] could be used to provide an accurate location estimation with the least amount of disruptions from the mentioned obstacles. However attaching a GPS receiver for each sensor would not be a scalable solution due to the cost factor associated with the GPS based solutions [90]. An optimally cost effective solution is preferable to the consumers. Motivated by above observations there are some interesting questions that can be asked. 1. Can there be improved localization schemes that can be deployed on already existing Wireless Sensor Networks without any hardware modifications? 2. Is there an ability to re-use Wi-Fi networks for localization purposes given that the incredible popularity and success of Wi-Fi networks? 3. Are there efficient location estimators which equally can be implemented in hand-held devices or mobile devices which have limited computational power? 4. Is there any mechanism which allows various parameters associated with Wireless Sensor Network to be used in localization? The research that is presented in this thesis is motivated by above questions. It is an attempt to determine suitable solutions to the mentioned questions. 3

18 Table 1.1: Publications and contributions in thesis. Type Journal paper Journal paper Source code Publication/Contribution An Improved Hybrid RSS/TDOA Wireless Sensors Localization Technique Utilizing Wi-Fi Networks. Low Cost Data Fusion Technique for Localization in Wireless Sensor Network. A re-usable MATLAB library, which contains the source code of the algorithm implementations. 1.1 Research Objective The localization of a sensor node, i.e. identification of a source node s location in a wireless sensor network, is a challenging problem. The objective of this research is to come up with accurate, cost effective and novel localization algorithms for localization in WSNs. 1.2 Publications and Contributions in Thesis 1.1. The major publications and contributions of this research work is listed in Table 1.3 Thesis Organization The thesis unfolds as follows: Chapter 2 provides the literature review. It covers an overview of the existing positioning techniques, their limitations, and their applications. Chapter 3 describes the first proposed scheme, the hybrid localization scheme of RSS and TDOA, together with the simulation results. It also describes the 4

19 set of suitable applications of the hybrid RSS/TDOA localization scheme. Chapter 4 is the explanation of the low cost data fusion technique for WSNs, including the derivation and the simulation results. The section ends with possible applications for this localization technique. Chapter 5 provides conclusive remarks and possible future direction of the research. This section presents Dempster-Shafer theory as a tool for localization in WSNs. Finally, the thesis ends with appendix which cover how to obtain the MATLAB source code of algorithm implementations (Appendix A). 5

20 Chapter 2 Literature Review Introduction Localization schemes determine the position of an object or person with respect to another known location or within an coordinate system [44]. During the last few years, several techniques have been proposed to provide an accurate estimation of the location of an unknown sensor node. As shown in Figure 2-1, localization algorithms can be divided mainly into two categories. 1. Range-Based positioning. 2. Range-Free positioning. This classification is based on the information used for localization. Range-based [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26] techniques use range measurements (such Localization algorithms Range Based Range Free GPS RSS AOA TDOA Connectivity based Localization Event Localization Event Figure 2-1: Classification of localization algorithms. 6

21 as distance or angle estimates), while range-free techniques [45, 46, 47, 48, 49, 50] only use connectivity information between unknown nodes and landmarks. Several range-free and range-based location technologies exist, with methods that vary from low accuracy based on cell identification to high accuracy, but costly approaches have been developed to address the sensor localization challenge. The range-free approaches include: i) Connectivity based localization techniques that use local neighborhood sensing to build hop based virtual distances for the network; ii) Event driven localization methods based on generating artificial events, laser beam scans, or blasts, which are distributed over the network area and analyzed to yield position information; and iii) Proximity based approaches, where the only available information between network nodes is linked to each node s radio visibility (e.g.wi-fi or ZigBee). The distance between these connected nodes cannot exceed a maximum threshold (i.e. short range methods), which is dependent on antenna gain, transmitted power, and propagation attenuation. However, the range-free methods have limited applicability because they suffer from low accuracy, are effective only under short range scenarios, are not suitable for sparse networks, and may require more anchor nodes. Range-based techniques have used Global Positioning System (GPS) [44], Received Signal Strength (RSS) [15, 16, 17], Angle of Arrival (AOA) [18, 19, 20], Time of Arrival (TOA) [24, 25, 26] and Time Difference of Arrival (TDOA) [21, 22, 23]. The new schemes proposed in this thesis are built on top of ranged-based localization schemes. The rest of the chapter will describe some of the most widely used range-based localization schemes in detail and compare the most widely used rangebased localization algorithm in terms of accuracy and ease of implementation. Then it will cover several factors which affect the accuracy of the location estimations. Mathematical methodologies that are utilized for solving the localization problem numerically are described towards the end of the chapter. 7

22 Parameter Estimation (RSS, AOA, TOA, TDOA) Location Estimation (Triangulation,Trilateration) (Longitude, Latitude, Elevation) Figure 2-2: Sensor localization process Source Localization Methods The position estimation of a target of interest can be determined by utilizing a set of signal measurements emitted from a signal source. The general approach for localization using range-based methods involve collections of various signal parameters (such as signal power, angle of arrival, etc...) followed by a numerical location estimation. This mechanism is shown in Figure 2-2. In the following sections, the measurement models for Received Signal Strength (RSS), Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Angle of Arrival (AOA) are described. In fact, all the measurement models can be summarized as r = f(x) + n (2.1) where r is the measurement vector, x is the source position to be determined, f(x) is a known nonlinear function in x, and n is an additive zero-mean noise vector. Let x = [x, y] T be the sensor (unknown target) position to be estimated and let the known coordinates of the i th receiver (anchor node, i.e. a node capable of measuring signal parameters from other nodes) be x i =[x i, y i ] T, i = 1, 2, 3,..., N, where the superscript T denotes the transpose operation and N is the total number of receiving sensor nodes. The distance between the sensor and the i th receiver is given by d i = (x x i ) 2 + (y y i ) 2 (2.2) This setup is shown in Figure 2-3. Following discussion, assume a two dimensional 8

23 S 1 (x 1,y 1 ) S i (x i,y i ) S N (xn,y N ) Figure 2-3: Localization using RSS, TOA, TDOA or AOA. (2-D) localization scenario, and the mathematical models can be easily extended for three dimensions (3-D) as well Received Signal Strength 1 (RSS) In the absence of measurement errors and/or noise, the received signal strength (RSS), or the received signal power from the unknown source measured at the i th receiver, denoted as P r i, can be modeled as [39] P r i Pi t = K i, i = 1, 2,..., N (2.3) d a i In equation (2.3), P t i is the transmitted power at the source, and d i is the distance from the source to the i th receiver. Furthermore, K i accounts for all other factors that affect the received power, including antenna heights and gains, and a is the path loss constant. Depending on the propagation environment, a can vary from 2 to 5. For free space a = 2. Without loss of generality, it is assumed that P t i, K i, and a are known beforehand. Then, taking into account measurement errors, the log-normal path loss model can be expressed as [40] ln(p r i ) = ln(k i ) + ln(p t i ) aln(d i ) + n rss,i, i = 1, 2,..., N (2.4) 9

24 Receiver 1 Receiver 3 (x 1,y 1 ) (x 3,y 3 ) Source (x,y) Receiver 2 (x 2,y 2 ) Figure 2-4: The interaction of three or more circle provides the location estimations in RSS and TOA. where {n rss,i } are the log-normal measurement errors. For simplicity, it is normally assumed that that each n rss,i is a Gaussian random variable with zero mean and RSS estimation variance σ 2 rss,i [41]. Let 1 r rss,i = ln(p r i ) ln(k i ) ln(p t i ) (2.5) The RSS signal model (equation 2.4) can then be simplified to r rss,i = aln(d i ) + n rss,i, i = 1, 2,..., N (2.6) The vector form of the equation (2.6) is then r rss = f rss (x) + n rss (2.7) 10

25 where r rss = [r rss,1 r rss,2... r rss,n ] T (2.8) n rss = [n rss,1 n rss,2... n rss,n ] T (2.9) and ln( (x x 1 ) 2 + (y y 1 ) 2 ) ln( (x x 2 ) 2 + (y y 2 ) 2 ) f rss (x) = a. ln( (x x N ) 2 + (y y N ) 2 ) (2.10) The source localization problem based on RSS measurements is then reduced to estimating x given that r rss comes from the actual measurements. Section describes estimators that can be used to solve equation (2.7). While RSS is fairly simple to implement, as it avoids heavy utilization of computer resources it is not suitable for outdoor location estimations Time of Arrival (TOA) The time of arrival (TOA) is the one way propagation time taken for the signal to travel from the source to the receiver [24, 25, 26]. In order to obtain the TOA measurement at more than one receiver, it is required that the source and receivers precisely be synchronized [24]. This can be avoided by measuring the round-trip or two-way TOA. The product of the TOAs by the known propagation speed, denoted by c, results in the distance between source sensor and receiver sensor. In a 2-D plane and in the absence of measurement error, each TOA corresponds to a circle centered at a receiver. The intersection of three or more circles (see Figure 2-4) result in the source sensor location. In a 2-D localization setup, two TOA measurements will produces two circles and will have two possible estimations. These circles may not intersect at the same point in the presence of measurement errors and other 11

26 disturbance. This leads the TOA problem into an optimization problem before the solution estimation. In the absence of measurement errors or disturbances, the TOA measured at the i th receiver, is denoted by t i and given by t i = d i, i = 1, 2,..., N (2.11) c where c is the speed of light as described. In the presence of disturbance and measurement errors, the range measurement based on t i, denoted by r toa,i is evaluated as [24]. r toa,i = d i + n toa,i = (x x 1 ) 2 + (y y 1 ) 2 ) + n toa,i, i = 1, 2,..., N (2.12) where n toa,i is the range error in r toa,i. For simplicity in the context of algorithm development and analysis, it is normally assumed that that each n toa,i is a Gaussian random variable with zero mean and TOA estimation variance σ 2 toa,i [41]. In vector form, equation (2.12) can be expressed as r toa = f toa (x) + n toa (2.13) where r toa = [r toa,1 r toa,2... r toa,n ] T (2.14) n toa = [n toa,1 n toa,2... n toa,n ] T (2.15) and (x x1 ) 2 + (y y 1 ) 2 (x x2 ) 2 + (y y 2 ) 2 f toa (x) =. (x xn ) 2 + (y y N ) 2 (2.16) 12

27 Receiver 1 (x 1,y 1 ) Source (x,y) Receiver 2 (x 2,y 2 ) Receiver 3 (x 3,y 3 ) Figure 2-5: The interaction of three or more parabola provides the location estimations in TDOA. The requirement for time synchronization among source and the receivers is a key challenge when implementing TOA based localization schemes. The source localization problem based on TOA measurements is to then estimate x given that r toa comes from the actual measurements. Section describes estimators that can be used to solve equation (2.13) Time Difference of Arrival (TDOA) 1 The time difference of arrival (TDOA) is the difference in TOAs of the received signal at a pair of receiver sensors, with respect to one of those receivers [22, 23]. Similar to TOA, this also requires synchronization among receivers, but it does not require synchronization at the source sensor to the same context as with TOA. Similar to TOA the product of the known propagation speed leads to the range difference between the source and the two receives. In a noise free environment each TDOA 13

28 generates a hyperbola on which the source may resides like in a 2-D plane. The target location is then given by the intersection of two or more hyperbolas (see Figure 2-5). In the presence of disturbance and measurement errors, the source location is estimated from a set of hyperbolic equations obtained from the TDOA measurements. In the absence of measurement errors and disturbances, using 1 st receiver as the reference, it can be easily shown that [38] r tdoa,i = (d i d 1 ) + n tdoa,i (2.17) = (x x i ) 2 + (y y i ) 2 ) (x x 1 ) 2 + (y y 1 ) 2 ) + n tdoa,i, i = 2,..., N where n tdoa,i is the range error in r tdoa,i. Note that if the TDOA measurements are directly obtained from the TOA measurements, then n tdoa,i = n toa,i n toa,1, i = 2,..., N (2.18) In vector form equation (2.17) becomes r tdoa = f tdoa (x) + n tdoa (2.19) where r tdoa = [r tdoa,2 r tdoa,3... r tdoa,n ] T (2.20) n tdoa = [n tdoa,2 n tdoa,3... n tdoa,n ] T (2.21) 14

29 Source (x,y) α 1 Recever 1 α 2 Recever 2 (x 1,y 1 ) (x 2,y 2 ) Line of Bearing Figure 2-6: The interaction of two or more line of bearing (LOB) provides the location estimations in AOA. and (x x2 ) 2 + (y y 2 ) 2 (x x 1 ) 2 + (y y 1 ) 2 (x x3 ) 2 + (y y 3 ) 2 (x x 1 ) 2 + (y y 1 ) 2 f tdoa (x) =. 1 (x xn ) 2 + (y y N ) 2 (x x 1 ) 2 + (y y 1 ) 2 (2.22) The source localization problem based on TDOA measurements is then to estiamte x given r tdoa. To facilitate the development and analysis of the localization scheme, n tdoa,i are assumed to be zero-mean and Gaussian distributed [41]. Section describes estimators that can be used to solve the nonlinear equation (2.19) Angle of Arrival (AOA) Time of arrival (AOA) is the arrival angle of the emitted source signal observed at a receiver. From each AOA, a line of bearing (LOB) [19, 20] can be drawn from the source sensor to the receiver sensor, and the intersection of two LOB (see Figure 2-6) will provide the possible location estimation for the unknown sensor node. 15

30 Although this scheme does not require any clock synchronization, it requires expensive antenna arrays at each receiver, for AOA measurement estimation. The AOA of the transmitted signal from the source at the i th receiver denoted by, α i, is realized as [41] tan(α i ) = y y i x x i, i = 1, 2,..., N (2.23) where,(x i, y i ) denotes the location of i th receiver. Geometrically, α i is the angle between LOB and the i th receiver with respect to some reference axis (for example x-axis). With the measurements errors and angle errors, the AOA measurements given by, r aoa,i can be modeled as [41] r aoa,i = α i + n aoa,i = tan 1 ( y yi x x i ) + n aoa,i, i = 1, 2,..., N (2.24) where n aoa,i is the noise in r aoa,i and are assumed to be zero-mean uncorrelated Gaussian processes with variance σaoa,i 2 [41]. Equation (2.24) can be expressed in vector form as r aoa = f aoa (x) + n aoa (2.25) where r aoa = [r aoa,1 r aoa,2... r aoa,n ] T (2.26) n aoa = [n aoa,1 n aoa,2... n aoa,n ] T (2.27) and ( ) tan 1 y y 1 x x 1 ( ) tan 1 y y 2 x x f aoa (x) = 2. ( ) tan 1 y y N x x N (2.28) 16

31 Then the source location estimation problem using AOA measurements is to estimate x given r aoa (obtain from measurements). To facilitate the development and analysis of the localization scheme, n aoa,i are assumed to be zero-mean and Gaussian distributed [41]. The nonlinear equation (2.25) can be solved using techniques presented in section Hybrid Localization Schemes To further improve the localization performance, one can use a hybrid location scheme in which individual approaches can be combined [27, 28, 29, 30]. For example, in [27], the combination of RSS and AOA was proposed. Hybridization of TDOA and AOA is proposed in [30]. Regardless of highly accurate location estimation of these schemes they might not be a scalable solution due to the fact that they require expensive antenna arrays at each of the receivers. Even the cost associated with the AOA based solution may make these less interesting localization schemes but they come handy for applications which require sophisticated location estimation. Given that a sensor node is a small and inexpensive device, the combination of two or more individuals, such as RSS/TOA [31], and TOA/TDOA [32] can be considered Comparison between Localization Schemes The location accuracy of each of these methods depends on the estimation method that is used in addition to the noise, measurement errors, etc.., [51]. The range-based schemes, such as TOA and TDOA, are proven to have very good accuracy due to the high time resolution (large bandwidth of UWB signals). While schemes such as RSS and TDOA easy to implement and might require low computational power compared to schemes depends on AOA. Table 2.1 provides a comparison between the mentioned localization schemes in terms of measurement, advantages, and disadvantages. 17

32 Table 2.1: Comparison of different localization methods. Method Signal measurement Advantages Disadvantages TOA Time Accuracy is high Time synchronization across source and all receivers is needed. LOS is assumed. TDOA Time-difference Accuracy is high. LOS is assumed. No time synchronization at source is required. RSS Signal power Sime and inexpensive. Accuracy is low. Time synchronization is not required. AOA Angle Only at least two Require expensive antenna arrays. receivers are required. LOS is assumed. Time synchronization is not required. Estimators Nonlinear Linear NLS ML LLS WLLS Subspace Figure 2-7: Classification of localization estimation schemes. 18

33 2.0.3 Source Localization Estimators There are two type of estimators that can be used to solve the nonlinear equations that have been presented so far, equations (2.7), (2.13), (2.19), and (2.25). They are Nonlinear approaches. Linear approaches. Figure 2-7 describes some methodologies that can be used to solve the mentioned nonlinear equations. Nonlinear methodologies [51, 52, 53] directly utilized equation (2.1) to solve for x by minimizing cost function derived using the least square (LS) or the weighted least square (WLS) obtained from the following error function [36, 55] e non linear = r f(ˆx) (2.29) where ˆx=[ x, ȳ] T is the estimated variable for x. This is produced using NLS or maximum-likelihood (ML) estimators. The linear approach coverts the equation (2.1) into a linear equation of unknown variable, x. b = Ax+c (2.30) where A and b are known vectors and c is the transformed noise vector in (2.1). Using equation (2.30), the linear estimator can be constructed as [36, 55] e linear = b Aˆx. (2.31) LLS [54, 56], WLLS [38, 55, 57], and Supspace [58, 59] estimators can be obtained by utilizing LS or WLS estimators on equation (2.31). A comparison summary for various position estimators are given in Table 2.2 [36]. 19

34 Table 2.2: Comparison of different localization estimators. Estimator Advantages Disadvantages NLS Generally accuracy is high. Global solution may not be Noise statistics are not needed. guaranteed. Complexity is high if grid or random search is used. ML Accuracy is highest. Global solution may not be guaranteed. Complexity is high if grid or random search is used. LLS/Subspace Global solution is guaranteed. Accuracy is generally low. Simple and computationally efficient. Noise statistics are not needed. WLLS Global solution is guaranteed. Noise statistics are needed. Highest accuracy can be achieved Iterations may be required. with constrains. In the next section two estimators, one per approach will be discussed. A detail explanation on these estimators and other types of location estimators can be found on [36] Nonlinear Estimator This section describes how to use nonlinear estimators to solve the TOA location. The same procedure can be extended to others, such as TDOA, RSS, AOA, without much effort. Based on equations (2.12) and (2.16), the NLS cost function given by J NLS,toa (ˆx) can be expressed as [36] J NLS,toa (ˆx) = N (r toa,i ) (ˆx x i ) 2 + (ŷ y i ) 2 i=1 = (r toa f toa (ˆx)) T (r toa f toa (ˆx)) (2.32) 20

35 The position estimate using NLS is then given by ˆx, which is the minimum value of J NLS,toa (ˆx) given by ˆx = arg min ˆx = J NLS,toa (ˆx) (2.33) In order to solve equation (2.33) iterative local search procedure can be used with a suitable initial guess, ˆx 0. Gauss-Newton method is explained in this section. More details about Gauss-Newton method and other local search schemes can be found in [36]. The iterative Gauss-Newton procedure for ˆx is [36], ˆx k+1 = ˆx k + (G T (f toa (ˆx k ))(G(f toa (ˆx k ))) 1 G T (f toa (ˆx k ))(r toa f toa (ˆx k )) (2.34) where G T (f toa (ˆx k )) is the Jacobina matrix of f toa (ˆx k ) computed at ˆx k by [36] G(f toa (x)) = = (x x 2 ) 2 +(y y 2 ) 2 x (x x 3 ) 2 +(y y 3 ) 2 x. (x x N ) 2 +(y y N ) 2 x (x x 1 ) 2 +(y y 1 ) 2 y (x x 1 ) 2 +(y y 1 ) 2 y. (x x 1 ) 2 +(y y 1 ) 2 y x x 1 [(x x 1 ) 2 +(y y 1 ) 2 ] 1/2 y y 1 [(x x 1 ) 2 +(y y 1 ) 2 ] 1/2 x x 2 [(x x 2 ) 2 +(y y 2 ) 2 ] 1/2 y y 2 [(x x 2 ) 2 +(y y 2 ) 2 ] 1/2. x x N [(x x N ) 2 +(y y N ) 2 ] 1/2. y y N [(y y N ) 2 +(y y N ) 2 ] 1/2 and given (2.35) Now with a suitable initial guess, ˆx 0, the iterative equation (2.34) will produce 21

36 the next estimation. The iterative process will terminate after a certain number of iteration or when the value ˆx k+1 ˆx k is sufficiently small [36] Linear Estimator When solving the nonlinear equation (2.1) using linear estimators, the nonlinear equation will first convert into a linear equation with a zero-mean disturbances, assuming that the measurement errors are sufficiently small or insignificant [36]. The below section will describe how to solve the TOA equation (2.13) and [36] describes how to use other linear estimators for location estimations. To arrange the TOA nonlinear equation (2.13) in linear form of x, the first step is to square both sides of equation (2.12) to produce rtoa,i 2 = (x x 1 ) 2 + (y y 1 ) 2 + 2n toa,i (x x1 ) 2 + (y y 1 ) 2 + n 2 toa,i, i = 1, 2,..., N (2.36) Define m toa,i = 2n toa,i (x x1 ) 2 + (y y 1 ) 2 + n 2 toa,i, i = 1, 2,..., N (2.37) to be the noise component in equation (2.36). Define R R = x 2 + y 2 (2.38) Substituting equations (2.37) and (2.38) into equation (2.36) generates the results r 2 toa,i = (x x 1 ) 2 + (y y 1 ) 2 + m toa,i (2.39) r 2 toa,i = x 2 2x i x + x 2 i + y 2 2y i y + y 2 i + m toa,i 2x i x 2y i y + R + m toa,i = r 2 toa,i x 2 i y 2 i, i = 1, 2,..., N 22

37 The matrix form of the equation (2.40) can be expressed as Az + c = b (2.40) where 2x 1 2y 1 1 2x 2 2y 2 1 A =... 2x N 2y N 1 [ ] z = x y R (2.41) (2.42) [ ] T c = m toa,1 m toa,2... m toa,n (2.43) and b = r 2 toa,1 x 2 1 y 2 1 r 2 toa,2 x 2 2 y 2 2. r 2 toa,n x2 N y2 N (2.44) When m toa,i are sufficiently small c becomes 2n toa,1 (x x1 ) 2 + (y y 1 ) 2 2n toa,2 (x x2 ) 2 + (y y 2 ) 2 c =. 2n toa,n (x xn ) 2 + (y y N ) 2 (2.45) which becomes a zero-mean vector [36]. Due to this reason equation (2.40) can be approximated as Az b (2.46) 23

38 The LS cost function based on equation (2.46), J LLS,toa (ẑ), is given by J LLS,toa (ẑ) = (Aẑ b) T (Aẑ b) = ẑ T A T Aẑ 2ẑ T A T b + b T b (2.47) By differentiating equation (2.47) and by setting the resulting expression to zero [36] z = (A T A) 1 A T b (2.48) The final location estimation is then obtained from ˆx = [[ẑ] 1 [ẑ] 2 ] T (2.49) where [ẑ] 1 and [ẑ] 2 represent the first and second element of the vector ẑ. 24

39 Chapter 3 An Improved Hybrid RSS/TDOA Wireless Sensors Localization Technique Utilizing Wi-Fi Networks 3.1 Overview This chapter presents a hybrid localization algorithm for wireless sensor networks (WSNs) that simultaneously exploits received signal strength (RSS) and time difference of arrival (TDOA) measurements. The accuracy and convergence reliability of the proposed hybrid scheme are also enhanced by incorporating RSS measurements from Wi-Fi networks via cooperative communications between Wi-Fi and sensor networks. To this end, first it is shown how to solve the nonlinear equations directly using Newton-Raphson and Gauss-Newton method. Then, two different types of linear estimators based on Taylor-series (TS) expansion and maximum-likelihood (ML) estimation are proposed to solve the set of nonlinear RSS/TDOA equations taking into account measurement errors. The corresponding Cramér-Rao lower bound (CRLB) 25

40 for the established scheme is then derived and utilized as a performance measure for the two estimators. Simulation results show that the proposed hybrid positioning approach significantly outperforms the previously considered localization solutions in WSNs, thanks to the joint process of the received signals power and time difference of arrival. The advantages of the proposed scheme in providing high location accuracy, fast convergence, low complexity implementation, and low power consumption make it an attractive localization solution via WSNs. Y source X WSN receiver Wi Fi receiver Figure 3-1: Networking structure of the proposed scheme. 1 26

41 3.2 Proposed Scheme Underline Scenario As illustrated in Figure 3-1, the considered system consists of at least three WSN receivers, i.e., anchor nodes, capable of processing RSS and TDOA measurements of a source/target. It is assumed that the source also exchanges additional RSS measurements with a Wi-Fi network that is common in today s wireless communications infrastructures. This assumption is realistic, thanks to wireless devices heterogeneity. In this new scheme, two improvements are proposed to advance the location accuracy. First, the source s RSSs and TDOAs can be measured by the anchor nodes. Then, the source exchanges signal power measurements with the Wi-Fi network through operation in a cooperate fashion. Given that the RSS might differ significantly across different devices and networks, the combination of these RSS measurements provides more degrees of freedom. As a result, more accurate location estimation can be expected Problem Formulation Assume that there are N anchor sensor nodes available. These nodes are distributed randomly in a 2-dimensional (2-D) plane as shown in Figure 2-3. As described in section , the RSS model measured from N WSN nodes can be modeled as r rss,i = aln(d i ) + n rss,i, i = 1, 2,..., N (3.1) The LHS of equation (3.1) denotes the RSS range estimation measurements. Now let s assume that the source corporately exchanges RSS measurements with another 27

42 M( 1) Wi-Fi receivers. These measurements can be written as: r rss,w,j = aln(d w,j ) + n rss,w,j, j = 1, 2,..., M (3.2) where d w,j = (x x w,j ) 2 + (y y w,j ) 2, j = 1, 2,..., M (3.3) and n rss,w,j represents the log normal measurement error vector between the source and Wi-Fi receivers, and d w,j is the distance between the source and the j th Wi-Fi receiver situated at (x w,j, y w,j ). If each i th receiver is capable of performing TOA measurements t i, N 1, TDOA equations can be defined as in section r tdoa,i = (d i d 1 ) + n tdoa,i (3.4) = (x x i ) 2 + (y y i ) 2 ) (x x 1 ) 2 + (y y 1 ) 2 ) + n tdoa,i, i = 2,..., N Here, the receiver with smallest TOA is considered as a reference. Next equations, (3.2), (3.3) and (3.4) are combined. By combining all the RSS and TDOA measurements from WSN and Wi-Fi network, a set of over determined nonlinear equations are obtained, which can be expressed in matrix form as [ ] x where x =, y r = f(x) + n (3.5) 28

43 r = r rss,1. r rss,n r rss,w,1. r rss,w,m r tdoa,2. r tdoa,n, n = n rss,1. n rss,n n rss,w,1. n rss,w,m n tdoa,2. n tdoa,n, and f(x) = aln(d 1 ). aln(d N ) aln(d w,1 ). aln(d w,m ) d 2 d 1. d N d 1 In (3.5), r is the measurement vector, x is the source position to be determined, f(x) is a known nonlinear function of x, and n is the measurement error vector. At this point it is important to mention that equation (3.5) will utilized three kind of data. They are; 1. RSS measurements from WSN. 2. TDOA measurements from WSN. 3. RSS measurements from short-range Wi-Fi network. 3.3 Solving the Proposed Hybrid Equations Location estimation can be obtained either directly solving the nonlinear equation or, by first converting the nonlinear equation into a linear equation and then solving that linear equation. The proposed enhanced location estimation was solved utilizing both approaches and they are described in next sub sections. 29

44 3.3.1 Nonlinear Estimators Newton-Raphson and Gauss-Newton iterative approaches were utilized when solving the nonlinear equation (3.5) directly Newton-Raphson Recall Newton-Raphson update rule is given by equation [41] ˆx k+1 = ˆx k H 1 (J(ˆx k )) (J(ˆx)) (3.6) and the cost functions for nonlinear components of functions for RSS (from WSN), RSS (from Wi-Fi network), and TDOA (from WSN) measurements are given by (see the nonlinear term in each of the equations (3.1), (3.2), and (3.4) [41] J NLS,rss (ˆx) = N i=1 ( r rss,i + aln (ˆx x i ) 2 + (ŷ y i ) 2 ) 2 (3.7) = (r rss f rss (ˆx)) T (r rss f rss (ˆx)) J NLS,rss,w (ˆx) = M j=1 ( ) 2 r rss,w,j + aln (ˆx x j ) 2 + (ŷ y j ) 2 (3.8) = (r rss,w f rss,w (ˆx)) T (r rss,w f rss,w (ˆx)) where ln( (x x w,1 ) 2 + (y y w,1 ) 2 ) ln( (x x w,2 ) 2 + (y y w,2 ) 2 ) f rss,w (x) = a. ln( (x x w,n ) 2 + (y y w,n ) 2 ) 30 (3.9)

45 N J NLS,tdoa (ˆx) = (r tdoa,i (ˆx x i ) 2 + (ŷ y i ) 2 + ) 2 (ˆx x 1 ) 2 + (ŷ y 1 ) 2 i=2 (3.10) = (r tdoa f tdoa (ˆx)) T (r tdoa f tdoa (ˆx)) Recall that f rss (ˆx) and f tdoa (ˆx) are defined in equations (2.10) and (2.22) respectively. Now following a similar approach new const function can be derived as N,M ( [ (r rss,i + aln(d i )) (r rss,j + aln(d w,j)) (r tdoa,i+1 d i+1 + d 1 ) ] T ) 2 (3.11) i,j=1 Let J(x) = J hybrid (x). Then the Hessian matrix and the gradient vector can be then defined as H = 2 J(x) x x T = 2 J(x) x 2 2 J(x) y x (J(x)) = J(x) x J(x) y 2 J(x) x y 2 J(x) y 2 (3.12) (3.13) By substituting equations (3.12) and (3.13) into equation (3.6) with a suitable initial estimation for x will produce the next estimation. This process is continued until estimation is sufficiently stable. In order for better estimation accuracy, the location estimation derived from RSS is used as the initial estimation Gauss-Newton Recall Gauss-Newton update rule for equation (3.5) is given by [41] ˆx k+1 = ˆx k + (G T (f(ˆx k ))G(f(ˆx k ))) 1 G T (f(ˆx k ))(r f(ˆx k )) (3.14) 31

46 where, r is the measurement vector of combined features and f(x) is defined in equation (3.5). G T (f(ˆx k ) is the Jacobian matrix of f(ˆx k ) evaluated at ˆx k and is given by [41] = [ G(f(x k )) = ( aln(d 1 )) x. ( aln(d N )) x ( aln(d w,1 )) x. ( aln(d w,m )) x (d 2 d 1 ) x. (d N d 1 ) x f(x) x f(x) y ( aln(d 1 )) y. ( aln(d N )) y ( aln(d w,1 )) y. ( aln(d w,m )) y (d 2 d 1 ) y. (d N d 1 ) y ] (3.15) where d i, i = 1, 2..., N and d w,i, i = 1, 2..., M is defined in equations (2.2) and (3.3) respectively. By substituting equation (3.15) into equation (3.14) with a suitable initial estimation for x will produce the next estimation. This process is continued until estimation is sufficiently stable. RSS solution is utilized as the initial guess for better location estimation Linear Estimators In this section location estimation is evaluated using linear estimators. Realizing this the nonlinear equation (3.5), is first converted into a linear combination of unknown sensor location utilizing the Taylor-series and a computationally inexpensive closed-form based on maximum-likelihood estimation. As a system benchmark, the CRLB is also derived to examine the accuracy of the proposed solutions. 32

47 Taylor-series From equation (3.5), let define M(x, y) as follows; M(x, y) = r f(x) n (3.16) Recall that Taylor-series expansion of M(x, y) around the point (x 0, y 0 ) is given by M(x, y) = M(x 0, y 0 ) + + δm(x, y) δy δm(x, y) δx x = x 0 (x x 0 ) (3.17) y = y 0 (y y 0 ) + higher terms Let (x x 0 ) = δx and (y y 0 ) = δy. It is straightforward to show that by considering equation (3.17) with a proper initial guess (x 0, y 0 ), equation (3.5) can be linearized as follows G ta = x 1 x d 1 a(x x i ) d 2 i a(x x w,j ) d 2 w,j x i+1 x d i+1 y 1 y d 1 a(y y i ) d 2 i a(y y w,j ) d 2 w,j r rss,i aln(d i ) h ta = r rss,w,j aln(d w,j ) r tdoa,i+1 (d i+1 d 1 ) y i+1 y d i+1 G ta δ = h ta + n (3.18), δ = δx and δy where n is defined in equation (3.5). d i and d w,j are computed from equations (2.2) and (3.3), respectively, with x = x 0 and y = y 0, while r rss,i, r rss,j, and r tdoa,i+1 are obtained from the RSS and TDOA measurements. Position deviations at each iteration can be calculated using the least-square estimation with (x 0, y 0 ) as an initial 33