3D Localization and Wireless Sensor Networks

Transcription

1 3D Localization and Wireless Sensor Networks Thesis submitted in partial fulfillment of requirements for the degree of Master of Science by Research in ELECTRONICS AND COMMUNICATIONS by BalaKrishna Pillalamarri International Institute of Information Technology, Hyderabad (Deemed to be University) Hyderabad , INDIA May 2017

2 Copyright c Balakrishna Pillalamarri 2017 All Rights Reserved

3 International Institute of Information Technology Hyderabad,India Certificate It is certified that the work contained in this thesis, 3D Localization and Wireless Sensor Networks submitted by Balakrishna Pillalamarri has been carried out under my supervision and is not submitted elsewhere for a degree. Adviser: Dr. Rama Murthy Garimella 22/05/2017 Date

4 Dedicated to My Guru Sri Sri Sri Swayam Prakasananda Sachidananda Saraswathi MahaSwamiji 3

5 Acknowledgments I am lucky to work with Dr Rama Murthy Garimella. My journey in IIIT- Hyderabad has been a journey worth it. It could not have been so without the support of many people. As I submit my MS thesis, I want to offer my gratitude to all those people who helped me in successfully completing this journey. First of all, I want to thank my guide Prof. Rama Murthy Garimella, for accepting me as a student and constantly guiding me. His guidance has helped me improve not only as a researcher but also as a person. I can never thank him enough for providing me support at my difficult times and helping me move forward. I am thankful to everyone in SPCRC for providing such a positive work environment. Many thanks to Tejaswini, Sumit, Viswanath, Srikanth, Kunal, Chandan, Priyanaka for all the help, discussions, study group sessions and support. Thanks to Prof. Rama Murthy for remaining by my side rock steady throughout this journey and for being my guide and mentor through my ups and downs. I could not have accomplished it without the support and understanding of my wife. I wish to thank my mom, dad and my wife and kids for being my constant support and motivation The most valuable person without whose support I would have not come to this stage is my beloved friend Dr.Balagangadhar Bathula, Research Associate, AT&T Bell Labs, USA. Last, but not the least, thanks to IIIT community for giving me such a beautiful campus and environment to grow. 4

6 Abstract Indoor positioning is gaining momentum for its various applications. As we know that Global Positioning System (GPS) does not work well indoors, while todays more sensitive GPS chips can sometimes get a location fix (via receiving signals from enough satellites to determine a location) inside a building. The resulting location is typically not accurate enough to be useful. The signals from the satellites are attenuated and scattered by roofs, walls and other objects. Besides, the error range of many GPS chips (tennis court) can be larger than the indoor space itself (small grocery store)! Some indoor positioning solutions work similar to GPS. Many companies tap into Wi-Fi signals that are all around us - including when we are indoors. With a good map of the locations of the access points, a Wi-Fi receiver like a cell phone can be located even indoors. Any application that would depend on indoor positioning may need an exact location. This work on indoor localization in 3D using spherical co-ordinates would have an edge to all the future needs. A combination of Pico, Femto, Wi-Fi, otherwise termed as hybrid localization techniques are used in conjunction with leveling and sectoring. Leveling and sectoring are discussed using base station and Wi-Fi access points and the received signal strength (RSS) finger prints are used to aid in precise localization. Indoor localization applied to physical analytics is also discussed. This thesis work also focuses in an improvement over our above discussed works in terms of achieving more accuracy and reduction of delay in the Wireless Sensor Networks (WSNs). This is achieved by using the Received Channel Power Indicator (RCPI) in contrast to RSS. We assume that RCPI shall be used by all chip vendor for all the Wi-Fi devices coming into the market due to its precise way of measuring the Received signal power. This work also focuses on Wireless Sensor Networks (WSN) with respect to the need for optimizing the parallel distributed computational architecture.it also discussed how it can be acheived using our proposed model. This gains importance as identification of an event in WSNs should be done as fast as possible by minimizing the delay. Optimizing the grid based architecture for time complexity, transmission delay and fault tolerance in computing the fusion functions, our work also focuses on localizing an event in an outdoor WSN and respond to the event based on the need as soon as possible. Hence our overall work on 3D localization and wireless sensor networks helps us localize events in both indoor as well as outdoor with reduced time-complexity as well as delay parameters.

7 Contents Acknowledgements 4 1 Introduction Overview Problem Statement Contribution of Thesis Concept of Localization Thesis Organization Precise Positioning in 3D Using Spherical Co-ordinates Introduction Related Work Precise Positioning Algorithm Horizontal Positioning Vertical Positioning Machine Learning Techniques into Positioning Indoor Localization applied to Physical Analytics Localization Accuracy Application of Proposed Approach for Outdoor Localization Improved Accuracy using RCPI Conclusion References Grid of Wireless Sensors:Distributed Computation Introduction Distributed Network Architecture for Primitive Recursive Functions Problem Statement Primitive Recursive Functions Grid based Network Architecture Fault Tolerance Probability of Error in Maximum Calculation Distributed Network Architecture for Median Problem Statement Tree based Network Architecture Computational Complexity of the Proposed Architecture Time Delay of the Proposed Tree based Architecture for Median Applications Dynamic Speed Boards i

8 3.4.2 Dynamic Time Estimate More Accurate Time Estimate Itinerary Planning Coloring Nodes Possible Improvements in Google Maps Conclusion References Outdoor Navigation: Efficient Order Statistics computation Introduction Localization Order Statistics Efficient Computation In Grid Based Architecture Temporal Statistics Conclusion References Conclusion and Future work Conclusion Future Work ii

9 List of Figures 2.1 Spherical Co-ordinate system Leveling and Sectoring in a Horizontal Plane Set up showing the sector formation by BS and AP Spherical Co-ordinates applied to position an object Flow Chart Example of a path; from source to destination Hierarchy of grid architecture Proposed Architecture showing the Row links Fault Tolerance scenarios Tree like Architecture Original Heap to Reduced Head Tree Example 1: Median of Medians Example 2: Median of Medians Example figure for Heap Sort Dynamic Time Estimate More Accurate Time Estimate Itinerary Planning Localization problem being addressed Grid based architecture Line architecture iii

10 List of Tables 2.1 Power leveling with the corresponding RSS levels Major conventions. Legend: Eastwards (E) Northwards (N) Upwards (U) List of values of k pivot for few values of N iv

11 Chapter 1 Introduction 1.1 Overview Indoor Localization is gaining more prominance in today s applications.with the advent of smartphones enabled with WI-FI and other technologies,it gives more ways to solve the challenges in indoor space.gps does not work well indoors: While todays more sensitive GPS chips can sometimes get a fix (receive signals from enough satellites to determine a location) inside a building, the resulting location is typically not accurate enough to be useful. The signals from the satellites are attenuated and scattered by roofs, walls and other objects. Besides, the error range of many GPS chips (tennis court) can be larger than the indoor space itself (small grocery store)! Some indoor positioning solutions work similar to GPS: Locata, an Australian company, offers beacons that send out signals that cover large areas and can penetrate walls. Locata receivers work similarly to how GPS receivers work. The U.S. Department of Defense is an early Locata user. Nokia uses beacons that send out Bluetooth signals. While any Bluetooth device can read them, they only cover a few square meters. Many companies tap into Wi-Fi signals that are all around us - including when we are indoors. With a good map of the locations of the access points, a Wi-Fi receiver like a cell phone can be located even indoors. RFID and inertial systems work very differently: Passive radio frequency identification tags (RFIDs) prompt a transaction when they pass near a sensor. For example, a closed door prompts the user to swipe the card to pass. Doors or gates force users into a queue or to slow down for the sensor to work properly. These passive systems detail only that a person or object entered a room; they do not provide detailed location information within the room. Active RFID tags are self-powered and regularly send out signals to receivers within the area of interest. This is the reverse of GPS. Knowing the location of the receiving sensors allows for accurate indoor locating in near real-time. Solutions that use inertial measurement work only if a starting location is known. With that information collected, these sensors use accelerometers, gyroscopes and other sensors including clocks to track orientation and distance to keep track of location in near real-time. The latest inertial solution, from DARPA, is a chip smaller than a penny (press release). Indoor positioning detects the location of a person or object, but not always its 1

12 orientation or direction: While indoor positioning systems can determine location, many need additional information to determine which way a person or object is facing. That can make providing directions or pitching a product in a store more challenging. The addition of an electronic compass to a receiver (many cell phones now have them), or a microelectromechanical systems (MEMS) orientation sensor or a prompt to turn toward a particular direction (to scan a bar code or QR code on a poster, for example) can provide more information regarding orientation. The best solution for indoor and outdoor positioning may be a hybrid: No single solution works perfectly in all environments. For that reason devices may support more than one positioning solution and switch between them as needed. Todays mobile phones use GPS (when its turned on) outdoors but may switch to Wi-FI positioning (when its turned on) when the signal is weak, such as when an individual goes indoors. Indoor location and commerce solution provider aisle 411 taps into both Wi-Fi and MEMS sensors for its retail store offerings. Indoor positioning is in demand for a variety of uses: While the goal of indoor positioning for some users, notably hospitals and malls, is to provide navigation aid, others want to use indoor positioning to better market to customers, provide just-in-time information via audio for tours, offer video or augmented reality experiences or connect people of interest in proximity to one another. The U.S. Federal Communications Commission hopes to use indoor positioning to provide timelier and more effective emergency services (see below). Major tech players are working in the indoor space: Apple, Google and Microsoft are all exploring the use of indoor positioning. At this time the effort is focusing on both indoor positioning technologies and creating the basemaps that will make such solutions more valuable. The Federal Communications Commission (FCC) is looking at indoor positioning to enhance emergency response: Results of a study conducted in late 2012 and published March 14, 2013 by the FCCs Communications Security, Reliability and Interoperability Council (CSRIC) suggests a current baseline for indoor positioning for use in emergency response. Three different vendors, using three different indoor technologies, participated (summary).one key concern is determining vertical location, that is, on which floor a person is standing in a multilevel building. The FCC report concludes: While the location positioning platforms tested provided a relatively high level of yield, as well as improved accuracy performance, the results clearly indicate additional development is required. Indoor positioning requires indoor maps: Locating a person or device indoors is only half of the solution. For the location to be meaningful for navigation or other purposes, service providers need accurate indoor maps. Theres a new industry creating those data. 1.2 Problem Statement Wireless Communications is a vast area, posing significant challenges in various directions. While there are many open research problems unsolved from many years, the technical revolution, we are witnessing with the explosion of smart phones has left the wireless research community with very interesting problems. Outdoor positioning is achieved with the help of GPS (Global Positioning Systems). On the 2

13 other hand, indoor positioning i.e., positioning of smart phone or a wireless sensor node precisely within a building has always been a challenge especially due to multipath and fading charectersitics of a wireless signal. To overcome this there are lot of techniques being proposed by researchers, and some of them include 2D localization as well as 3D, but always have some degree of error Contribution of Thesis (A) To overcome and minimize the error in localizing a node or an event we propose a new technique which shall increase the accuracy of the positioning and localization in 3D. (B) The network architectures formed or used during localization process also play a vital roles with respect to the delay in the information processing. Hence, we thought to address this problem by reducing the delay of transmission for a given architecture. 1.3 Concept of Localization Determine physical position or logical location is termed as localization. This Precise positioning is very much required and necessary for various applications as applied to physical analytics. Today with the convergence of different technologies like GPS, A-GPS (Assisted GPS) also known as satellite and node base stations, we are able to approximately locate the position of any smart object on this earth outdoors. Due to factors such as multipath and fading, it is always a challenge to precisely locate the position of a user with a smart phone indoors. 1.4 Thesis Organization Chapter 2 gives about how we can achieve localization accuracy achieved via new technique called Leveling and sectoring. It is achieved using base station, Wi- Fi accesspoints points and the received signal strength (RSS) finger prints & an improved technique using Received Channel Power Indicator (RCPI). Chapter 3 talks about Grid of wireless sensors in distributed computation, focusing on investigating the problem of design of optimal parallel distributed computational architecture, inturn helping in localizing the event faster. Chpater 4 descirbes about outdoor navigation and efficient order statistics computation in Wireless Sensor Networks (WSN) exploiting the grid based architecture. Chapter5 Conclusion discusses on different areas of applications these improvements shall help and the future work. 3

14 Chapter 2 Precise Positioning in 3D Using Spherical Co-ordinates as applied to Indoor Localization 2.1 Introduction Today with the convergence of different technologies like GPS, A-GPS also known as satellite and node base stations, we are able to approximately locate the position of any smart object on this earth outdoors. Due to factors such as multipath and fading, it is always a challenge to precisely locate the position of a user with a smart phone. Hence, we use a combination approach using Femto cell, Pico cell and Wi-Fi access points to more precisely locate the smart objects in indoors, i.e. inside a big malls or complex buildings. This gives rise to one of the following challenges, as to precisely locate the position with respect to a building and decide which floor of the building and what part of a floor. Previous works concentrate more on 2D positioning and sparsely on 3D localization algorithms. In [1], the position of the user in 2D space is centrally calculated using EZ localization algorithm. Research pertaining to 3D localization is proposed in [2], [3] where in, algorithms such as isolines and k-means clustering algorithms etc are employed to model 3D localization. Hybrid localization using k-medoids algorithm is proposed in [4], where the three dimensional space is subdivded into number of service areas. Precise indoor localization helps in different ways, especially during evacuation of building at emergencies. The rescue teams would be able to direct their focus and save lives within time. Some other applications include finding the missing persons in a big shopping mall or a carnival, disaster management, space management etc. 4

15 Figure 2.1: Spherical Co-ordinate system To mitigate the problem of locating smart object precisely, we make use of their position, by measuring it 3-dimensionally, to tell on which floor and in which part of the floor. We can use spherical co-ordinate system to solve it. From Fig. 1 it is possible to precisely locate the position of an object using spherical coordinates. The azimuthal angle θ, radial distance r and the polar angle φ are represented in the figure. With change in φ, we will be able to locate the position on a linear plane, and with change in azimuthal angle θ, we can find altitude of the object with reference to the plane. Also the spherical co-ordinates can be mapped to corresponding local geographical directions, which give us an edge to use this spherical co-ordinate system. 5

16 2.2 Related Work Controneo et al. [5] proposed a naive partition positioning method, wherein the sub region to which a mobile belongs to, is determined based on the signal strength it receives from an AP. Xu et al. [6] divided the location space into multiple zones. In the positioning phase, they used the maximum likelihood theory to determine the location of the mobile terminal. Samama et al. [7] pointed out that many indoor positioning scenarios often do not require high accuracy and it is good enough to intimate the user some symbolic information, such as which corridor or room the current place is at. In addition, an algorithm is proposed, which uses 3D symbol positioning. It divides the location space into various positioning symbolic subspaces and further designed a symbolic subspace resolution to convey the location information to the user. Gansemer et al. [6] points that the 3D indoor positioning can be more realistic by RFID(Radio Frequency Identification Devices), UWB (Ultra Wide Band) and other technologies. They stressed the need for 3D indoor positioning using wireless local area networks (WLAN) and a method was proposed that extends isolines algorithm [9], used in 2D WLAN indoor positioning to 3D space. Zhong-liang et al. [3] adopted k-means clustering algorithm to partition a three dimensional indoor space into multiple regions; namely, location fingerprints with similar Euclidean distance are clustered into one region and the central fingerprint of every region is saved. In the positioning phase, the fact that the fingerprint received by the closest mobile terminal estimates the location of the mobile terminal. But location information (location of the mobile terminal) is confined to floor, which is strong limitation in this paper. The exact positioning of a mobile on the floor is not proposed. 2.3 Precise Positioning Algorithm Our precise positioning algorithm employing the leveling and coning techniques is proposed in this section. In our algorithm, the precise position of an object is found by applying horizontal positioning followed by vertical positioning algorithms. Throughout this paper, horizontal position is the location of an object with respect to the access point and vertical position is the location of an object with respect to the base station (as shown in Fig. 2). We use leveling and sectoring algorithms in finding the horizontal position where as the coning algorithm is applied in case of vertical positioning. The following setup is needed in order to implement our algorithm. A placement of base station near the building is assumed along with the placement of at least one access point (IEEE ac or a femto cell or a combination) on each of the floors of the building. It is further assumed that, each access point includes an electronically steered unidirectional antenna, now the horizontal and vertical positioning algorithms are elucidated in the below sub sections. 6

17 2.3.1 Horizontal Positioning As we discussed before, the horizontal position is calculated with respect to the access point situated on each floor of the building. In this paper, the concepts of leveling and sectoring algorithm [8] are brought into indoor positioning. The levels and sectors are formed with respect to the access point to find the horizontal position. The sectors are segregated with respect to direction of antenna located on the access point and the levels are segregated with respect to the power levels as presented in [8]. The mobile, whose position has to be found out, sends a probe request to the access point. Based on the RSS levels, the position of the mobile with respect to access point is determined. This concept is presented in Fig. 3. Figure 2.2: Leveling and Sectoring in a Horizontal Plane As shown in Fig. 3, in a horizontal plane, using the access point directional antenna and power level, we broadcast the beacons. The stations send responses and based on it the RSS is derived and we can estimate the liner distance from each of the access points. Then for each power level in a given sector S1, we have different levels namely L 1, L 2, L 3, etc. The sectors are also formed based on the horizontal angle and number of sector depend on the φ namely S 1, S 2, S 7, etc. 7

18 2.3.2 Vertical Positioning We determine the vertical position using the base station employing the coning technique. The azimuthal angle between the antenna and the mobile(situated on the floor of the building) gives us the vertical position. This brings in the concept of 3- dimensional sectors and thus the 3D-cone is formed and such cones are packed together in 3-dimensional space and form a sphere. The azimuthal angle is fixed based on the number of floors in a building. To our experiments our campus building with 5 floors, hence the vertical rotation is fixed to 60 degrees per step. Since, we have our base station placed at the corner of the building on the ground floor; we think that a hemi-sphere area of RF finger print coverage in 3D would be sufficient to precisely calculate the position. Even in a case of large buildings or circular shaped buildings, if the base station is placed in the middle, still calculating the position is easy as the second half of the sphere is a mirror reflection. As shown in Fig. 2, with the help of the base station and the vertical angle or azimuthal angle we know the floor of the building and at the same time, the power leveling done by each access point at each floor would help us the precise location of the user in two ways: one is the radial distance from the base station and the other is the relative distance from the AP per floor. All these APs are connected in tandem to a localization server, which would use software algorithm to calculate the precise position of the user and the same information is passed to the user. Let A, B, C be the mobiles whose position has to be found out and BS be the base station to determine the vertical positioning and AP1, AP2,..., AP5 be access points to determine the horizontal positioning. Localization Server is employed to place the data statistics which can further be used to dump data. We take the RSS from each user in different power levels and the required distance is calculated from the obtained RSS Machine Learning Techniques into Positioning Once we calculate the positions of the users this training data can be fed to a Support Vector Machine (SVM) classifier [1], which gives us a precise finger printing map, which can be reversed mapped to the dynamic positioning of the object in real time. Power level Average RSS Distance L1-10 db 10 L2-30 db 20 L3-45 db 40 L4-80 db 100 Table 2.1: Power leveling with the corresponding RSS levels In addition, the system can be enhanced, i.e., the formation of sectors, levels and cones can be more efficient after the training data is fed to the SVM. Combining the Fig.2 and Fig.3 for a given access point and Base station(bs) in 3D gives a sphere and a vertical angle that helps us determined its position.hence, the location of an object can now be precisely located using these levels and sectoring 8

19 Figure 2.3: Set up showing the sector formation by BS and AP. in 3 dimensions. With this we will be able to tell in which floor of a building and in which direction the user is heading more precisely. 2.4 Indoor Localization applied to Physical Analytics Physical analytics is possible only with an accurate positioning in indoor, which we were able to achieve using our said techniques. Co-ordinates (Z, X, Y ) right/left-handed (r, θ el, φ az ) (U, S, E) right (r, θ inc, φ az ) (U, E, N) right (r, θ el, φ az ) (U, N, E) left Table 2.2: Major conventions. Legend: Eastwards (E) Northwards (N) Upwards (U). Local azimuth angle can be measured with above said technique. Physical analytics is to perform study of patterns of users. Such information would be very helpful in a wide variety of contexts and applications. Once we know the precise location of a user(s), it can be analyzed and crowd sourced. This can help in a variety of ways like disaster management, space management, life style management, etc. For example, during fire accident, based on the density of the 9

20 users in a given location, the rescue team can act quickly to save them and with this precise location even a single person at any corner of the building, still can be reached and saved. Also, we can analyze the physical behavior of a user, like, where he spends his time most,like office, home, shopping and if so what kind of stores/shopping, which helps even the marketing teams to concentrate on those specific user for their trends. We can apply the indoor precise positioning to a variety of applications that use other technologies like NFC(Near Field Communication) infrared and Bluetooth, etc. For example, a user goes for a gymnasium and when he places his phone close by and has another sensor technology gadget on his body, that can still beacon to the smart phone to update its application regarding users physical behavior like humidity levels in body, pulse rate, heartbeat, etc. With this information, we can set threshold levels and hence, rescue team could come and uplift to the respective place and save them. This can be applied when someone is drowning in a swimming pool (indoor: Also a Electromagnetic waves does not propagate in water, as in case of SONAR technology, sound waves are used for determining and propagating the location of a drowning individual). Figure 2.4: Spherical Co-ordinates applied to position an object 10

21 Figure 2.5: Flow Chart 11

22 2.5 Localization Accuracy Using GPS in outdoor localization resolution of localization (positioning on earth) can be achieved to certain accuracy. In addition, hop count based localization methods rely on power control. Localization up to certain hop count value (from a specified transmitter) leads to certain accuracy depending on the power level value (in homogeneous wireless nodes). But in Indoor Localization using leveling and sectoring/coning, RSS (Received signal Strength) is used as a foot print. The accuracy depends on resolution of varying power levels (for leveling) and the beam Angle (of the radiating pattern) of the antenna being steered (in 2D & 3D). Thus 3D indoor localization is achieved by quantization of the spherical co-ordinates (r, θ, φ) using power control at the transmitter and steering control (of the antenna). 2.6 Application of Proposed Approach for Outdoor Localization As in the case if Micro/Pico/Femto Base Station, the triangulation procedure can be utilized using macro cellular base stations as Anchors. Leveling and Sectoring approach cab be utilized using the macro cellular base stations. Leveling and coning can be utilized for 3D localization of say Helicopters, Fighter air-crafts, civil air-crafts with macro cellular base stations as anchors. 2.7 Improved Accuracy using RCPI Due to the way the RCPI is measured vs. the RSS, the RCPI gives more precise data. A received signal strength indicator (RSSI) is defined at the antenna input connector, but it is not fully specified, because there are no unit definitions and no performance requirements, such as accuracy or testability. It is not possible to extract meaning from a comparison of RSSIs from different stations and from different channels/physical layers (PHYs) within the same station. RSSI may have limited use for evaluating access point (AP) options within a station, such as a wireless local area network (WLAN) station, and within a given PHY, but is not useful for evaluations between PHYs. RSSI is rescaled between direct sequence spread spectrum (DSSS) and orthogonal frequency division multiplex (OFDM) PHYs. RSSI from one station does not relate to RSSI from any other station. In high interference environments, RSSI is not an adequate indicator of desired signal quality, since it indicates the sum of: desired signal+noise+interference powers. A Receiver analyses a signal in order to obtain a received channel power indicator (RCPI) value. The RCPI value is a measure of the received radio frequency (RF) power in the selected channel, measured at the antenna connector. This parameter is a measure by the PHY sublayer of the received RF power in the channel measured over the physical layer convergence protocol (PLCP) preamble and over the entire received frame. RCPI is a monotonically increasing, logarithmic function of the received power level defined in dbm. 12

23 Hence due to its non-reliability due to its non-uniformity between different stations, the accuracy levels are not so precise.eg: when we measured RSSI between two different chip vendors in the market, one smart phone connect to a particular access point at a given position and instant shows -21dBm of RSSI, the other at the same point and instant showed -17dBm,which is a variation of 5dBm which leads to a localization error. 2.8 Conclusion Precise positioning is possible using the spherical coordinates and at a macro level. This technique can also be applied on the base stations. Apart from locating the position of the users on earth, even flying object above the base station can be detected using smart antennas, which could aid military applications too. In the next chapter we deal with reducing the delay in grid based WSN networks. They aid in event localization by computing the aggregated data from different cluster heads to a sync/base station within less time. 2.9 References [1] Krishna Chintalapudi, Anand Padmanabha Iyer, Venkata N. Padmanabhan. Indoor Localization Without the Pain. In Proceedings of the sixteenth annual international conference on Mobile computing and networking, pages 12. ACM Press, [2] S. Gansemer, S. Hakobyan, S. Puschel, and U. Gromann. 3d WLAN indoor positioning in multi-storey buildings. In International Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS -09), pages , Sep [3] D. Zhong-liang and W. Wen-jie and X. Lian-ming. A k-means based method to identify floor in WLAN indoor positioning system. Computer Engineering & Software, 33(12):114117, [4] J. Cheng, Y. Cai, Q. Zhang, J. Cheng, and C. Yan. A new threedimensional indoor positioning mechanism based on wireless, page 23, Feb [5] D. Cotroneo, S. Russo, F. Cornevilli, M. Ficco, and V. Vecchio. Implementing positioning services over an ubiquitous infrastructure. In Software Technologies for Future Embedded and Ubiquitous Systems, Proceedings. Second IEEE Workshop on, pages 1418, May [6] F.-Y. Xu and L.-B. Li and Z.-X. Wang. New WLAN indoor localization system based on distance-loss model with area partition Journal of Electronics and Information Technology, 30(6): , [7] N. Samama. Symbolic 3d wifi indoor positioning system: a deployment and performance evaluation tool. In Proceedings of the 13th World Congress of the International Association of Institutes of Navigation (IAIN -09), page 23, Oct

24 [8] A. Mirza, A. Mohed, and R. Garimella. Energy efficient sectoring based routing in wireless sensor networks for delay constrained applications: A mixed approach. In TENCON IEEE Region 10 Conference, pages 16, Nov [9] C.-C. Chang and C.-J. Lin. LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 3(27), [10] U. Gromann and M. Schauch and S. Hakobyan.The accuracy of algorithms for WLAN indoor positioning and the standardization 14

25 Chapter 3 Grid of Wireless Sensors:Distributed Computation 3.1 Introduction Wireless Sensor Networks (WSNs) consist of a set of sensor nodes that are deployed in a field and interconnected with a wireless communication network. Each of these scattered sensor nodes have the capabilities to collect data, fuse and route the data back to the sink/base station (Ian F. Akyildiz, Weilian Su, Yogesh Sankarasubramaniam & Erdal Cayirci, 2002); (Akyildiz, Weilian, Sankarasubramaniam, Cayirci, 2001). To collect data, each of these sensor nodes makes decision based on its observation of a part of the environment and on partial a-priori information. As larger amount of sensors are deployed in harsher environment, it is important that the distributed computation should be robust and fault-tolerant. The identification of an event in a wireless sensor network should be done as fast as possible, thus the computations are done in parallel. Here we investigate the problem of design of optimal parallel distributed computational architecture. In distributed system components located on networked computers communicate and coordinate by passing messages to perform the specified task. Similarly distributed computation is done on distributed nodes connected over the network with defined computational model. A model of computation is a formal description of a particular type of computational process. More details about computability theory can be found in the book by (Barry Cooper, 2003). This paper assumes the no memory computational model of sensor nodes in the architecture for primitive recursive functions. No memory computational model means the sensor node just has registers to store two values; whenever the sensor node receives any value from the other sensor nodes, it simply computes the function with its own measured value and the received value and passes the results to other sensor node(s). The distributed architecture for WSN needs to be optimal from most of the following points (Rotem, Santoro & Sidney, 1985) : Computational complexity Transmission delay required for computations 15

26 Deployment / Reconfiguration Fault Tolerance The rest of the chapter is as follows: Section II describes the problem statement. Section III gives the optimal architecture for primitive recursive functions and discusses the class of functions, i.e. primitive recursive functions, which can be solved using grid like architecture and also the fault tolerance capability of the proposed architecture. Section IV discusses the network architecture for distributed computation of median. Section V explores the possible applications of WSNs in transportation system like itinerary planning, dynamic speed boards etc, which makes it user friendly. Finally section VI concludes the paper. 3.2 Distributed Network Architecture for Primitive Recursive Functions Problem Statement The problem is to define a globally optimal data structure for calculating the defined fusion function over the sensor field. The architecture should be as optimal as possible from the point of view of all the performance measures as discussed in the above section. The computational model considered is also important while defining the suitable distributed architecture. This paper assumes the no memory computational model as discussed before. Thus the problem statement is re-defined; To find the globally optimal architecture, we need to fix some of the performance measures and try to optimize the other measures. The modified problem statement is: Given the maximum allowed delay D 0, define the globally optimal data structure of the wireless sensor network, for the distributed computation of fusion functions of sensed values, in the no memory computational model Primitive Recursive Functions This section discusses the class of functions, i.e. primitive recursive functions, which can be computed optimally on grid like architecture. The basic primitive recursive functions are given by these axioms (Piergiorgio Odifreddi & Barry Cooper, 2012) : Constant function: The 0-ary constant function 0 is primitive recursive. Successor function: The 1-ary successor function S, which returns the successor of its argument, is primitive recursive. That is, S(k) = k + 1 (3.1) Projection function: For every n 1 and each i with 1 i n, the n-ary projection function P n i, which returns its i th argument, is primitive recursive. 16

27 More complex primitive recursive functions can be obtained from the initial functions by means of composition and primitive recursion. Composition: If g is a function of m arguments h 1, h 2... h m, where each of h 1, h 2... h m is a function of n arguments, then the function f is defined by composition from g and h 1, h 2... h m f(x 1, x 2...x m ) = g(h 1 (x 1, x 2...x m ), h 2 (x 1, x 2...x m ),... h m (x 1, x 2... x m )) (3.2) We write and in the simple case where m = 1 and h 1 is designated h, we write f(x) = [goh](x) (3.3) Primitive Recursion: A function f is definable by primitive recursion from g and h if: f(x, 0) = g(x) (3.4) f(x, s(y)) = h(x, y, f(x, y)) (3.5) We write f = P R(g, h) when f is definable by primitive recursion from g and h. Here s is the successor function, which when given an argument n, returns its immediate successor. The primitive recursive functions are the basic functions and those obtained from the basic functions by applying these operations a finite number of times. In WSN domain, simple aggregation techniques i.e., maximum, minimum, and average have been used to save energy while monitoring (Abdelgawad & Bayoumi, 2012). In case of more complex fusion functions also, the fusion function can be represented using primitive recursive function class. Some of the examples of primitive recursive functions which can be used in fusion are: addition, multiplication, exponentiation, factorial, proper subtraction, defined as a b then a b else 0 ; Minimum (a 1, a 2... a n ), Maximum (a 1, a 2... a n ) absolute value, mean, weighted mean, and weighted energy i.e Grid based Network Architecture a 1 x a 2 x a n x 2 n (3.6) This subsection discusses the optimal distributed architecture for homogeneous and heterogeneous wireless sensor networks. Homogeneous WSN consists of sensor nodes with same abilities while heterogeneous WSN consists of sensor nodes with different abilities such as different computing power. 17

28 Homogeneous WSN The solution for the above defined problem is a grid like architecture as shown in Fig. 3.1 Figure 3.1: Example of a path; from source to destination In this section, we first discuss the computational complexity of fusion functions like the minimum/maximum, where only one comparison is needed at every node. Later we show that the same comparisons can be done for other functions as well. Assume that the total number of processors P is equal to the number of sensor nodes in the network. Calculations are as follows: The number of nodes in each branch is defined as D 0, computational complexity in each branch is D 0 1, total number of such branches are N/D 0. So, total computational complexity: = (N/D 0 )(D 0 1) + N/D = N (N/D 0 ) + N/D 0 1 = N 1 (3.7) We can see that the number of comparisons is equal to the minimum comparisons required for any architecture, which is the lower bound of the computational complexity. This is also possible by a tree kind of architecture. In tree architecture for maintaining the delay requirement, one node will have multiple child nodes. Also, as any sensor node will receive more number of values simultaneously, more 18

29 number of registers are needed. Hence, tree kinds of architectures are not suitable in this computational model. Now let us consider the special class of functions which require x comparisons at each sensor node. Computational complexity in the case of such functions is computed as follows. Computational complexity in each branch is (D 0 1)x, number of such branches is N/D 0 1 So, total computational complexity: = (N/D 0 )(D 0 1)x + N/D = Nx (N/D 0 )x + xn/d 0 x = (N 1)x (3.8) Here again the number of comparisons is equal to the minimum required comparisons. Also this architecture is very suitable for the sensor field from the point of view of deployment and coverage. Heterogeneous WSN Clustering of sensor networks has proved to be very effective in conserving energy in heterogeneous networks. For each cluster, one Cluster Head (CH) is selected using the articles (Heinzelman, Chandrakasan & Balakrishnan, 2000); (Younis & Fahmy, 2004). CH is responsible for the collection, fusion and transmission of data for the cluster, and also, only cluster heads participate in routing other cluster data to the base station/sink. Thus in heterogeneous WSN, we consider three types of nodes: Sensor Nodes Cluster Heads Base Station/Sink The proposed architecture for this kind of network consists of a hierarchy of grid architecture as shown in Fig In the hierarchical grid architecture, each node of the final grid architecture is actually a cluster head and this cluster head is connected to other sensor nodes of the cluster using another grid based architecture. Similarly for more complex networks, multiple hierarchies of clusters can be done and in such cases multi-hierarchical grid based architecture can be used Fault Tolerance Fault tolerance of a network is a measure of its ability to do the intended job if some node(s), link(s) or both fail. To increase the fault tolerance of the proposed architecture we included the row links as shown in Fig

30 Figure 3.2: Hierarchy of grid architecture Figure 3.3: Proposed Architecture showing the Row links 20

31 In this architecture if a node or link goes down, then another path is available to send the value computed so far, which can be used while calculating the fusion function of the other branch. Also identification of error can be done in this architecture. The steps for error detection are as follows: 1. Calculate row wise fusion function Calculate the row wise fusion function for each row. Calculate the fusion function with each rows calculated value. 2. Similarly calculate column wise fusion function Calculate the column wise fusion function for each column. Calculate the fusion function with each columns calculated value. 3. If the result of step 1 and 2 are not the same then there is some error in the computation. Example of Fault Tolerance The example here considers the maximum as the fusion function to be computed. Fig. 3.4(a) shows the correct functionality without any link or node failure. Fig. 3.4(b). Fault tolerance example. Fig. 3.4(c) shows the node failure scenario of the example considered. Node failure is considered when the reading from a particular node is not available. The node failure doesnt provide the reading for the respective node. If the failed node is the one giving maximum value then this affects the distributed computation and cant be detected as shown in Fig. 3.4(c). But if some other node(s) (not giving the maximum value) fails then the computation is correct and hence the node failure cant be detected. It is not such a restrictive idea to assume that the maximum over the sensor field is sensed by a single node. But multiple nodes could also sense the maximum value. Here if all the nodes giving maximum value fail only then the computation is incorrect otherwise the computation is correct. Figure 3.4: Fault Tolerance scenarios 21

32 From this example it is clear that the one link failure (if the one is passing the maximum value) can be detected in the architecture Probability of Error in Maximum Calculation This subsection calculates the probability of error in grid based architecture for maximum calculation. Let total number of sensor nodes be N. Lets assume nodes fail independently with probability and number of nodes containing the maximum value be M. So the probability of error is given by: P e = 1 ( N M)P M f (1 P f ) ( N M) (3.9) 3.3 Distributed Network Architecture for Median Problem Statement The problem is to find globally optimal architecture for the computation of median.we need to fix some of the performance measures and try to optimize the others as discussed before. The modified problem statement is: Given the maximum allowed computational complexity O(N logn), define globally optimal data structure for the distributed computation of median in a wireless sensor network Tree based Network Architecture This subsection gives the optimal architecture for distributed computation in homogeneous and heterogeneous wireless sensor networks. The solution for the above defined problem is a tree like architecture as shown in Fig.3.5. The proposed architecture uses the basic heap tree and median of medians algorithm which are standard algorithms (Cormen, 2009). Figure 3.5: Tree like Architecture 22

33 Assumptions A parent node can communicate with both its left and right child. At each level in the tree, parallel computation is assumed. Hence D 0 is the delay for each level. In the architecture, there is one special node with registers. Heap Tree Architecture A heap tree is built from the tree architecture shown in Fig. 3.5, using the book by (Cormen, 2009).At each level, every parent node checks if it is less than both of its children. If it is not, the sensor nodes communicate and swap their values so that the parent is less than both of its children. In a single level, since all the comparisons and swapping to be done by the parent nodes takes place simultaneously independent of the other nodes in the level, this becomes a parallel computation. Fig. 3.6 shows example tree architecture and a heap tree constructed from the same. Figure 3.6: Original Heap to Reduced Head Tree 23

34 Optimal Reduction of the Heap Tree An optimal pivot is selected from the set of sensor values of the tree using median of medians algorithm. The pivot is computed at the special node. All the nodes, which are below the pivot in the heap tree are greater than the pivot and are made passive. Rests of the nodes are active nodes. So all the nodes in levels higher than the level where the pivot is present are passive. We can see that the median doesnt lie among these passive nodes. All these passive nodes, below the pivot need not be considered further in the computation of median. So ignoring the passive nodes, the effective heap tree is the tree with only active nodes. An illustrative example is shown in Fig. 3.7 and Fig.3.8. Figure 3.7: Example 1: Median of Medians Figure 3.8: Example 2: Median of Medians 24

35 Heap Sort The median is now computed using the heap sort algorithm applied to the reduced heap tree (Cormen, 2009). An illustrative example is shown in Fig In the illustrated example, median is 6 and smallest element is 9. Figure 3.9: Example figure for Heap Sort Computational Complexity of the Proposed Architecture Computational complexity of median of medians algorithm for optimal pivot selection is O(N). Computational Complexity of heap sort algorithm (Cormen, 2009) is O(NlogN) and so total computational complexity is given by: = O(N) + O(NlogN) = O(N logn) (3.10) O(N logn) is the best possible (optimal) computational complexity that can be achieved Time Delay of the Proposed Tree based Architecture for Median The heap sort algorithm is effectively being applied to a reduced size of the tree as discussed in the above sections. It is seen that only some of the nodes are being considered in the median computation. The time delay is thus reduced compared to an architecture considering all the nodes of the tree. The pivot selected by the median of medians algorithm is guaranteed to be between the 30th and 70th percentiles of the numbers; this is a standard result. 25

36 Thus the heap tree reduces by a decent proportion, i.e. at least 30% and at most 70%. Hence the proposed architecture works well in reducing the delay by a decent extent. This architecture uses a combination of median of medians and min heap algorithm resulting in worst case computational complexity of and reduced time delay. 3.4 Applications This section discusses the extension of WSNs to exploit its applications in transportation system. The Internet of Things (IoT) technology will revolutionize life as we know it. WSNs act as a key enabling technology for IoT to come into reality. IoT along with Vehicular Ad-Hoc networks (VANETs) can be used to make the transportation system user-friendly and hassle free. This section presents the applications in transportation system that can revolutionize life of the users. The traffic problems can be suitably solved as graph problems i.e. using graph theory (Darshankumar Dave & Nityangini Jhala, 2014); (Baruah, 2014). The following applications can involve the use of current technologies like IoT, GPS, and VANETs etc Dynamic Speed Boards As of today, we do not have dynamic speed boards available but only static speed boards. The aim of this application is to update the speed boards regularly i.e. every 15minutes. For this we need an estimate of the traffic flow in the routes, which can be estimated using the article by (Baruah, 2014). The complete traffic information of a network can be obtained and using this, the nominal speed in a given route which can be safe for a vehicle to travel with, can be estimated as per the traffic congestion information available in the particular route (Baruah, 2014). This nominal speed is displayed on the speed board in that route. The traffic flow information obtained using (Baruah, 2014) can be obtained every 15minutes so that the speed estimate can be updated regularly on the speed boards. Speed limit indications at school zones can be based on school timings i.e. dynamic variation in the speed board limits in the morning during school opening and in the evening during school closing can be done. A special case will be considered in the following sub-section. In case an accident occurs on a highway, it would be better to indicate a lower speed on the speed board in a route which leads to that particular route in which the accident has happened so that the user does not have to wait near the place where the accident has happened. Instead if he slows down before reaching that route itself, by the time he reaches the place of accident, the place may be cleared of traffic/crowd. This particular speed, at which a user must drive so that by the time he reaches the place of accident the traffic clears off, can be estimated by knowing the time of clearance. This time of clearance can be estimated using (Jiang, Ming, Chung & Yang beibei, 2014). 26

37 3.4.2 Dynamic Time Estimate The aim of this application is to give a dynamic time estimate i.e. the approximate time that a vehicle can take from a selected source to a selected destination as per the traffic flow present at that particular time. From the above sub-section, we have an estimate of the average speed of a vehicle in every route. The example illustrated in Fig explains how the time estimate from a source to destination is obtained. Figure 3.10: Dynamic Time Estimate In Fig. 3.10, let the source be A and the destination be C. If the route covers vertices 1, 2 and B from source to destination, the path becomes A-1-2-B-C. The time estimate from A to C would be d(a, 1) d(1, 2) d(2, B) d(b, C) v(a, 1) v(1, 2) v(2, B) v(b, C) (3.11) d(a, c) is the distance from a to c; v(a, c) is the speed estimate obtained in the a c route from the above subsection as per the traffic congestion at that particular time. As soon as a particular source and destination are selected, this kind of calculation is done and the time estimate is displayed for the user. If multiple paths from a source to a destination through different via-routes are available, the time estimate in every path is displayed similarly, for the user to choose a route as per his convenience; for example, the minimum time estimate one i.e. the route which takes shortest time to reach the destination. Time estimate from a source to destination is already available on Google Maps, but it is not a dynamic one while the time estimate calculated here is dynamic. It is made dynamic as the speed estimate used is a dynamic one i.e. the nominal speed in the routes is estimated regularly as discussed before More Accurate Time Estimate The time estimate can be made much more accurate. For example, a person is inside a university in the 8th floor of one of its blocks. He wants to know the time that it takes for him to reach a destination which is somewhere outside the university. The time estimated in the above sub-section did not include the time 27

38 taken for him to come down to the ground floor of the block. Even this time can be included in the time estimate as follows. The latitude, longitude and altitude of his position in the 8th floor and the nearest GPS location of a place in the ground floor or just outside the block/building that he is in, can be known (Pillalamarri, Murthy, 2015). Considering an average speed of the person, we can calculate the time it takes for him to reach the ground floor of the building. This time added to the time estimate calculated in the above sub-section makes it more accurate. An example is illustrated in Fig Figure 3.11: More Accurate Time Estimate In the example considered, the person is in the 8 th floor of a building and he wants to reach the destination place C. The latitude, longitude and altitude of his position in 8 th floor i.e. at node 8 and that at node 0 which is the ground floor of the building can be known Pillalamarri, Murthy, 2015). By calculating the difference in both the altitudes and dividing it by the average speed of a person, we get the time taken for him to reach 0 from 8. Now from 0 to reach place C, the time taken for the path 0-A-B-C can be calculated as discussed before.the accuracy is increased by including the path from 8 to 0, where previously the path for the time estimate included only 0 to C Itinerary Planning Itinerary planning for a passenger is done by taking inputs of source, destination and via-route from him. Itinerary planning would revolutionize and make users life hassle free. Itinerary planning for example in bus transport is that; given a selected source, destination and a via-route, the user should get the list of buses that he/she should take in order to reach the destination. There would be multiple paths possible for a given source and destination through various via-routes. That entire list has to be given out to the user along with the approximate time estimated for each of the routes. This is illustrated by an example in Fig In Fig. 3.12, source is A and destination is B. Few of the various paths possible from A to B are A-1-2-B A B 28

39 Figure 3.12: Itinerary Planning A B The user for suppose has selected the via-routes to include 4 or 2. Then the final routes to be displayed to the user should have only A-1-2-B and A B paths. Now, from the database of the buses, their routes and the timings available, the list of the buses to be taken for each of the paths along with the final time estimate that particular list of buses take, is to be displayed to the user. Here the final itinerary for the user is being planned. The user can then directly follow any of the list of buses shown by the itinerary planning as per his choice of via-route and convenience. This can be extended to other modes of transport like railways etc. Multiple modes of transport can also be combined in the itinerary Coloring Nodes The aim of this application can be explained with an example below. The main problem here is equivalent to that of coloring nodes in a graph. Following are the colors given. Hospitals Gas Stations Police Station Schools Zebra Crossing Red Orange Blue Stripes So given a route, from a source to destination, if the user wants to know for example, all the hospitals in the route, this particular application should show/highlight all hospitals in that route. Whatever the user chooses to see, the application highlights all of those particular colored nodes in the route i.e. in the above case red; hospitals. This application can be implemented by using the 29

40 very recent technique of identifying buildings with zippr code, invented by Aditya Vuchi. Every building has got a unique zippr code. Every location on the earth has got a latitude, longitude and altitude associated with it and they can be found with the present technology of Google Maps. The latitude, longitude and altitude of both the source and destination can be found using this. We then obtain the zippr codes of all buildings with their latitude and longitude lying in the range between those of the source and destination; equivalently we are obtaining all the buildings which lie between the source and destination. According to the zippr code of the buildings obtained, we can identify the buildings as restaurant/hospital/school/police station etc, as most probably the zippr code assigned to a building would be dependent on the type of building that it is, while registration. Once we get the zippr code of a building, the zippr application itself gives us the route from our present location then to the building. This makes life easier to search for schools/hospitals/police stations etc, in a particular route. For this application to come into reality the use of zippr codes for buildings has to increase; this may take time Possible Improvements in Google Maps Traffic patterns as of today, are given from 8am to 8pm which can be improved to make it 24/7. Time estimates from a source to destination can be made dynamic. The applications given in the above sub-sections can be included in the Google Maps. 3.5 Conclusion This chapter discusses the optimal architecture for distributed computation in wire- less sensor networks. Computational complexity for a fixed maximum allowed delay is calculated, which shows that this architecture is the solution for the given computational model. It is also shown that the proposed architecture is very efficient with respect to faults in the network. An optimal architecture for distributed computation of median, with reduced time delay and optimal worst case computational complexity is discussed. The applications of WSN like, itinerary planning that can revolutionize the present transportation system are presented. In the next chapter, we discussed how we can reduce the transmission delay in grid based architecture which aid us in localizing an event (ex: temperature recorded or any such similar parameters). 30

41 3.6 References [1] Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., & Cayirci, E. (2002). A survey on sensor networks. Communications magazine, IEEE, 40(8), [2] Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., & Cayirci, E. (2002). Wireless sensor networks: a survey. Computer networks, 38(4), [3] Cooper, B. S. (2003). Computability Theory. Chapman Hall/Crc Mathematics Series. [4] Rotem, D., Santoro, N., & Sidney, J. B. (1985). Distributed sorting. IEEE Transactions on Computers, 34(4), [5] Odifreddi, P., & Cooper, S. B. (2005). Recursive functions. [6] Abdelgawad, A., & Bayoumi, M. (2012). ResourceAware data fusion algorithms for wireless sensor networks (Vol. 118). Springer Science & Business Media. [7] Heinzelman, W. R., Chandrakasan, A., & Balakrishnan, H. (2000, January). Energy-efficient communication protocol for wireless microsensor networks. In System sciences, Proceedings of the 33rd annual Hawaii international conference on (pp. 10-pp). IEEE. [8] Younis, O., & Fahmy, S. (2004). HEED: a hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks. Mobile Computing, IEEE Transactions on, 3(4), [9] Cormen, T. H. (2009). Introduction to algorithms. MIT press. [10] of medians [Active as on ] [11] Darshankumar Dave, & Nityangini Jhala. (2014). Application of Graph Theory in Traffic Management. International Journal of Engineering and Innovative Technology, 3(12). [12] Baruah, A. K. (2014). Traffic Control Problems using Graph Connectivity. International Journal of Computer Applications, 86(11). [13] Jiang, R., Qu, M., & Chung, E. (2014). Traffic incident clearance time and arrival time prediction based on hazard models. Mathematical Problems in Engineering, [14] Pillalamarri, B., & Murthy, G. R. (2015, April). Precise positioning in 3D using spherical co-ordinates as applied to indoor localization. In Communication Technologies (GCCT), 2015 Global Conference on (pp. 8-11). IEEE. [15] [Active as on ] 31

42 Chapter 4 Outdoor Navigation: Efficient Order Statistics computation 4.1 Introduction Wireless sensor networks (WSNs) are widely employed to perform distributed sensing in various fields. The sensing is done in order to have a better understanding of the monitored entity.wsns provide a bridge between the real physical and virtual worlds. Recent advances in wireless communications and electronics have enabled the development of low power, low cost, multifunctional sensor distances. Each of these scattered sensor nodes have the capabilities to collect data, fuse data and route the data back tothe sink/base station. To collect data, each of these sensor nodes makes decision based on its observation of a part of the environment and on partial a-priori information. Each sensor node simply computes the fusion function with its own measured value and the received value and passes the results to the other sensor node(s).the identification of event in a wireless sensor network should be done as fast as possible, thus the computations are done in parallel. In purview of such efficient individual sensor nodes, we will consider few deeper problems that can be addressed in WSNs. This paper assumes each of the sensor nodes to have self-configurable and data processing ability. The network architectures discussed in this paper are capable of collecting, routing and fusing the data. This paper is an extension of our previous paper [1], giving solutions to a few deeper problems and exploiting the grid based architecture to increase the efficacy of the computation in regards to various aspects. The rest of the paper is organized as follows: Section II addresses the localization problem in WSNs. The optimal computation of order statistics is discussed in Section III. Section IV discusses the efficient grid based architecture, which addresses the challenge of reducing the transmission delay. Section V describes the temporal aspect in computing the statistics in WSNs. Finally, Section VI concludes the paper. 32

43 4.2 Localization Here we investigate the problem of localization in parallel distributed computational grid architecture. The distributed computation is done across the nodes, connected over the network with defined computational model. In many real life scenarios, we would be more interested in finding the geographical location of the event, if occurred rather than just finding if the event has occurred. One such real life scenario that we can look into is that of wildfire [2]. Equivalently we can consider recording a fire accident in a zoo, per say. In these scenarios, one of the most important problems is not just to find out if a fire accident has happened, but to find out the location where the fire accident is actually happening or has started so that immediate measures can be taken in that identified area, to put off the fire. Our previous paper [1], has already accounted to an extent, the challenges like minimizing the time complexity, transmission delay and fault tolerance in computing the fusion function, Maximum by employing a grid based architecture. Here we are taking it a step ahead to find out the location where the event has actually occurred i.e. to find out where the fire has actually started. So we need to get the geographical location of maximum temperature recorded or any such similar parameters in order to locate the fire. Figure 4.1: Localization problem being addressed 33