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The Computer Journal
, Volume Advance Article (6) – Nov 9, 2017

15 pages

/lp/ou_press/energy-efficient-approach-for-effective-estimation-of-delimited-node-c0h4aGanV0

- Publisher
- Oxford University Press
- Copyright
- © The British Computer Society 2017. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
- ISSN
- 0010-4620
- eISSN
- 1460-2067
- D.O.I.
- 10.1093/comjnl/bxx102
- Publisher site
- See Article on Publisher Site

Abstract Wireless sensor network (WSN) has a wide range of monitoring and tracking applications. Most of these applications require sensor node’s location information. Thus, location information is most important for these applications. Manual configuration of node’s position is rarely used as applications demands for random deployment. Resource constraint WSN does not afford using GPS for each node. Thus, WSNs bank on node location estimation (localization) methods to find sensor nodes’ location information. This paper focuses on estimating delimited position of unknown sensor nodes by limiting the number of references. With proposed heuristic function, proposed method converges with lesser number of iterations, and, as a result, it decreases network setup time as well as energy consumption. Reference nodes’ location accuracy is calculated using the proposed heuristic function. Required references with better accuracy are selected from the available references for unknown node’s location estimation and consequently selection method increases localization accuracy. Results show that proposed method gives better location accuracy compared with traditional methods as well as state of the art methods. It uses lesser number of references as well as iterations compared with state of the art methods. It also reduces energy consumption and network setup time compared with state of the art methods. 1. INTRODUCTION Wireless sensor networks (WSNs) are gaining more and more research interest of research community because of its Omnipresence in ones’ life [1, 2]. Wireless sensor node is the main entity of WSNs. The main objective of wireless sensor node design is to make them small in size, low in cost and energy efficient [3]. This is because nodes are deployed in large number to measure the phenomena where they are deployed. Once they are deployed, it is not possible to access them and replace batteries as well as reuse them for other applications. As wireless sensor nodes are smaller in size, low in cost, large in numbers and inaccessible in nature make sensor nodes resource constrained. It is necessary to manufacture them in smaller size as sometimes we need to deploy them in human body or in a system where size of node matters. Miniaturization of sensor nodes prevents from employing more resource on sensor nodes. This is the first reason sensor nodes are resource constrained. Most of the nodes are battery operated and after deployment it is not possible to access sensor nodes physically to replace or recharge its battery this is the second reason in terms of battery capacity it is resource constrained. WSN applications need large numbers of nodes which are disposable in nature. Cost consideration of whole application forces designer of sensor node to lighten the resources availability of sensor nodes. This is the third reason for resource constrained WSNs. These design requirements prohibit the incorporation of some enviable components like GPS. Most of the WSN applications require lesser amount of data transfer from one node to another node. This characteristic requires lesser bandwidth to make WSN operational. WSNs node need not to have high-end processing capabilities as WSN application does not demand for that. Cost and size constraint prohibits the use of larger memory modules. Lesser memory requires smaller and efficient Operating System footprint. Apart from this, routing tables that contain entries for each possible destination in a network may be too large to fit into a sensor’s memory. Thus, sensor nodes memory stores lesser information in the form of routing cache. Mutual coordination among resource constrained sensor nodes enables to form WSN which is a special case of Wireless Ad hoc Network [4]. Sensor nodes in WSNs are responsible for measuring phenomenon where they are deployed. Sensor (sender) nodes in WSN measure properties (like temperature, humidity, pressure, light, etc.) of the phenomenon using different types of sensors and send it to sink or receiver node (central processing node). Most of the time there is no single hop connection between the sink node and the sender sensor node. Hence, after measuring phenomena, sender node sends measured information to sink node using multi-hop path. Using WSNs, it is possible to implement various monitoring and tracking applications [3]. Monitoring applications include enemy troop detection, habitat, inventory, structural, infrastructure security, factory, machine, chemical, health, weather, pressure and temperature monitoring. Tracking applications include human tracking, animal tracking, enemy tracking and traffic tracking. To support these applications, a large number of sensor nodes need to be deployed to cover the phenomena under consideration. These sensor nodes are deployed randomly, means their node location information is not known beforehand. Having node location information is the prime requirement of such monitoring and tracking applications. In monitoring and tracking applications, sensor nodes are sending sensed data to sink nodes with its identity. These applications demand for location information of sender node instead of its identity. Thus, from where the information is being sent is of more importance than who is sending the information. In such applications, sensor nodes measuring phenomena without awareness of the location is meaningless. Thus, location awareness is must for these applications. For example, location information is necessary for applications like inventory management, intrusion detection and surveillance. Finally, localization is fundamental for sensor network services that rely on the knowledge of sensor positions, including geographic routing. Sink (receiver) node is more interested in knowing the location of sensor nodes sending sensed data instead of their identity (i.e. node number). Most of the applications as mentioned above need to send location information of sensor (sender) nodes along with measured information to the sink node. To clarify the above discussion with forest fire detection application, assume that a large number of sensor nodes is deployed having temperature, humidity and gas sensors in a forest. Every sensor node measures relative humidity, atmospheric pressure and temperature and sends it to sink node along with its location information. Sink node raises alarm signal to rescue team with location information of the sender node if some of these measurement goes above the set threshold. Using sender location information rescue team will be able to know the exact location where the fire is spreading and react accordingly by reaching the location sent by sender node. With location information of each sensor, WSNs would be able to achieve some functionality for their applications with added efficiency [5]. Deployment method depends on phenomenon being measured. Manual deployment of sensor node allows us to fix the position of each node. But manual deployment is rarely used in most of the sensor network applications. Sometimes, the area where WSN needs to be deployed is inaccessible. Thus, manual deployment is not possible, and this leads us to a scenario where random deployment is the only option for WSNs. As the manual configuration of the node position is not possible, the efficient method needs to be devised to determine the position of nodes. Low cost and low power consumption are the key design requirements of WSNs. It is impractical to load every sensor node with GPS due to energy consumption and cost considerations. GPS is also not suitable for indoor application of WSNs. In the absence of infrastructure, triangulation methods (like A-GPS) and Wi-Fi-assisted location techniques would not work. Therefore, to determine the location of nodes is a very challenging task for these applications. Recently, many localization algorithms for WSNs have been proposed for location estimation of sensor nodes. Resource constrained WSNs demand for location estimation method which is simple and energy efficient. A large number of sensor nodes are required to cover large area. Initially, it is assumed that some of these sensor nodes are preconfigured with their positions known as beacons. One class of localization methods depends on more numbers of beacons to increase the accuracy of location estimation. The complexity of localization algorithm is directly proportional to the number of beacons/references used. Increased complexity increases the energy consumption of every sensor node, and in turn it reduces the lifetime of WSN. It also increases network setup time. To reduce computational complexity, network setup time as well as energy consumption; it is desirable to use lesser number of references for position estimation. Methods of this category use lesser number of references which helps unknown nodes to estimate its position. At least three beacon/reference nodes are required to localize unknown node. Using exactly three references does not estimate node position accurately if these references are not beacons. More than three references are required to increase the accuracy of the localization method. Increased number of references comes with the cost like increased energy consumption and network setup time. Keeping accuracy in mind, a tradeoff is required to achieve better accuracy, energy efficiency and reduced network setup time. After estimation of position of an unknown node, it may become reference for other unknown nodes. With necessary tradeoff, proposed method falls into the same class as explained above. This paper presents an energy-efficient node position estimation method which delimits sensor nodes’ position using a limited number of references. Means proposed method is not using all available references but references having accurate position information. To calculate accuracy of estimated position, proposed method has also devised new heuristic function. Correct accuracy (of node position estimation) is calculated using proposed heuristic function. More realistic accuracy information (of node position estimation) enables the proposed method to estimate unknown node’s position information very accurately and with lesser number of accurate references. The use of limited number of accurate references decreases complexity of the proposed method compared methods of its class. Thus, the proposed method estimates node’s position in a lesser amount of time. The objective is to get location accuracy, energy efficiency and reduced network setup time compared with the state of the art methods using iterative approach as well as more than three references for node location estimation. Two key design requirements of any WSN are low cost and low power consumption. Various standards for WSNs have been developed to achieve these requirements up to some extent [3, 6]. IEEE 802.15.4 is one of the standards for implementing various applications of WSNs. This standard closely fulfills both of these key design requirements, and this is the reason it is gaining more focus of the research community. IEEE 802.15.4 standard has specified physical layer (PHY) and MAC layer protocols. It is becoming landmark specification of protocols for the development of WSN applications that require low data rate, low complexity, low cost, low power consumption and short-range communication [6]. Configuring IEEE 802.15.4 complaint nodes in a peer-to-peer topology, it is possible to have WSN for the desirable application. The proposed method has been implemented using recognized network simulator NS-2 by configuring IEEE 802.15.4 (LR-WPAN) complaint nodes in a peer-to-peer topology. Section 2 gives a review of the related methods available in the literature. A detailed discussion of preliminaries for proposed method is given in the first subpart of Section 3, and proposed algorithm is given in the second subpart of Section 3. Simulation environment and simulation details are given in first part of Section 4. The second part of Section 4 presents results to validate the proposed method by comparing it with basic and state of the art methods. 2. RELATED WORK The explosion of sensor nodes in the day to day life draws an attention of research community towards WSNs. These days, it is possible to design miniature sensor nodes due to technological advancements. These nodes are also cheap in cost and consume very less power while operational. As discussed in Section 1, monitoring and tracking applications can be benefited by WSNs. Most of these applications demand for location information of sensor nodes deployed in phenomena and for this reason localization method is needed as nodes are not preconfigured with location information. Localization methods are also demand of the resource constrained WSNs as it is not possible to load sensor nodes with GPS due to cost considerations. Any of the WSN localization methods fall into one of the two classes: range-free localization methods or range-based localization methods [7]. The first category of (i.e. range-free localization) methods [7–11] does not need to employ additional hardware as they do not require distance or angle measurement between nodes. Node location estimation given by these methods possesses location errors. Thus, these methods suffer from location inaccuracy. Contrary, range-based localization methods use Triangulation, Trilateration, Time of Arrival (ToA) or Time Difference of Arrival (TDoA) for node position estimation. Comparison of these methods is shown in Table 1. Range-based methods need to measure point to point distance [12] between beacons/reference nodes and unknown nodes. To determine node position, a method of this category may employ additional hardware if necessary. Compared with range-free methods, these methods estimate nodes’ position more accurately using different measurement techniques. Table 1. Cost, energy, accuracy and hardware comparison of different methods under focus. Method Cost Accuracy Energy efficient Hardware size Extra hardware Centralized methods Few nodes are costlier High Less More for central node Depends on method used Decentralized methods Low Low High Based on method used Depends on method used Angle of Arrival High Low Medium Large Antenna arrays Time of Arrival High Medium Less Large High processing capabilities, Synchronization required Time Diff. of Arrival Medium High High Large Speaker, microphones, base stations synchronization Trilateration using RSSI Low Medium High Small No extra hardware required Scene Analysis using RSSI High Medium Medium Large Resources required Proximity Analysis using RSSI Medium Medium Medium Medium Non-infrastructure based Method Cost Accuracy Energy efficient Hardware size Extra hardware Centralized methods Few nodes are costlier High Less More for central node Depends on method used Decentralized methods Low Low High Based on method used Depends on method used Angle of Arrival High Low Medium Large Antenna arrays Time of Arrival High Medium Less Large High processing capabilities, Synchronization required Time Diff. of Arrival Medium High High Large Speaker, microphones, base stations synchronization Trilateration using RSSI Low Medium High Small No extra hardware required Scene Analysis using RSSI High Medium Medium Large Resources required Proximity Analysis using RSSI Medium Medium Medium Medium Non-infrastructure based Table 1. Cost, energy, accuracy and hardware comparison of different methods under focus. Method Cost Accuracy Energy efficient Hardware size Extra hardware Centralized methods Few nodes are costlier High Less More for central node Depends on method used Decentralized methods Low Low High Based on method used Depends on method used Angle of Arrival High Low Medium Large Antenna arrays Time of Arrival High Medium Less Large High processing capabilities, Synchronization required Time Diff. of Arrival Medium High High Large Speaker, microphones, base stations synchronization Trilateration using RSSI Low Medium High Small No extra hardware required Scene Analysis using RSSI High Medium Medium Large Resources required Proximity Analysis using RSSI Medium Medium Medium Medium Non-infrastructure based Method Cost Accuracy Energy efficient Hardware size Extra hardware Centralized methods Few nodes are costlier High Less More for central node Depends on method used Decentralized methods Low Low High Based on method used Depends on method used Angle of Arrival High Low Medium Large Antenna arrays Time of Arrival High Medium Less Large High processing capabilities, Synchronization required Time Diff. of Arrival Medium High High Large Speaker, microphones, base stations synchronization Trilateration using RSSI Low Medium High Small No extra hardware required Scene Analysis using RSSI High Medium Medium Large Resources required Proximity Analysis using RSSI Medium Medium Medium Medium Non-infrastructure based The first objective of this paper is to get delimited node position estimation. So, range-free methods are opted out as they do not provide accurate location estimate due to its nature. So, the obvious choice is to go with range-based localization method. Range-based methods are briefly discussed as below: Angulation methods need extra hardware in the form of an array of antenna elements. Receiving node determines the angle of arrival by looking into a phase of the incident signal on different antenna elements on the same node. A difference in arrival time of this signal derives angle information if the geometry of antenna elements is known. This angle information is being used for node position estimation by angulations methods. Triangulation methods come under this category and using the angle of arrival (AoA) for the estimation of node’s position [13, 14]. In Time of Arrival (TOA), the speed of signal and time taken by a signal traveling between the reference node and unknown nodes is used to calculate the distance between the reference and unknown nodes. These distance values are being used to estimate node position [15–17]. GPS also uses the same method as it is a highly delimited method for node position estimation. ToA requires high processing capabilities to achieve to get high accuracy in node position estimation. In Time Difference of Arrival (TDoA) methods, the location of the node sending information is determined by calculating the difference in arrival time of the signal at geographically separated nodes. Synchronization between base stations is required for this method to work [18–20]. Lateration methods [21] use the distance between reference nodes and unknown nodes to estimate unknown node’s position. Trilateration and multilateration come under this category. In trilateration method, unknown node measures distance with three reference nodes and estimates its position. In multilateration method, instead of using exactly three nodes more than three nodes are being used to estimate unknown node’s location. The distance between the reference node and the unknown node is calculated using received signal strength indicator (RSSI). Distance is estimated using signal loss factor known as attenuation. Received signal strength depends on the distance between transmitter and receiver node. With trilateration accuracy of node localization is limited but using multilateration (more than three references), it is possible to increase localization accuracy. Summary of Cost, energy, accuracy and hardware requirements for methods discussed above is presented in Table 1. There are two key design requirements of WSNs: energy efficiency and lesser cost. Methods discussed above i.e. Time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA) and Lateration (using RSSI) need to calculate the distance between two nodes for node location estimation. As discussed and shown in Table 1, the methods using AoA require an array of antenna elements which is expensive [22]. Method proposed in [23] uses two antenna anchors to estimate node location with required accuracy. Method proposed in [23] also uses multiple parallel arrays to provide space diversity. Employing such antennas increases the cost of sensor nodes as well as energy consumption while operational. Thus, it opposes both of the key design requirements of WSNs. Localization methods using ToA require clock synchronization for all participating nodes. Apart from these it also uses high processing capabilities for node position estimation. After synchronizing all nodes’ clock, as time passes they will not remain synchronized due to clock skew and clock drift. They need to resynchronize periodically for accurate node estimation. If they are not periodically synchronized, location error will come in the picture due to drifting of clocks. It leads to the wrong estimation of node’s location. To achieve system-wide clock synchronization cost has to be paid regarding the exchange of messages. It becomes an overhead for the complete system and consumes lots of energy and opposes first key design requirement. Another issue with these methods is that requirement of high processing capabilities. It is known that Sensor Nodes are resource constraint nodes having limited processing and storage capabilities. Estimation of node location using AoA needs more calculations, compared with other methods, and it may take longer with limited processing power and increase network setup time. ToA-based methods generate high location errors as synchronization in distributed environment is very difficult to achieve [24]. An alternative to clock synchronization is to use exchange timing information by certain protocols such as a two-way ranging protocol [25]. Location estimation methods using TDoA need to employ small sized hardware (like speaker and microphones, etc.) [26] for methods to work correctly. Synchronization among (unknown) nodes is not required in TDoA-based methods, but maintaining synchronization among reference nodes [5, 25] is the key requirement of these methods. Thus, methods of this category consume more energy for maintaining synchronization. To achieve this, every reference node requires extra hardware up to some extent. Points discussed above oppose both of the key design requirements of WSNs. Hence none of the methods from AoA, ToA or TDoA fits for WSN’s node localization. The use of extra hardware for these methods increases the cost of individual sensor nodes and in turn, increases the cost of the whole system. Maintaining clock synchronization requires the exchange of messages which leads to more energy consumption whereas energy is the scarce resource for WSNs. Some of the methods require a complex operation for the node position estimation which means number of processing operations and require more setup time. The method is required in which angle, time of arrival or time difference of arrival information is not being used for node location estimation. The method is required which does not demand extra hardware and synchronization. Employing RSSI to determine distances and turn to estimate node locations resolves the issue. RSSI itself does not demand any extra hardware or clock synchronization. Trilateration with RSSI provides means for low cost and energy efficient localization methods. Thus, RSSI for node localization fulfills both of the key design requirements of WSNs i.e. low cost and energy efficiency. Mainly, there are three types of methods using RSSI for node localization: trilateration, scene analysis and proximity analysis [27, 28]. Scene analysis methods using prior collected features called fingerprints of a scene for node localization [27]. Fingerprinting a large area, where dense network needs to be deployed is not feasible as it requires a large amount of resources and high network setup time [29]. This leads to non-applicability of these methods for sensor networks. The second type of methods employing RSSI is proximity analysis for node localization. These methods use device or application-based approach instead of infrastructure-based approach, and this requirement becomes the reason for proximity analysis methods are not being used in for localization of WSN nodes [27]. The third method is lateration for node localization using RSSI. With the help of propagation models, it is possible to estimate node position by employing trilateration when RSSI values from more than two references are available. The use of this method (i.e. RSSI) is advisable instead of ToA or TDoA as these methods require a clear line of sight between references and unknowns [28]. Thus, the obvious choice is to go with RSSI. Specifically, to go with trilateration or multilateration using RSSI as it achieves both of the key design goals of WSNs. But, as mentioned in the literature and as indicated in Table 1, the problem with RSSI is it estimates node location with a moderate level of accuracy. During literature review, it is observed that more of the research work is focused on increasing the accuracy of node localization using trilateration or multilateration with RSSI. This paper is also focused on proposing a method which uses multilateration for node position estimation using RSSI. The main objectives of the proposed method are to increase the accuracy of the node localization along with increasing lifetime of network and decreasing network setup time. To increase accuracy, most of the lateration-based localization methods depend on employing all the available references as described in for unknown node’s location estimation. The use of all the available references increases space requirement and also increases computational complexity of the method. This leads to increase in energy consumption and also network set up time. So it is prudent to use lesser number of references for node localization. Using at exactly three references or all the available references are the two extremes. Methods using exactly three references gains in energy efficiency and network setup time but fails in estimation accuracy. On the other hand, methods using all the references gains in accuracy and fails in achieving energy efficiency and reduced network setup time. Thus, tradeoff is required regarding number of references. Rest part of the section considers methods available in the literature which uses some references from both of the extremes (i.e. 3 to all the available references) to achieve better accuracy, energy efficiency and network setup time. The method proposed in [30] uses trilateration for node localization. When RSSI values from desired references are not available, this method exposes its inability for node localization. D-Log [31] gives an improved distance approximation for an IEEE 802.11 complaint node under the region of given Access Point (AP). Over the period, it logs some RSSI values from various nodes. It also takes help of neighboring APs for improved distance approximation. The accuracy of this method is a function of the size of the log being used. This method also requires infrastructure for node localization. Methods proposed in [32, 33] estimates node position without using anchor nodes. These node localization methods and methods of this class are internal by nature i.e. node position is relatively derived and has no relation with global location. The issue with this algorithm is it works in a scenario with a lesser number of nodes (approximately up to 10). Accuracy is not the objective of these methods. The concern is not given to accuracy but relative location estimation. Random Sample Consensus (RANSAC) proposed in [34] uses regression to keep and use all utile references for unknown node’s location estimation and rule out other references which are not following certain criteria. In a case, where required number of utile references is not available, this method is not able to estimate unknown node’s position. The method proposed in [35] uses lateration for node localization. In this method, reference nodes’ location information is assumed to be error free. A set of anchor nodes or beacon nodes is denoted as β and R denotes a set of reference nodes. If R is not a subset of β, then assumption made above leads to wrong convergence of location estimation algorithm. The method proposed in [36] uses RSSI for node location estimation. The use of probability density function increases computational complexity of this method. In turn, it increases network set up time. RSSI-based lateration method proposed in [37] calculates node’s position using anchor nodes, and efficiency is achieved with the help of MAC layer. This method keeps on running for several iterations to achieve better accuracy. A criterion to stop iterative estimation is not specified in the method. The method proposed in [38] uses only better references to estimate node’s position. The heuristic used by [38] treats beacon nodes and every other node that became references the same way. When at least one beacon node is participating in heuristic used by [38] method, then it miscalculates node’s location accuracy during the process of node localization. The method proposed in this paper uses lesser but better references by selecting them from all available references and neglects the rest references which affect location estimation accuracy. To calculate the accuracy of node position estimation (which is less faulty), the new heuristic function is proposed in this paper along with refinement in the localization process. Method proposed in this paper requires lesser number of iterations to estimate delimited location and this became possible because of correct calculation of accuracy of location estimation. 3. PROPOSED METHOD The first subpart of this section explains preliminary concepts required for proposed method. The second subpart gives the proposed method in the form of an algorithm with its explanation. 3.1. Preludes Node localization is a process of node location estimation with the help of other nodes knowing its node positions i.e. beacon or reference nodes. The method proposed in this paper uses few nodes known as beacons for node localization. These nodes have their preconfigured location information either by manual deployment or using GPS. The rest of the (unknown) nodes want to know their location and localization method help doing that. 3.1.1. Symbols used Sensor nodes are classified into three categories: first is the beacon nodes having preconfigured (manually or using GPS) location information. These nodes are assumed to have most accurate location information with zero error in it. The second type of nodes is the unknown nodes. These nodes do not know their location information and need to be localized. The third type of nodes is reference nodes. These nodes were initially unknowns, but after the application of localization, these nodes may become reference nodes. Along with beacons upon becoming reference from the unknown node, these nodes help to localize rest of the unknown nodes. Beacon, unknown and reference nodes are denoted as bi, ui and ri, respectively, as given below: B={bi|iisfrom1ton(B)} (1) U={ui|iisfrom1ton(U)} (2) R={ri|iisfrom1ton(R)} (3)where B, U and R are sets of the beacon, unknown and reference nodes, respectively. bi, ui and ri denote ith node in set B, U and R, respectively. n(B), n(U) and n(R) denote the number of nodes in a particular set at the moment of time. Objective function of localization system is as given below: Initial state: B={bi|iisfrom1ton(B)} (4) U0={ui|iisfrom1ton(U0)} (5) R0={ri|iis0}=∅ (6) In Equations (4) and (7), B is having a fixed number of nodes, and it is always n(B) >= 3. According to literature value of n(B) is at least 16% of (n(B) + n(U0)). The number of unknown nodes is always larger than the number of nodes in B means n(U0) ≫ n(B) as shown in Equation (5). In an initial state, this set is non-empty. Initially, set R is empty as shown in Equation (6) it means n(R) = 0. Intermediate or final/objective state: B={bi|iisfrom1ton(B)} (7) Rj={{ri|iisfrom1ton(U0)}forj=1{ri|iisfrom1ton(Rj−1)}for2≤j≤finalstate (8) U={ui|iisfrom1ton(U)}=∅ (9) In the first intermediate state i.e. value of j = 1, R is filled with all the members of U0 and n(R) = n(U0) as shown in Equation (8). When R gets all the members of U, it becomes empty as shown in Equation (9) and n(U) = 0. In both the intermediate and the final state, U is empty. Intermediate and final states are different regarding the accuracy of node position information. The number of nodes in R remains same in both of these states but moving from the intermediate state to the final state accuracy of node position information is improved. In the final state, all the unknown nodes are localized with greater accuracy. The objective function of the method is to increase accuracy of node position estimation with lesser number of iterations i.e. j. 3.1.2. Sources of errors Sources of errors are identified in [39] are as follows: (a) sensing errors occur due to the limitations in sensing elements of nodes and unstable phenomena. With the help of digital signal processing (DSP) techniques, it is possible to remove these errors. (b) Computers represent quantities with limited precision as it is digital in nature. This limitation is a source of computational errors. WSNs are resource constrained networks as this is not feasible to increase precision to decrease computational errors. One way to reduce computation error is to make localization method simpler. (c) Some errors spawn due to incomplete objective function. The solution to this problem is to design an objective function which fully covers the objective of the problem. (d) The other type of error is the result of an intractable objective function. To remove these errors, proposed objective function should be simple enough to make it tractable. (e) Localization errors are the result of using inaccurate references for the node position estimation of unknown nodes. Estimated or refined node position of the ith node is denoted by Ne(i). The actual position of the ith node is denoted by Na(i). After localization process, location information of the node being localized may have some error. The value of location error is in terms of distance between actual position Na(i) and estimated position Ne(i). The value of location error of node i is denoted by El(i). Errors in localization are also because of distance measurement techniques. The distance is measured between reference node and node being localized. Method proposed in this paper measures the distance using the RSSI method. Dm(i,j) denotes the measured distance between node i and reference j. Da(i,j) denotes the actual distance between node i and j. The difference between measured distance Dm(i,j) and actual distance Da(i,j) is the distance measurement error denoted by De(i,j). Both of these errors i.e. location error El(i) and distance measurement error De(i,j) are affecting the accuracy of the localization algorithm. To improve the accuracy of the proposed method, it is necessary to reduce the effect of these errors. To remove these errors (i.e. location and distance measurement errors), it is necessary to consider only those references have accurate node location information. Delimited node position estimation is possible if the concern is given to these errors. 3.1.3. Multilateration and distance measurement methods for proposed algorithm As derived from the literature survey multilateration is the only option for the node localization for WSN applications. Multilateration gives cost-effective solution as it does not require any extra hardware for node localization method. To estimate or refine node position n (n ≥ 3) number of beacons or references is being used. Figure 1 explains the process of multilateration. Figure 1 illustrates four reference/beacon nodes denoted by Ri(xi,yi) indicating node number with its location information. For example R1(x1,y1) is first reference’s location information given by (x1,y1). The distance between Ri(xi,yi) and Unknown node U(x,y) is given by Di(U,Ri). Figure 1. View largeDownload slide Position estimation using multilateration. Figure 1. View largeDownload slide Position estimation using multilateration. Knowing this information Ri(xi,yi) and Di(U,Ri), it is possible to calculate unknown node’s location using the following system of equations: The equation for the distance between the unknown node and any of the reference is thus given by Di2=(x−xi)2+(y−yi)2 For all the reference or beacon nodes set of the equation is given as below: D12=(x−x1)2+(y−y1)2 (10) D22=(x−x2)2+(y−y2)2 (11) D32=(x−x3)2+(y−y3)2 (12) D42=(x−x4)2+(y−y4)2 (13) Rearranging Equations (10)–(13) system of equation changes as given below: D42−D12+x12−x42+y12−y42=2(x1−x4)x+2(y1−y4)y (14) D42−D22+x22−x42+y22−y42=2(x2−x4)x+2(y2−y4)y (15) D42−D32+x32−x42+y32−y42=2(x3−x4)x+2(y3−y4)y (16) Rearranging Equations from (14) to (16) converts it into the following equation: X=(ATA)−1ATB (17)where A, B and X are matrices as given below: A=[2(x1−x4)2(y1−y4)2(x2−x4)2(y2−y4)2(x3−x4)2(y3−y4)] B=[D42−D12+x12−x42+y12−y42D42−D12+x12−x42+y12−y42D42−D12+x12−x42+y12−y42] X=[xy] Evaluating Equation (17), it is possible to get unknown node location information (U(x,y)) using four reference nodes’ position information and the distance between these reference nodes and unknown node. The distance between reference nodes j and unknown nodes i (Dm(i,j)) is measured using RSSI. The value of RSSI is measured using one of the propagation models as explained below: To design efficient protocols and algorithms for wireless sensor networks, it is required to assess the characteristics of wireless communications. Wireless propagation models are the important building block of the WSNs. These models give a characterization of radio wave propagation in terms of transmission power, receiving power and distance between transmitter and receiver. The free space propagation model (FSPM) is being used in a situation where there are no obstacles between transmitter and receiver nodes. Means there is a clear line of site between reference nodes and unknown nodes. The value of measured distance between the unknown node and the reference node using free space propagation model is as given below in the following equation: Dm(i,j)=PtGtGrλ2Pr(4π)2L (18) Two-ray ground model (TRGM) is another model which gives better estimates of the distance between unknown node i and reference node j as it considers both the direct and the ground-reflected path. If the transmitter and the receiver are far from each other, this model gives better result compared with free space model. The value of measure distance between the unknown node and the reference node using TRGM is as given below in the following equation: Dm(i,j)=PtGtGrht2hr2PrL4 (19)where Dm(i,j) is the measured distance between the node being localized and reference/beacon node j. Pt and Pr are the transmitting and the receiving power, respectively. Gt and Gr are the transmitter and the receiver antenna gain, respectively. λ is the wavelength of the radio wave and L is the path loss factor. ht and hr are the transmitter and the receiver antenna height, respectively. In the proposed method, unity gain antennas are assumed. Thus, Gt and Gr are 1 and L is also assumed to be 1. However, the later model does not give better distance estimates if the distance between sender and receiver is short. This is because of the fluctuation caused by straight and reflected ray. For this reason, if the distance between unknown and reference nodes are short it is suggested to use free space propagation model. The method proposed in this paper also uses the distance criteria for the selection of propagation model. The actual distance between the unknown node and the reference node is Da(i,j) and for some threshold distance Dt, if Da(i,j) < Dt, then free space propagation model is used else TRGM needs to be employed. The value of Dt is as given by the following equation [40]. Dt=4πhthrλ (20) Above two models (i.e. FSPM and TRGM) are best suitable for outdoor environment and we have incorporated these two in simulator NS-2 as we are using either of these models for our experimental purpose. If WSN application is in the indoor environment, then above two models do not give better result for this situation, thus it is suggested to use the log-distance path loss model. Model is expressed by the following equation: Li=L0NlogD(i,j)D0+Rg (21)where Li is the total path loss in an indoor environment, L0 is the reference path-loss, N is the path loss distance exponent and Rg is Gaussian random variable with 0 mean. The log-distance model is a generalization of models mentioned above. 3.2. Algorithm An effective approach for node position estimation is presented in this section. The method given in this section achieves accurate and highly delimited node position estimation in a lesser amount of time with reduced number of references used. Considering and using all the discussion given above, this section describes the method proposed in this paper. The proposed method is given in the form of an algorithm which runs on every unknown node for position estimation. The method proposed in this paper is compared with state of the art methods available in the literature. One of the methods under consideration for validation of proposed method is AlWadHA localization algorithm. Thus, for comparison point of view and result analysis point of view, the algorithm proposed in this paper is in line with algorithm available in [38]. This helps readers to differentiate proposed method with state of the art methods. Highlighted part of the algorithm achieves objectives differently compared with state of the art methods. These differences make proposed approach efficient and effective. Description of the proposed algorithm, Energy Efficient and Delimited Node Position Estimation (EE_DPE) is as given below: Flag mentioned in the algorithm described below is a Boolean flag, and it is being used for termination criteria for node localization algorithm. If the flag is set it means that node position estimation has achieved enough accuracy for the given node, then no further refinements/iterations required. Initially, the flag is not set. Step 1 indicates termination if the flag is set. In Step 2, the unknown node broadcasts location requests message to get location information of neighboring beacons or reference nodes. Requesting node Ui receives response messages containing location information from the nodes in set R or B if ri or bi is in the transmission range of Ui as given in Step 3. Responses are saved in a list called Resi. Every unknown node creates this response list as per Step 4. According to Step 5, if a number of responses are lesser (i.e. less than 3), then the node has to wait for some predetermined time and then it again starts with Step 2. This waiting time is always very much lesser than network setup time. This waiting time let some unknown nodes to estimate their position. After position estimation, these nodes may become a reference for unknown nodes Ui and this way Resi may get a required number of references for the position estimation of node Ui. If a number of nodes in Resi are greater than 2 (means 3 or more than 3), then first of all beacons are selected from Resi and added to list Si. After populating Si with beacon nodes, if the size of Si is greater than 2 then Ui will be localized with all beacon nodes with the greatest accuracy. Algorithm EE_DPE () 1. if (flag is set) then return endif 2. Ui sends location request to all its neighboring nodes 3. Requesting nodes receives responses containing location information from B and/or R nodes. 4. Received responses are saved in list Resi for node Ui 5. if (n(Resi) < 3) thenwait forTitime and jump to step 2 else if (n(Resi) ≥ 3) thenselect beacons from Resiand add them to subsetSi if (n(Si) < 3) thenselect References having a certain level of accuracy and append toSi elseset the flag endif endif endif 6. if (Da (i,j) <Dt) if(not in Indoor Environment) thenuse Equation (18) for distance measurement elseuse Equation (19) for distance measurement. endif else Use Equation (21) for distance measurement endif 7. Apply Equations (10)–(17)to estimate initial node position Pi for Ui 8. if(flag is not set) thenposition refinement is required for(each nodejinSi) De(i,j) = | ||Pi−Pj||−Da(i,j)| if (De(i,j) >Dthresh) then goto step 9 endif endfor goto step 11 endif 9. for (each node j in Resi) De(i,j) = │║Pi−Pj║−Di(i,j)│ if (De(i,j) > Dthresh) then remove node j from Resi endif endfor 10. Re-estimate position of Pi using step 6 and 7 11. Det=∑j=1n(Si)|‖Pi−Pj‖−Di(i,j)| 12. if (Det < Prev(Det) then Pi is accepted endif 13. if (Det < Min(Det) then flag is set endif 1. if (flag is set) then return endif 2. Ui sends location request to all its neighboring nodes 3. Requesting nodes receives responses containing location information from B and/or R nodes. 4. Received responses are saved in list Resi for node Ui 5. if (n(Resi) < 3) thenwait forTitime and jump to step 2 else if (n(Resi) ≥ 3) thenselect beacons from Resiand add them to subsetSi if (n(Si) < 3) thenselect References having a certain level of accuracy and append toSi elseset the flag endif endif endif 6. if (Da (i,j) <Dt) if(not in Indoor Environment) thenuse Equation (18) for distance measurement elseuse Equation (19) for distance measurement. endif else Use Equation (21) for distance measurement endif 7. Apply Equations (10)–(17)to estimate initial node position Pi for Ui 8. if(flag is not set) thenposition refinement is required for(each nodejinSi) De(i,j) = | ||Pi−Pj||−Da(i,j)| if (De(i,j) >Dthresh) then goto step 9 endif endfor goto step 11 endif 9. for (each node j in Resi) De(i,j) = │║Pi−Pj║−Di(i,j)│ if (De(i,j) > Dthresh) then remove node j from Resi endif endfor 10. Re-estimate position of Pi using step 6 and 7 11. Det=∑j=1n(Si)|‖Pi−Pj‖−Di(i,j)| 12. if (Det < Prev(Det) then Pi is accepted endif 13. if (Det < Min(Det) then flag is set endif Algorithm EE_DPE () 1. if (flag is set) then return endif 2. Ui sends location request to all its neighboring nodes 3. Requesting nodes receives responses containing location information from B and/or R nodes. 4. Received responses are saved in list Resi for node Ui 5. if (n(Resi) < 3) thenwait forTitime and jump to step 2 else if (n(Resi) ≥ 3) thenselect beacons from Resiand add them to subsetSi if (n(Si) < 3) thenselect References having a certain level of accuracy and append toSi elseset the flag endif endif endif 6. if (Da (i,j) <Dt) if(not in Indoor Environment) thenuse Equation (18) for distance measurement elseuse Equation (19) for distance measurement. endif else Use Equation (21) for distance measurement endif 7. Apply Equations (10)–(17)to estimate initial node position Pi for Ui 8. if(flag is not set) thenposition refinement is required for(each nodejinSi) De(i,j) = | ||Pi−Pj||−Da(i,j)| if (De(i,j) >Dthresh) then goto step 9 endif endfor goto step 11 endif 9. for (each node j in Resi) De(i,j) = │║Pi−Pj║−Di(i,j)│ if (De(i,j) > Dthresh) then remove node j from Resi endif endfor 10. Re-estimate position of Pi using step 6 and 7 11. Det=∑j=1n(Si)|‖Pi−Pj‖−Di(i,j)| 12. if (Det < Prev(Det) then Pi is accepted endif 13. if (Det < Min(Det) then flag is set endif 1. if (flag is set) then return endif 2. Ui sends location request to all its neighboring nodes 3. Requesting nodes receives responses containing location information from B and/or R nodes. 4. Received responses are saved in list Resi for node Ui 5. if (n(Resi) < 3) thenwait forTitime and jump to step 2 else if (n(Resi) ≥ 3) thenselect beacons from Resiand add them to subsetSi if (n(Si) < 3) thenselect References having a certain level of accuracy and append toSi elseset the flag endif endif endif 6. if (Da (i,j) <Dt) if(not in Indoor Environment) thenuse Equation (18) for distance measurement elseuse Equation (19) for distance measurement. endif else Use Equation (21) for distance measurement endif 7. Apply Equations (10)–(17)to estimate initial node position Pi for Ui 8. if(flag is not set) thenposition refinement is required for(each nodejinSi) De(i,j) = | ||Pi−Pj||−Da(i,j)| if (De(i,j) >Dthresh) then goto step 9 endif endfor goto step 11 endif 9. for (each node j in Resi) De(i,j) = │║Pi−Pj║−Di(i,j)│ if (De(i,j) > Dthresh) then remove node j from Resi endif endfor 10. Re-estimate position of Pi using step 6 and 7 11. Det=∑j=1n(Si)|‖Pi−Pj‖−Di(i,j)| 12. if (Det < Prev(Det) then Pi is accepted endif 13. if (Det < Min(Det) then flag is set endif Thus, the flag is set for termination of the algorithm for node i. After adding beacons in Si if the size of Si is less than 3 then it is required to add reference(s) into Si. References are added into Si by accuracy criteria. For beacon nodes, accuracy is not calculated as they are most accurate nodes. The accuracy of all beacon nodes is 100% as they are deployed with preconfigured location information. Proposed algorithm calculates the accuracy of reference node using the newly derived heuristic function. This function helps calculating accuracy with a less faulty value of accuracy. Correct accuracy value given by the heuristic function leads to convergence of localization process in short amount of time. Proposed algorithm offers flexibility in distance measurement method using Dt known as threshold distance. Dt is calculated using Equation (20). If actual distance between unknown node i and reference node j is lesser than Dt, then distance is measured by FSPM using Equation (18) else by TRGM using Equation (19). In the case of the indoor environment, distance is measured by LDM using Equation (21). Unknown node’s position is calculated using a system of Equations from (10) to (17). De(i,j) is the distance measurement error. It is given by the difference of measured distance and calculated distance between the localized node and the reference node. A check is performed for each node j in Si that value of De(i,j) is within limits or not (subject to Dthresh). If the value is not within limits for any of node j in Si, refinement is required. If not so refinement is not required at all and the localized node is tested for acceptability first and termination criteria at last as explained in Steps 11, 12 and 13. Refinement step removes each node j from Resi if having unacceptable distance error i.e. De(i,j) > Dthresh. Removing nodes from Resi is followed by re-estimation of node position using Steps 6 and 7. Steps 11 and 12 explain that if total distance error of the current iteration is lesser than total distance error of the previous iteration, then location estimation is accepted otherwise current location estimate is not accepted. If total distance error of the current iteration is satisfying minimum error criteria, then algorithm sets the flag i.e. reaches to termination state. 3.3. Complexity of algorithm The number of iterations taken by proposed method is not more than 3 and the number of references used is not more than 4 for every node being localized. The average number of iterations and references is 2.36 and 3.34, respectively. Complexity of localization method is given in the following equation: Complexity∝(CLCRS) (22)where CL is the complexity of lateration method (either trilateration or multilateration), and CRS is the complexity of the reference selection method. Complexity of multilateration method (CL) is directly proportional to the number of references (m = n(Si)) being used to localize the node. Thus, complexity of multilateration (CL) is O(m). From the available references (i.e. M = n(Resi)), only few references with better accuracy are selected for localization of the unknown node. To do this, amount of effort depends on the number of available references (M). The complexity (CRS) of the proposed method for reference selection is O(M), where m ≤ M. Thus, complexity of proposed method is given in the following equation: ComplexityP∝O(mM) (23) 4. SIMULATION SETUP AND RESULT ANALYSIS The algorithm proposed above has been implemented and incorporated in well-known and recognized network simulator NS-2 for testing and validation of the proposed method. Parameters used for simulation is listed in the first part of this section. The simulation run generates trace files and these trace files are used to derive results for validation of the proposed method. The second subsection shows validation of the proposed method by comparing it with state of the art methods in [37, 38, 41, 42] known as RBLS, ALWadHA, N_THREE and LOCAL, respectively. Apart from these methods, proposed method is also compared with the naïve iterative method by implementing it in NS-2. 4.1. Simulation parameters Most of the values of simulation parameters used are in accord with methods being compared. Simulation parameters and values are listed in Table 2. Table 2. Parameters for NS-2 simulation. Parameter Value MAC Mac/802_15_4 PHY Phy/802_15_4 BO = SO 3 Simulation time 50 s Simulation setup area 100 m × 100 m Number of nodes 100 Node to beacon ratio 20 Standard deviation 0–0.1 Transmission range 15 m Initial node energy 1 Joule Node deployment method Random Distance measurement method RSSI Propagation model FSPM/TRGM/LDPLMa Parameter Value MAC Mac/802_15_4 PHY Phy/802_15_4 BO = SO 3 Simulation time 50 s Simulation setup area 100 m × 100 m Number of nodes 100 Node to beacon ratio 20 Standard deviation 0–0.1 Transmission range 15 m Initial node energy 1 Joule Node deployment method Random Distance measurement method RSSI Propagation model FSPM/TRGM/LDPLMa aFSPM, free space propagation; TRGM, two ray ground; LDPLM, log distance path loss model. Table 2. Parameters for NS-2 simulation. Parameter Value MAC Mac/802_15_4 PHY Phy/802_15_4 BO = SO 3 Simulation time 50 s Simulation setup area 100 m × 100 m Number of nodes 100 Node to beacon ratio 20 Standard deviation 0–0.1 Transmission range 15 m Initial node energy 1 Joule Node deployment method Random Distance measurement method RSSI Propagation model FSPM/TRGM/LDPLMa Parameter Value MAC Mac/802_15_4 PHY Phy/802_15_4 BO = SO 3 Simulation time 50 s Simulation setup area 100 m × 100 m Number of nodes 100 Node to beacon ratio 20 Standard deviation 0–0.1 Transmission range 15 m Initial node energy 1 Joule Node deployment method Random Distance measurement method RSSI Propagation model FSPM/TRGM/LDPLMa aFSPM, free space propagation; TRGM, two ray ground; LDPLM, log distance path loss model. As explained in Section 1, IEEE 802.15.4 fulfill all the requirement of WSN applications i.e. it provides a specification for low power and low cost Physical and MAC layer protocols. For this reason, it is being used in the sensor network research community. IEEE 802.15.4 Physical and MAC layer protocols are part of NS-2. Beacon Order (BO) and Super Order (SO) value for simulation setup are 3. The proposed method is fused into NS-2 tool. The initial state of simulation setup is 80 unknown nodes (nodes not having its position information) and 20 beacon nodes (nodes having accurate position information of its own). Applying the proposed method on initial state gives final state as an outcome. The outcome of the simulation run is all the unknown nodes are localized at the end of sim in particular amount of time. The time required to localize all unknown nodes is the network setup time. This network setup time varies from 1 s to 50 s for different methods available in the literature. This is the reason the value of simulation time is 50 for the proposed method. According to [43, 44], it is necessary to use at least 16% of beacons in a simulation setup to localize 84% of unknown nodes. To localize all the unknown nodes, we should use more than 16% beacons in simulation setup. Hundred nodes are deployed randomly including 20% (i.e. 20) of beacon nodes. Distance error model has been used with a value of standard deviation from 0 to 0.1. Transmission range of every sensor node in WSN in simulation setup is the same, and it is 15 m. As our objective is just to localize unknown nodes and that would be completed in short amount of time, each node is configured with 1 Joule of energy in the initial state. Distance measurement technique used here is RSSI. As IEEE 802.15.4 supports this feature, it is possible to use RSSI value for distance measurement. The propagation model is being used according to the distance between transmitter and receiver as explained in Section 3.1.2. 4.2. Simulation results After simulation run for 50 s, trace files are obtained. Results have been obtained by analyzing these trace files, and it is as follows. Spectrum of methods under consideration is state of the art methods (i.e. Iterative, ALWadHA and RBLS) and traditional methods (i.e. N_THREE and Local). Method proposed in this paper has been compared with the state of the art methods to validate the claims. Apart from this, the proposed method is also compared with traditional methods for the sake of completion. Location estimation accuracy is the primary goal of the localization method. The goal of the proposed method is to improve location estimation accuracy and energy efficiency using limited number of references. The only traditional method i.e. N_THREE performs better in terms of network setup time, number of iterations and number of references. But reduced this performance comes with the cost of important requirement of any node localization that is location estimation accuracy. N_THREE performs worst in terms of location estimation accuracy. It estimates location with 30% of error in location estimation. Hence, this method is not being used for node localization in an application where accurate location information is the prime requirement. Traditional method like LOCAL selects only three references out of available references. LOCAL method selects three references such that it reduces Cramer–Rao lower bound (CRLB). Minimization of CRLB takes lots of effort for selecting best combination of three nodes from available references. Efforts made to get lower CRLB consume lots of energy and take lot of time to localize the node. Thus, energy consumption and network setup time of LOCAL method is on higher side compared with some state of the art methods as well as proposed method. Computational errors are resultant of the inability of digital computers to represent quantities with precision. In the absence of error model, error in location estimation is all because of computational errors. The graph shown in Fig. 2 compares computational error of traditional as well as state of the art methods with the proposed method. It is indicated by the graph that the proposed method performs better compared with all other methods either it is state of the art methods or it is traditional methods as far as computational error is concerned. As shown in Fig. 2, computational error of proposed method is 0.00062. On the other hand, computational error of ALWadHA, Iterative, RBLS, N_THREE and LOCAL is 0.0009, 0.031, 0.072, 0.011 and 0.006, respectively. Figure 2. View largeDownload slide Simulation time vs. relative computational error. Figure 2. View largeDownload slide Simulation time vs. relative computational error. Location error of node i (denoted by El(i)) is a distance between actual location of node i (denoted by Na(i)) and estimated location of node i (denoted by Ne(i)). Location error is given by Equation (22). Location error is of not that much importance, but relative location error is an indicator of performance. Relative location error is calculated by dividing location error by transmission range of sensor node. Localization error of the full system is given by overall relative error or mean error at given point of time. Mean error is calculated by adding relative errors of all localized nodes and dividing it by number of localized nodes as given in Equation (23), where TR is transmission range in meters and ME is mean error. Performance evaluation of the proposed method by comparing it with other methods is shown in Fig. 3. Figure 3. View largeDownload slide Simulation time vs. average localization error. Figure 3. View largeDownload slide Simulation time vs. average localization error. It is clearly indicated from the results that the proposed method is far better compared with N_THREE, Local, Iterative, RBLS and ALWadHA in terms of mean error. Relative location error of the proposed method is 1.88%. Relative location error for N_THREE, Local, Iterative, RBLS and ALWadHA is 32.2, 19.8, 6.4, 22.4 and 2.38%, respectively. The use of newly derived heuristic for calculation of node location accuracy leads to better performance in this aspect. Flexibility in the use of propagation model also results in accurate distance measurement using RSSI. This also helps reducing mean error: El(i)=‖Na(i)−Ne(i)‖ (24) ME=1n(R)∑i=1n(R)El(i)TR (25) To localize unknown nodes, minimum three reference/beacons are required. At given point of time, the number of references or beacons used to localize unknown nodes is one of the performance measures. An average number of references are derived by summation of references being used by all nodes being localized is divided by the number of nodes being localized. Two methods i.e. N_THREE and LOCAL use minimum and fixed number of references (i.e. 3) for localization algorithm. So, an average number of references used by these methods remain lowest. This comes with the cost of localization error. Proposed method gives better result in terms of an average number of references compared to state of the art methods i.e. ALWadHA, RBLS and Iterative methods. Maximum average number of references for proposed method goes up to 3.34. Maximum average value of references for ALWadHA, RBLS, and Iterative is 4.32, 6.4 and 11.63, respectively. The comparison is shown in Fig. 4. Figure 4. View largeDownload slide Simulation time vs. average number of references. Figure 4. View largeDownload slide Simulation time vs. average number of references. In terms of an average number of iterations of algorithm required to localize every unknown node, the proposed method performs better compared with ALWadHA, RBLS and Iterative methods as shown in Fig. 5. As N_THREE and LOCAL methods use single (i.e. 1) iteration to localize unknown nodes that does not achieve the goal of localization i.e. accuracy. The proposed method uses on average 2.36 iterations at maximum while ALWadHA, RBLS and Iterative methods take 5.6, 4.7 and 28.9 iterations, respectively. Thus, in terms of iterations, the proposed method outperforms state of the art methods i.e. ALWadHA, RBLS, and Iterative methods. Less number of iterations leads to the lesser time required to set up the whole network. The method with lesser iterations requires lesser computational operations. Lesser iterations also reduce cumulative computational and location errors. With lesser iterations, energy consumption is also lesser. Figure 5. View largeDownload slide Simulation time vs. average number of iterations. Figure 5. View largeDownload slide Simulation time vs. average number of iterations. At given point of the time, average energy consumption for a node is given by total energy consumed by all nodes divided by a total number of nodes. Regarding energy consumption, proposed method outperforms LOCAL, ALWadHA, RBLS and Iterative methods as shown in Fig. 6. Energy consumed by LOCAL, ALWadHA and RBLS is almost two times compared with the proposed method. Energy consumed Iterative method is almost four times higher compared with the proposed method. Summary of all the results is given in Table 3. Table 3. Result summary. N_THREE LOCAL Iterative RBLS ALWadHA Proposed Figure Computational error (%) 0.011 0.006 0.031 0.072 0.0009 0.00062 2 Relative location error (%) 32.2 19.8 6.4 22.4 2.38 1.88 3 Average no. of references 3 3 11.63 6.4 4.32 3.34 4 Average no. of iterations 1 1 28.9 4.7 5.6 2.36 5 Average energy consumption (J) 0.045 0.16 0.329 0.145 0.16 0.08 6 Network setup time (s) 22.2 38 >40 26 312 23.8 7 N_THREE LOCAL Iterative RBLS ALWadHA Proposed Figure Computational error (%) 0.011 0.006 0.031 0.072 0.0009 0.00062 2 Relative location error (%) 32.2 19.8 6.4 22.4 2.38 1.88 3 Average no. of references 3 3 11.63 6.4 4.32 3.34 4 Average no. of iterations 1 1 28.9 4.7 5.6 2.36 5 Average energy consumption (J) 0.045 0.16 0.329 0.145 0.16 0.08 6 Network setup time (s) 22.2 38 >40 26 312 23.8 7 Table 3. Result summary. N_THREE LOCAL Iterative RBLS ALWadHA Proposed Figure Computational error (%) 0.011 0.006 0.031 0.072 0.0009 0.00062 2 Relative location error (%) 32.2 19.8 6.4 22.4 2.38 1.88 3 Average no. of references 3 3 11.63 6.4 4.32 3.34 4 Average no. of iterations 1 1 28.9 4.7 5.6 2.36 5 Average energy consumption (J) 0.045 0.16 0.329 0.145 0.16 0.08 6 Network setup time (s) 22.2 38 >40 26 312 23.8 7 N_THREE LOCAL Iterative RBLS ALWadHA Proposed Figure Computational error (%) 0.011 0.006 0.031 0.072 0.0009 0.00062 2 Relative location error (%) 32.2 19.8 6.4 22.4 2.38 1.88 3 Average no. of references 3 3 11.63 6.4 4.32 3.34 4 Average no. of iterations 1 1 28.9 4.7 5.6 2.36 5 Average energy consumption (J) 0.045 0.16 0.329 0.145 0.16 0.08 6 Network setup time (s) 22.2 38 >40 26 312 23.8 7 Figure 6. View largeDownload slide Simulation time vs. average energy consumption. Figure 6. View largeDownload slide Simulation time vs. average energy consumption. The time at all the nodes have final location information is called network setup time. At this point of time, an algorithm stops iterating from current iteration to next iteration. No further refinement in nodes’ location information takes place after network setup time. Figure 7 compares network setup time of proposed method with other methods. Every node in the proposed method gets its location information on or before 23.8 s. Iterative method iterated up to complete simulation time as there are no stopping criteria. ALWadHA algorithm goes for refinement 312 s if we set simulation time of 500 s. Other algorithms i.e. Local, RBLS and N_THREE have network setup time of 38, 26 and 22.2 s, respectively. Figure 7 depicts the comparison in terms of network setup time. Network set up time of ALWadHA and Iterative methods is far beyond 40 s. Figure 7. View largeDownload slide Network setup time comparison. Figure 7. View largeDownload slide Network setup time comparison. 5. CONCLUSION It is not feasible to deploy sensor nodes with preconfigured location information. Most of the WSN applications need to know location information of sensor nodes. Localization algorithm estimates unknown nodes position information. As range free algorithms suffer in terms of accuracy very heavily, range-based algorithms are under focus. Angulation, ToA, and TDoA require one or more from additional hardware, high processing capabilities or clock synchronization. Using any one of these may increase cost or energy consumption of the system. Thus, the proposed method is based on Lateration method as it does not require additional hardware, high processing capabilities or clock synchronization. Lateration method estimates node position using beacon/reference nodes and distance measurement. According to the literature, lateration-based methods offer a less accurate estimate of unknown node’s location because location information of reference node or distance measurement has an error. The method proposed in this paper uses references having better location information i.e. having least location error. The use of better references gives highly delimited node position estimation. Proposed heuristic function calculated location error of each reference node with less deviation in it. Due to lesser deviation in location error, accumulation of deviation is lesser over number of iterations. The proposed method also reaches to the final state in the lesser number of iterations using the newly proposed heuristic function. Reduced number of iterations helps reducing network setup time. It also reduces computational steps to reach the final state of the localization system and this way with reduced computational operations it increases energy efficiency. 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The Computer Journal – Oxford University Press

**Published: ** Nov 9, 2017

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