Impact of static trajectories on localization in ... - Semantic Scholar

Wireless Netw DOI 10.1007/s11276-014-0821-z

Impact of static trajectories on localization in wireless sensor networks Javad Rezazadeh • Marjan Moradi • Abdul Samad Ismail • Eryk Dutkiewicz

Ó Springer Science+Business Media New York 2014

Abstract A Wireless Sensor Network (WSN) consists of many sensors that communicate wirelessly to monitor a physical region. Location information is critical essential and indispensable for many applications of WSNs. A promising solution for localizing statically deployed sensors is to benefit from mobile location-aware nodes called beacons. However, the essential problem is to find the optimum path that the mobile beacon should travel in order to improve localization accuracy, time and success as well as energy efficiency. In this paper, we evaluate the performance of five mobile beacon trajectories; Random Way Point, Scan, Hilbert, Circles and Localization algorithm with a Mobile Anchor node based on Trilateration (LMAT) based on three different localization techniques such as Weighted Centroid Localization and trilateration with time priority and accuracy priority. This evaluation aims to find effective and essential properties that the trajectory should have. Our simulations show that a random movement cannot guarantee the performance of localization. The results also show the efficiency of LMAT regarding accuracy, success and collinearity while the Hilbert space filling curve has lower energy consumption. Circles path

J. Rezazadeh (&) M. Moradi A. S. Ismail Department of Computer Science, Faculty of Computing, Universiti Teknologi Malaysia (UTM), Johor, Malaysia e-mail: [email protected] M. Moradi e-mail: [email protected] A. S. Ismail e-mail: [email protected] E. Dutkiewicz Macquarie University, Sydney, NSW, Australia e-mail: [email protected]

planning can help to localize unknown sensors faster than others at the expense of lower localization precision. Keywords

Localization Trajectory Mobile beacon

1 Introduction Wireless sensor networks (WSNs) are promised as the enabling technology for exploring and detecting a wide range of applications in military, health, environment monitoring, household and other commercial areas [2, 56]. The majority of the applications require that the measured value be tagged with time and location information. Hence, the measured data are meaningless without knowing the location from where the data are obtained [25]. The process of determining physical coordinates of a sensor node or the spatial relationships among objects is known as localization [34]. Different services provided by WSNs such as routing [1, 63] and data collection [59, 61], coverage [33], the concept of internet of things [53], and security [41] are matured enough, however localization as a critical service still requires further emphasis. Global positioning system (GPS) [21] is a commonly used and precise method for sensor localization. Unfortunately, the GPS solution is neither cost-effective nor energy-efficient [28]. Additionally, the deployment-ability of sensor nodes which are equipped with GPS may be reduced due to the increased size. Finally, these GPS equipped sensors have limited applicability because GPS works only in an open field [35]. Localization algorithms can cope with the problem where they are able to estimate the location of sensors by using the knowledge of the absolute positions of a few sensors. Generally, these small proportions of sensor nodes with known location

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information are called beacons, while their locations can be obtained using either GPS or installing beacons at points with known positions. Ordinary sensors which urgently need to be localized are called unknown nodes. On the other hand, WSNs are usually applied for missions where human operation is impossible. So, installing beacon nodes in a predetermined location is often infeasible. This means that beacon nodes equipped with GPS receivers must be employed for localization. Another observation is that the precision of the localization increases with the number of beacons [8, 49, 50], but they increase the energy consumption and the cost of the WSN. The large number of required beacons, their costs and their high power consumption motivated the use of mobile beacon assisted localization instead of having several static beacons. Comparatively, localization through the use of a mobile beacon is inherently more accurate and cost-effective than localization using static beacons [29, 54, 55]. The mobile beacon travels around the region of interest where unknown sensor nodes are deployed and transmits the beacon signal that includes its location information [38]. Taking advantages of such a mobile beacon in location estimation is of importance. Since mobile beacon-assisted localization algorithms offer significant practical benefits, a fundamental issue is finding an optimum path for mobile beacon trajectory to take advantage of such an architecture. In fact, the mobile beacon trajectory has a direct impact on the performance of the localization approach in terms of localization accuracy, localization success and the time required for localization as well the energy consumption. Hence, considerable research attention has been attracted toward determining optimum trajectories for mobile beacon assisted localization. To well reflect the efficiency of the mobile beacon trajectory on the localization approaches, this paper is motivated to evaluate and compare the performance of some existing path schemes. These schemes are Scan [27], Hilbert space filling curve [4, 27], Circles [24] and Localization algorithm with a Mobile Anchor node based on Trilateration (LMAT) [16]. They are referred to as static path planning where the mobile beacon follows a deterministic path. We also compare all the above static path planning mechanisms with a random trajectory (Random Way Point (RWP) [9]) to confirm the efficiency of the predefined path as opposed to a random movement. The main contribution of this paper is evaluating and comparing four existing static trajectories for mobile beacon assisted localization with a random trajectory to investigate the efficiency of a deterministic path planning scheme in terms of localization accuracy and localization success. Moreover, the trajectories are analyzed based on some critical and novel metrics such as the ineffective position rate, localization time and energy consumption per

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node localization. Since the evaluation is based on the simulation results, we investigate a reliable and accurate wireless channel model to provide realistic results for the evaluation of all the trajectories. To the best of our knowledge, this paper is the first study on evaluation of static path planning mechanisms considering a reliable channel model and introducing some novel critical evaluation metrics. The rest of the paper is organized as follows: Sect. 2 summarizes the state-of-the-art in mobile beacon trajectories and some highlighted localization schemes in mobile beacon, static sensors domain. In Sect. 3 we introduce the Random Waypoint, Scan, Hilbert, Circles and LMAT trajectories. We discuss the simulation results in Sect. 4 followed by the conclusions in Sect. 5.

2 Related work There has been a large body of research on localization for wireless sensor networks. Most existing localization schemes for WSNs are classified based on a key classification into two main groups: range-based or range-free. Range-free techniques only use connectivity information between sensors and beacons. In [8, 20, 37, 47] some rangefree methods have been presented. Range-based techniques use distance or angle estimates for localization, such as the methods proposed in [6, 19, 36, 42]. Although it is a comprehensive categorization of localization algorithms, it is not distinct enough for further research in the presence of mobile beacon or mobile sensor nodes. In a wide range of applications, a fully static network is not realistic [48]. One important factor is to let localization algorithms benefit from node mobility. To capture this possibility, we reclassify localization methods with respect to the mobility state of beacons and sensor nodes into four groups: (1) static beacon and static nodes such as the methods proposed in [19, 39, 40, 51], (2) static beacons and mobile nodes such as the schemes in [8, 45, 52], (3) mobile beacons and static nodes proposed in [11, 14, 54, 55], and (4) mobile beacons and mobile nodes like the methods in [3, 22, 25, 58]. This paper focuses on the category of mobile beacons with static sensor nodes, because this group of localization technique promises a wide spectrum of application scenarios. An example can be a military application or a monitoring task like fire detection, where sensor nodes are dropped from a plane on land, and transmitters are attached to soldiers or animals acting as mobile beacons. Localization studies with mobile beacons generally focus on two major problems, either proposing an efficient localization algorithm or developing an optimum mobile beacon movement strategy. In the rest of this section, we briefly survey representative methods for both issues.

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Fig. 1 Mobile beacon trajectories overview

2.1 Mobile beacon, static nodes localization algorithms Reducing the number of expensive GPS-equipped sensors as well as responding to essential applications, has led to promise localization techniques in order to localize a set of static sensors relying on only one mobile beacon. A key paper presented in [54], localized static nodes based on the RSSI of a mobile beacon and Bayesian inference. The paper employed statistical principles for processing the received information from the mobile beacon, instead of imposing geometrical constraints. The major drawback of the scheme is its relatively high computation complexity which increases energy consumption. The method proposed by Galstyan et al. [14], estimated the location of static unknown nodes based on geometrical constraints. A possible area was delimited to minimize the uncertainty in the localization results. A mobile assisted localization (MAL) method was proposed in [43] where a mobile node is responsible for collecting the necessary pair wise distances from node to node. The proposed method is not energy efficient especially for large-scale networks while the mobile node is responsible for discovering all unknown nodes, one by one. Ssu et al. [55] proposed a prior method for localization of static sensor nodes with four mobile beacon points. The authors in [55] developed a range-free localization mechanism using the geometry conjecture and can achieve higher accuracy than other range-free methods. Obstacles in the sensing field are tolerated, although it causes radio irregularity. The major drawback of this mechanism is its long execution time and high beacon overhead. In order to further improve localization accuracy in Ssu’s scheme, Lee et al, also proposed another geometric constraint-based localization method in [29]. Only one mobile beacon moves around the network field. The main drawback of this scheme is the increasing location error when enlarging the communication range.

In [11], a cooperative localization algorithm has been proposed. A novel convex position estimation method has been developed for the case the static sensor nodes are between the maximum transmission radius and half of that radius. Authors have discussed that it is possible there is no communication between two nodes although their relative distance is smaller than their ideal transmission radius. 2.2 Mobile beacon trajectories The mobile beacon trajectories can be classified into two classes based on the considerations to the real distribution of unknown sensors: static or dynamic trajectory. In the static path planning, the mobile beacon sticks to the predefined and deterministic trajectory. On the contrary, the dynamic or real time trajectory considers the real distribution of sensor nodes in the sensing field [38]. Topology control [31] may be addresses as a critical issue of such trajectories to well connected the pair of sensor and beacon. Both classes are investigated in this section. Figure 1 denotes an overview on the proposed trajectories. 2.2.1 Static path planning Localization schemes can take advantage of mobility to improve the accuracy and coverage when they rely on mobile beacon with an optimum trajectory. However, how to find the optimal path for the mobile beacon is the basic problem. Some fundamental properties of an optimum beacon path have been introduced in [54]. The authors made some observations, such as traveling along a shortest path whilst fully covering the region of interest. Moreover, the mobile beacon should also pass closely to as many unknown nodes as possible and provide at least three noncollinear beacon positions (messages transmitted by the mobile beacon where at least one of them is not on a straight line). Static mobile beacon path planning schemes

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are addressed here where they use deterministic path without the reference to the actual distribution of the unknown nodes. Here, a brief review is presented on the existing static mobile beacon trajectories for localization. Scan, Double Scan, and Hilbert space filling curve are three well-known trajectories proposed in [27]. All the path types can successfully achieve higher precision location estimation than RWP [9, 54]. However, their accuracy directly depends on the resolution of the trajectory (the distance between two successive beacon positions). CIRCLES and S-CURVES were proposed in [24] to reduce the amount of straight lines and mitigate the collinearity problem of path planning methods. Although they produce the shortest path length amongst the other methods, CIRCLES leaves the four corners, uncovered. A spiral trajectory for mobile beacon was proposed in [23]. The trajectory has trivial differences with CIRCLES and effectively solves the collinear problem as well the localization accuracy. However, the trajectory suffers from long path lengths and uncovered areas near the border of the network field. An optimal movement scheduling method has been proposed in [11] for mobile beacon. The main concerns of the proposed path are to achieve the shortest path length and fully localize all the sensors even with error no greater than . Hence, a hexagonal tiling of the entire region has been considered and the mobile beacon moves while it simply connects the centre of each hexagon. The movement trajectory cannot count as an optimum path due to the collinear positions provided by the straight lines. However, the trajectory considers the existence of obstacles in the region of interest. Han et al. [17] introduced a path planning scheme for localization based on trilateration. The mobile beacon moves according to an equilateral triangle to broadcast its current position. The path type successfully copes with the collinear beacons problem but it cannot maintain the trajectory through the whole network field. Moreover, the path length travelled by the mobile beacon is long. 2.2.2 Dynamic path planning In real-time or dynamic path planning schemes, each sensor node gathers its neighborhood information based on the message exchange and then provides it to the mobile beacon. Indeed, the goal is to develop a beacon mobility scheduling algorithm, by which mobile beacon is able to dynamically determine its own trajectory. The major drawback of real time path planning schemes in localization is the high numbers of message exchanges and high energy consumption. Authors in [30] have studied the dynamic path planning of the mobile beacon using graph theory. WSN is regarded

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as a connected undirected graph and the path planning problem is translated into having a Spanning Tree and a traversing graph. The paper has considered the BreadthFirst (BRF) and Backtracking Greedy (BTG) algorithms. Breadth-First (BRF) and Backtracking Greedy (BTG) algorithms have been presented for Spanning Tree. Wang et al. [57] chose the shortest path traversing as the trajectory of the mobile beacon. An adaptive path planning scheme has been proposed in [26] which considered the length of movement path and number of beacon messages for its energy efficiency. The path comprises a regular triangle with the length of the communication range. Unlike static path planning schemes, the mobile beacon determines its next destination adaptively while it analyzes the request messages received from unlocalized sensors. An anchor guiding mechanism has been developed in [10] to improve the location inaccuracies of all the sensors and minimize the length travelled by the mobile beacon. The statically deployed sensors have estimated their locations using previous range-free localization algorithms with different location inaccuracies. The size of the estimative region guides the mobile beacon to construct an efficient path. A novel DeteRministic dynamic bEAcon Mobility Scheduling (DREAMS) has been presented in [32] to determine the best beacon trajectory. In this paper, the trajectory has been performed dynamically as the track of Depth-First Traversal (DFT) of the network graph, thus in a deterministic manner.

3 Static path planning of mobile beacon for localization 3.1 Random way point The RWP mobility model [9] is a widely used model because of its simplicity. The mobile beacon selects a random destination and travels toward the newly chosen location. Firstly, authors in [55] have employed the RWP for mobile beacon movement to help localization of static nodes. In each destination, the mobile beacon transmits beacon position message. As it is clear in Fig. 2(a) the main drawback of the RWP is its non-uniform coverage of the field. It is likely that each point is visited several times by the mobile beacon while some different points are never visited. Formulating the path length traversed by the mobile beacon in RWP is impossible where the movement would be terminated after a specific time or predefined path length. 3.2 SCAN In [27], the authors have presented a basic and simple static path planning scheme named SCAN which uniformly

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Fig. 3 Hilbert mobile beacon trajectory. a Level-1. b Level-2. c Hilbert space filling curve

covers the network field. It is expected that the offering uniformity keeps the localization error low and ensures that all unknown sensors are able to receive beacons. As shown by Fig. 2(b), in SCAN, the network field is divided into n n sub-squares and the mobile beacon traverses the network area along one dimension such as the Y axis while connecting the centers of the sub-squares using straight lines. It is apparent that the straight lines create collinear beacons (messages transmitted when the beacon moves on a straight line) and prevent highly precise location estimation. Moreover, the distance between two successive lines parallel to the Y axis, which is defined as resolution ðdÞ, should be small to make sure that all the sensors will be able to receive beacon messages. In SCAN, the resolution should be not more than d ¼ 2r where r denotes the communication range. For a higher resolution, many nodes will receive beacons only from one line segment and one direction, which is one of the sources of localization error. Since the mobile beacon divides the network size of S S by the resolution d. The total distance traversed in SCAN trajectory is calculated by:

lengthðScanÞ ¼

S2 2d d

ð1Þ

3.3 CIRCLES In [24], the authors consider a deterministic path planning for mobile beacon assisted localization. Since the straight lines invariably introduce collinearity, authors propose a mobile beacon trajectory to reduce the amount of straight lines on the beacon path. Figure 2(c) depicts the CIRCLES path planning scheme. CIRCLES consists of sequence of concentric circles centered with the deployment area. Since the resolution d is defined as half of the radius of the innermost circle, the mobile beacon moves along the static deterministic trajectory to periodically transmits the beacon positions in an equivalent distances. To pass over the inner circle, the radius is sequentially increased by d at each outer circle. It successfully tackles the collinearity problem through the interior circles which avoids the straight lines. However, the collinear beacon positions problem arises with increasing the radius. So, the

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3.4 Hilbert In [27] the authors study different trajectories for the mobile beacon including the Hilbert space filling curve. However, the Hilbert approach has been investigated by literature in [4, 5]. In [4] the Hilbert curve has been proposed to tackle both the localization and coverage tasks at once, while the key motivation of studying the Hilbert curve in [27] is to solve the collinearity problem of localization where such a curve makes many turns compared with SCAN. This implies that if the mobile beacon moves on the Hilbert curve, the sensors will have the chance to receive noncollinear beacons and obtain a good estimate for their positions. The basic curve of the Hilbert trajectory is shown in Fig. 3(a) for a 2 2 grid that is also known as level 1. A level-l Hilbert curve divides the field into 4l square cells and connects the centers of those cells in a linear ordering of points. To derive a curve of level-l each square cell of the basic curve is replaced by the curve of level-l 1 which may be appropriately rotated and/or reflected to fit the new curve. For further clarification, Fig. 3(b) depicts level-2 of Hilbert space filling curve. Intuitively, a higher level leads to better localization precision, but leads to a longer path travelled by the mobile beacon. The trajectory length of the Hilbert curve approach is calculated by: lengthðHilbertÞ

S2 ¼ d ¼ ð4l 1Þd d

: Lmat Trajectory

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Fig. 4 LMAT mobile beacon trajectory

periodically transmits the beacon messages including the beacon position information. LMAT trajectory is depicted in Fig. 4. The unknown node is able to estimate its coordinates using the trilateration method where the distance between an unknown sensor and the mobile beacon is measured using RSSI. The aim of the LMAT trajectory is to design the optimal traveling trajectory of mobile beacon node assisted localization. To achieve the aim, the LMAT algorithm is required to consider two essential requirements. These two requirements are discussed as follows: 3.5.1 Minimizing the localization error

ð3Þ

where d denotes the resolution of the Hilbert curve defined as the side of a square cell and l shows the level of the curve. On the other hand, the mobile beacon will never move on the border of the network field. So, the unknown sensors near the borders will possibly estimate their positions with lower precision. 3.5 LMAT The equilateral triangle configuration idea has been initially proposed in [15] for the beacon nodes placement to help localize the mobile sensors. Based on the literature [15], the LMAT algorithm has been presented in [16] where the authors target optimal beacon positions for the mobile beacon node to improve localization accuracy and coverage. LMAT assumes that the mobile beacon moves according to an equilateral triangle trajectory and

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CIRCLES trajectory solves neither accuracy nor coverage where it could not cover the four corners of the field, effectively. Dividing the network size into n n subsquares, the total path length traveled by CIRCLES trajectory can be represented as a function of d and n as follows: n2 pd n ð2Þ D¼ þ 1 d 4 2

As shown in Fig. 5, the measurement error exists in the process of calculating the coordination of the unknown node where three circles form a small region instead of an exact point. The size of the small region can be regarded as the size of the localization error. Then, with minimizing the size of the region the localization error will be decreased. Assume ðx0 ; y0 Þ denotes the coordinates of the unknown node p and three distinct beacon positions pi ¼ ðxi ; yi Þi ¼ 1; 2; 3. A circle is formed inside the small region where the measurement error e [ 0. It is denoted by: Sp ¼ fðx; yÞjðx x0 Þ2 þ ðy y0 Þ2 ¼ e2 g

ð4Þ

Let lp;pi denotes the straight line passing through both p and pi where the line intersects Sp at two points qi;j j ¼ 1; 2. The intersection of the line passing through qi;j and tangent to Sp form the lines to map Sp into a hexagonal region. To minimize the size of the region, an optimum configuration of beacon positions is required. As can be seen in Fig. 5,

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Fig. 5 Analysis of localization error in LMAT Fig. 6 Analysis of optimal coverage in LMAT

the optimum configuration is achieved when pd 1 p2 ¼ p d p ¼ p p ¼ . pd 2 3 3 1 3 3.5.2 Maximizing localization coverage In order to mitigate the coverage problem during the localization process of the unknown nodes, the LMAT algorithm determines the relationship between the resolution (the distance of consecutive beacon positions) and the communication radius of the mobile beacon node. In other words, since the optimum configuration is provided by the equilateral triangle trajectory the second problem is finding the side length of the equilateral triangle to achieve the largest coverage area without a hole. As can be seen in Fig. 6, the overlap region of the three mobile beacon positions needs to be minimized in order to maximize the coverage area. It can also be deduced from Fig. 6 that if the side pffiffiffi length of the equilateral triangle is set to d ¼ 3r then the area coverage without a hole can be achieved. Let d and r denote the resolution and the communication radius of mobile beacon, respectively. O and H represent the center of gravity and the midpoint B1 B2 . So: pffiffiffi 3 d OB3 ¼ 3 pffiffiffi 3 1 OH ¼ OB3 ¼ d 2 6 ð5Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi d 2 2 HE ¼ ðB1 EÞ ðB1 HÞ ¼ r 2 4 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 3 d2 OE ¼ HE OH ¼ r 2 d 4 6

pffiffi On the other hand, in MDEF; OE ¼ ð 33ÞDE. Consequently: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3 2 1 DE ¼ 3r 2 d d 4 2 ð6Þ pffiffiffi 3 DE2 AreaMDEF ¼ 4

AreaETF ¼ ðAreaofSectorAEFÞ ðAreaMAEFÞ DE DE pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4r 2 DE2 ¼ r 2 arcsin 2r 4

ð7Þ

We can deduce from Fig. 6 that SDEF ¼ ðArea 4 DEFÞþ ð3AreaETFÞ. From Eqs. 6 and 7 we derive: pffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 1 DE ð 3r 2 d2 dÞ2 þ 3r 2 arcsin SDEF ¼ 4 2 2r 4 ð8Þ 3DE pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 4r 2 DE2 4 where SDEF denotes the overlapping area of the three circles centered by the beacon positions. Thus when pffiffiffi oSDEF =od ¼ 0, we can obtain d ¼ 3r. The trajectory length of LMAT in the network of size S S is calculated by: pffiffiffi 2 S lengthðLMATÞ ¼ pffiffiffi S þ ðS þ 3dÞ ð9Þ d 3 4 Performance evaluation In this section, we first describe different localization techniques which are considered in the performance evaluation. Then, a simulation setup with related parameters is

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described. Moreover, the employed wireless channel is discussed in details. We also generate a variety of results through simulations and discuss them in this section. 4.1 Localization techniques A fundamental issue in studying the effectiveness of mobile beacon trajectories is the employed localization technique. In some localization methods all received location information by the unknown nodes is contributed in the localization process such as the methods proposed in [8, 54], while other techniques rely on selected beacon messages for location estimations like the techniques in [55]. Since the efficiency of path planning is influenced by different localization techniques, we consider both types of position calculation. Moreover, since single hop networks have higher performance than multi-hop networks [13], all results in this paper consider single-hop localization techniques. Three different position estimation methods are utilized including Weighted Centroid Localization, Time-Priority Trilateration and Accuracy-Priority Trilateration. 4.1.1 Weighted centroid localization (WCL)

After replacing wij by RSSij the final equation is formed: P Nr

j¼1 ðRSSij :bj ðx; yÞÞ PNr j¼1 RSSij

ð11Þ

4.1.2 Time-priority trilateration (TPT) Trilateration, as a comprehensive and most common method for deriving position of unknown nodes is considered in this section. Once the number of the beacon messages to start the localization process is large enough, an unknown node calculates its corresponding distance with received beacons and estimates its position via trilateration. So, for computing the position of si ðxi ; yi Þ in a 2-D space, the following system of equations must be solved:

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ð12Þ

We compute the distance from beacons, distðbj ; si Þ, using the RSS technique. Time-Priority Trilateration (TPT) localizes unknown sensors with employing three earlier received messages. The main objective of this approach is estimation of the sensors’ location within the shortest possible time. 4.1.3 Accuracy-priority trilateration (APT) Since higher precision of estimated location is desired for all localization methods, we evaluate all the findings and results using the Accuracy-Priority Trilateration (APT) technique. It is similar to the TPT approach in the general concept and calculation, but it derives the location of the unknown sensors relying on the three nearest received messages from the mobile beacon in Eq. 12. It provides the chance to estimate the location with higher accuracy while the three strongest RSS values are utilized in trilateration. 4.2 Simulation setup and wireless channel

Unknown sensors, si calculate their own positions, pðsi Þ based on averaging the coordinates of all Nr received beacons. To investigate the impact of different received coordinates bj ðx; yÞ, the WCL method proposed in [7], defines a weight function wij which depends on the RSS value of the mobile beacon at different positions. It is formulated as follows: P Nr j¼1 ðwij :bj ðx; yÞÞ pðsi Þ ¼ ð10Þ PNr j¼1 wij

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qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 > ; s Þ ¼ ðx1 xi Þ2 þ ðy1 yi Þ2 distðb > 1 i > > < qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi distðb2 ; si Þ ¼ ðx2 xi Þ2 þ ðy2 yi Þ2 > > qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > : distðb3 ; si Þ ¼ ðx3 xi Þ2 þ ðy3 yi Þ2

4.2.1 The wireless channel All the mentioned position estimation methods are employed to evaluate the performance of the described trajectories in Sect. 3 under different and essential evaluation metrics. Fundamental performance limitations must be well understood when establishing a network protocol to ensure that the protocol is appropriate for a particular network design choice [60]. In order to perform a reliable evaluation, a realistic wireless link model is important. Hence, in this section we consider the channel model, modulation, and encoding scheme to extract the relationship between the transmission power and packet reception rate. Since the signal strength decays due to wireless propagation, path loss and bit error rate must be modeled for analyzing the physical layer [62]. Let Prr denote the packet reception rate which means the probability of successfully receiving a packet. The nature of Prr is a Bernoulli random variable which takes the value 1 if the packet is received and 0 for failure. It is given by: Prr ¼ ð1 Pbe Þ8f M

ð13Þ

where f ¼ 20byte is the size of the frame based on the TinyOS implementation after being encoded (the packet consists of preamble, network payload and CRC). The Manchester encoding scheme is employed, so M ¼ 2. Pbe

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is the probability of bit error which depends on the modulation scheme. Here, we selected non-coherent FSK modulation which is used in MICA2 motes and formulated by [62]:

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where BN is the noise bandwidth and R is the data rate in bits. MICA2s use the Chipcon CC1000 radio [12] which R ¼ 19:2 kbps and BN ¼ 30 kHz. The signal to noise ratio ðSNRÞ at the receiver is calculated by: dB SNRdB ¼ PdB rec Pn

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dB where PdB L and Ptrans are the power loss and transmitting power, respectively. To model the shadowing path loss effect, a log-normal model [44], as the most common model is utilized which gives:

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where F ¼ 13 dB is the noise figure, k the Boltzmann’s constant. T0 ¼ 27 C the ambient temperature and BN is the equivalent bandwidth. The average noise floor is approximately -105 dBm which has a 10 dBm difference with the analytically computed value. On the other hand, Prec is given as: PdB rec

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Prec shows the reception power and Pn defines noise floor. Pn depends on both, the radio and the environment [44]. It is given by: Pn ¼ ðF þ 1ÞkT0 BN

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Fig. 7 Propagation model, r ¼ 4; PL ðd0 Þ ¼ 55dB; c ¼ 3:3; Ptrans ¼ 0dBm

Table 1 Simulation parameters Parameter

Value

Network size

100m 100m

Unknown sensors number

250

Mobile beacon number

1

Beacon speed (m/s)

0.5, 1, 2, 3, 4

Rc d

1 3 4 3 7 5 2 ; 4 ; 1; 3 ; 2 ; 4 ; 2; 2 ; 3

Path loss ðcÞ

3.3

Standard deviation ðrÞ

2, 4, 6, 8

PL ðd0 Þ

55 dB

d0

1

Transmission power ðPt Þ

20dBm\Pt \10dBm

Simulation run

50

The simulation results and the resulting analysis are discussed next. 4.3.1 Accuracy

4.2.2 Parameter setting The performance of the proposed path planning mechanism was evaluated by a series of simulations using MATLAB. We assume a random deployment of static sensors and a single mobile beacon moving around them. The other parameters are listed in Table 1.

4.3 Results and evaluations The performance of the various path planning mechanisms was evaluated using some essential metrics and variables.

To analyze the accuracy of the estimated locations, we consider the average localization error ratio. Localization error of unknown sensor si is calculated by measuring the distance between the real location of the node ðxi ; yi Þ and its estimated location ðxei ; yei Þ [46]. Hence, the average localization error, Le , for the total numbers of n unknown sensors is given as: ! n X Le ¼ errorðiÞ n i¼1 ð19Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 errorðiÞ ¼ ðxei xi Þ þ ðyei yi Þ

123

Wireless Netw 1.8

0.6 0.5 0.4 0.3 0.2 0.1 0 1/2

1

0.14

3/2

2

5/2

3

RWP

RWP HILBERT SCAN CIRCLES LMAT

1.6 1.4

Localization Error Ratio (R)




0.7

1.2 1 0.8 0.6 0.4 0.2 0 1/2

1

3/2

2

5/2

3

HILBERT

SCAN

CIRCLES

LMAT

0.12 0.1 0.08 0.06 0.04 0.02 0 1/2

1

3/2

2

5/2

3

The Ratio of Range to Resolution (R/d)



(a)

(b)

(c)

Fig. 8 Variation of the localization error versus different ratio of Rc =d. a WCL technique. b TPT technique. c APT technique

Localization error is divided by communication range Rc to get the average localization error ratio. We can consider another aspect of localization accuracy to effectively evaluate the performance of localization. The standard deviation of the localization error, ðstdÞ, is a measure of how spread out the average localization error is. It is defined by the following equation: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn ð20Þ std ¼ ðerrorðiÞ Le Þ2 i¼1 n A low value of std indicates that the error estimated for the location of the nodes tends to be very close to the average localization error. We evaluate the accuracy of the trajectories under two different variables, namely the ratio of communication range to resolution (Rc =d) and the standard deviation of noise (r). The ratio of communication range to resolution The localization errors are shown in Fig. 8. Regardless of what localization technique is employed, LMAT outperforms the other trajectories. As we expected, the higher precision is achieved by the APT localization approach for all the path planning algorithms since the method filters the received beacons by the shortest distance. We consider six different ratios of communication range to resolution for each trajectory. However, the provided accuracy by each trajectory in the same value of Rc =d is different for various localization techniques. For example, LMAT, as the most accurate trajectory in this set of simulation results, reaches its higher precision in Rdc ¼ 32 ; 12 ; 52 for WCL, TPT and APT localization techniques, respectively. Figure 8(a) shows that the error reaches the lower value for Scan, Circles and LMAT when Rc =d ¼ 3=2. The Hilbert curve technique estimates the accurate position when the ratio of communications range to resolution is around 2. To generalize, all the trajectories give smaller errors with the communication range approximately two times larger than the resolution. This behavior is interpreted by the fact that each node receives high signal strength beacons.

123

In Fig. 8(b), we observe that the average localization error increases with enlarging the communication range. The trend is observed since three earlier messages required for localization can be collected from farther beacon positions. Hence, it is clear that a higher precision is achieved when the communication range is smaller than the resolution (Rc =d ¼ 12). We also observe that LMAT, Hilbert and Scan have almost the same localization errors and they outperform Circles and RWP. Figure 8(c) shows that the increment of the ratio of Rc =d did not have a significant impact on the localization error. This can be explained by the fact that the three closest beacons will be selected for localization by APT. So, increasing the communication range does not have an effect on beacon selection. Standard deviation of noise In order to provide more reliable results and evaluations, we consider the impact of different values of the standard deviation of noise, ðrÞ, on the average localization error of the trajectories. Figure 9 depicts the results for the localization techniques where Rc =d ¼ 53. It is readily observed that the accuracy decreases as the standard deviation of noise is increased for all the path planning mechanisms. However, APT in the localization techniques and LMAT among the path planning mechanisms outperform in terms of accuracy for different values of the standard deviation of noise. As a conclusion, Fig. 10 reports a comparison of accuracy achieved by the various trajectories based on the three localization techniques. We summarize the average localization errors and the related standard deviations of the estimated errors where the ratio of the communication range to resolution was adjusted by Rc =d ¼ 5=3; 1and2 for the WCL, TPT and APT approaches, respectively. It can be deduced from Fig. 10 that any deterministic trajectory can improve the accuracy of localization, as opposed to a random movement. Regardless of the employed localization technique, RWP has a higher localization error and standard deviation of error compared

Wireless Netw 6

1.2 1 0.8 0.6 0.4 0.2 0


5





1.4

4

3

2

1

4

6

0.8

0.6

0.4

0.2

0

0 2

2

8

4

6


1

8

2

(a)

4

6

8

Standard Deviation of Noise



(b)

(c)

Fig. 9 Variation of the localization error versus standard deviation of noise ðrÞ. a WCL technique. b TPT technique. c APT technique

0.7 RWP HILBERT SCAN CIRCLES LMAT


0.6 0.08

0.11

0.5 0.06 0.11

0.4 0.09

0.3

0.08 0.08

0.2

0.042 0.04 0.03

0.038

0.1

0.023 0.007 0.007

0

WCL

TPT

0.006

APT

Localization Techniques

Fig. 10 Average and standard deviation of errors for three approaches at the fine value of Rc =d

with the static path planning mechanisms (except Circles in the TPT technique which has a higher localization error than RWP). LMAT outperforms the other trajectories since the localization error remains small (0.017 R). It also has the lowest value of the standard deviation of error. It means that it has a more stable precision. 4.3.2 Localization time

None of the existing path types consider the localization time as a critical metric to evaluate the mobile beacon trajectory. Accuracy or coverage provided by the mobile beacon is imperfect without considering the average localization time spent per unknown sensors. In some crucial applications such as natural disaster monitoring or early warning and rescue, location estimation of the sensors should be done in the shortest time. We define the average localization time, Lt , as:

Lt ¼

m X

! ðtlocðiÞ trecðiÞ Þ

m

ð21Þ

i¼1

where m defines the total number of localized sensors and tlocðiÞ and trecðiÞ show the completed time of localization and the received time of the first beacon message, respectively. We study the performance of the trajectories in terms of the average localization time with regard to two variables: the ratio of communication range to resolution ðRc =dÞ and various traveling speeds of the mobile beacon. The ratio of communication range to resolution In this set of simulations we measure the average localization time of the trajectories under different values of Rc =d where the mobile beacon velocity is set to 2m/s [27]. We consider two trilateration approaches (APT and TPT) illustrated in Fig. 11. The WCL technique is not investigated in this section as it has a similar policy with APT for calculating the required localization time. It is observed from Fig. 11(a) that increasing the ratio of Rc=d does not have a significant enhancement on the required time for localization in most cases (except RWP). Hilbert, Scan and LMAT have a common trend under varying values of Rc =d. The Circles trajectory scheme outperforms the others in this approach as it properly solves the collinearity problem and the location is obtained in a shorter time. However, it has the largest error as shown in Fig. 10. On the contrary, increasing the ratio of the communication range has a direct impact on increasing the average localization time in the APT technique as illustrated in Fig. 11(b). Since an unknown node should wait to collect all the beacon messages for estimating its location, the time required for localization increases as the communication range is increased. In other words, the higher the number of received beacons, the longer the localization time. The Hilbert trajectory requires a shorter localization time than the other trajectories. Traveling speeds of the mobile beacon Figure 11(c) plots the average localization time per node under various

123


90 80 70 60 50 40 30 20 10 1/2

1

3/2

2

5/2

400

Average Localization Time per Node

100



Wireless Netw

300 200

100 60 40 RWP HILBERT SCAN CIRCLES LMAT

20

3

1/2


1

3/2

2

5/2

3

200 RWP HILBERT SCAN CIRCLES LMAT

180 160 140 120 100 80 60 40 20 0 0.5

1


(a)

1.5

2

2.5

3

3.5

4

Speed of Mobile Beacon (m/s)

(b)

(c)

Fig. 11 Localization time. a TPT technique. b APT technique. c Time versus travelling speed (TPT technique)

1

The Percentage of Localization Success

The percentage of Localizable Sensors

1

0.95

0.9

0.85


0.75

0.7 1/2

3/4

1

5/4

3/2

7/4

2


(a)

0.95

0.9

0.85


0.75

0.7 1/2

3/4

1

5/4

3/2

7/4

2


(b)

Fig. 12 Localization success. a Percentage of localizability. b Percentage of successfully localized sensors

traveling speeds of the mobile beacon from 0.5 to 4 m/s where Rc/d = 3/2. This set of results is measured where the TPT localization approach is employed. It is observed that the traveling speed greatly influences the localization time and a higher speed degrades the average localization time per node. The Circles path planning method requires less time for localizing every unknown sensors than the other trajectories. This superiority of Circles is explained by the fact that it successfully copes with the collinearity problem. So, three non-collinear beacon messages will be collected earlier. 4.3.3 Localization success Through all the covered unknown sensors by the mobile beacon (the sensors that received at least one beacon message), some of them are localizable while they collected more than three messages. However, the important issue is the percentages of successfully localized sensors.

123

The number of successfully localized sensor nodes (m) to the total number of unknown nodes (n) is defined as localization success LS . It is clear that the non-localized sensors are shown by localization failure. The performance of static path planning in terms of localization success is independent from the localization approach and various filters of location estimation such as accuracy or time. The localization success is only affected by the fact that the sufficient numbers of proper beacon messages will be received by the unknown sensors. So, in this set of simulations, we do not consider any of the mentioned position estimation techniques, but we simply assume the node is localizable when it receives sufficient numbers of beacon messages. The ratio of communication range to resolution Localizability and localization success of the existing trajectories are investigated under different values of (Rc =d) as depicted on Fig. 12(a, b), respectively. An increase in the communication range produces a significant enhancement

Table 2 Percentage of covered, localizable, localized sensors and localization failure Technique

RWP (%)

HILBERT (%)

SCAN (%)

CIRCLES (%)

LMAT (%)

Coverage

88.8

100

100

97.2

100

Localizable

87.2

99.6

98.4

92.4

100

Localization success

86.0

Localization failure

14

99.2 0.8

97.6 2.4

89.6 10.4

100 0

on the percentage of the localizability and localization success for all the trajectories. The improvement is due to the larger number of received messages by unknown nodes. LMAT and Hilbert mechanisms outperform the other trajectories for both localizability and success. It is observed from Fig. 12(b) that LMAT is able to successfully localize all the localizable sensors when the communication range is large enough compared with the resolution (Rc =d ¼ 3=2). Considering the localizability of LMAT in Fig. 12(b) at the same ratio of communication range to resolution indicates that the total numbers of sensors are localizable. It also is observed that Hilbert has almost the same localization success (99.2%). The RWP trajectory has the lowest percentage of localized nodes. As a comparison between the percentages of covered, localizable and successfully localized sensors, the results are shown in Table 2 where Rc =d ¼ 3=2. To show the efficiency of the trajectories, localization failure is defined as the percentage of the non-localized sensors amongst the deployed unknown nodes. In this table, the superiority of LMAT is confirmed. Percentage of time The progress of localization success under different fractions of time is shown as localization acceleration in Fig. 13. Indeed, the monitoring of the localization success behavior with time for the path planning mechanisms is non-negligible when the successfully localized sensors should timely report their gathered data for further processing. We assume that the total required time for the mobile beacon to traverse the entire network is divided into 100 time units. In this result Rc =d ¼ 3=2 and beacon speed is 2m=s. When 10 % of the time passed, Circles has more than 10 % success. At the same time, Scan is not able to localize any sensors. As shown in Fig. 13, the localization acceleration of the Circles path scheme surpassed the others when 50 % of the time is passed. However, it does not guarantee its efficiency while its success is lower than 90 % when the time is over. At the same time, LMAT reaches 100 % localization success.

Percentage of Localization Success (%)

Wireless Netw


100 90 80

250

248 244 224 215

70 148

60 127

50

124 108

40

91

30 20 32

27

10

12

0

22 0

10 %

50 %

100 %

Percentage of Time

Fig. 13 Localization acceleration

4.3.4 Ineffective position rate In spite of the fact that increasing the average number of the received messages by the unknown sensors can improve the localization success, we introduce a new related metric which analyzes the efficiency of trajectories with regards to the created useful positions obtained from the received messages. Ineffective position ðIp Þ is produced by the number of triple beacons which are collinear. Let Np denote the total number of ways for selecting three different beacon positions extracted from the received messages per unknown sensor Nr . So, Nr Nr ! ð22Þ Np ¼ C ¼ 3!ðN 3 r 3Þ! consequently, Ip ¼ Np Ep

ð23Þ

where Ip and Ep denotes ineffective positions and effective positions, respectively. Ep refers to the number of noncollinear triple beacons. Let ðc1 ; c2 ; c3 Þ denotes a set of triple beacon messages. We define matrix MSG as follows:

x c2 x c1 y c2 y c1 MSG ¼ ð24Þ x c3 x c1 y c3 y c1 Hence, the three received beacons are non-collinear, if: jMSGj ¼ ðxC2 xC1 ÞðyCo yC1 Þ ðyC2 yC1 Þ ðxCo xC1 Þ 6¼ 0

ð25Þ

The ineffective position is divided by successfully localized sensors to get the ineffective position rate, Ipr . In other words:

123

Wireless Netw

20

400

15

350

Localization Success Ineffective Position

250

10

300 5

250

0.5 1/2

200

3/4

1

150 100


50 0 1/2

3/4

1

5/4

3/2

7/4

250 225

200

200 175

150

150 125

100

100

Ineffective Position Rate

450

Number of Localized Sensors

Ineffective Position Rate

500

75 50

RWP

HILBERT

SCAN

CIRCLES

LMAT

50

Trajectories 2

Fig. 15 Localization success versus ineffective positions


Fig. 14 Ineffective position rate

Ipr ¼

n X

! Ipi

m

ð26Þ

i¼1

Our concern is the reduction of the ineffective position rate amongst the received beacon messages per unknown sensor. Indeed, the ineffective position rate explains the collinearity of the methods. The efficiency of a path planning mechanism will be confirmed by fewer ineffective positions with higher localization success. These useless positions increase the computation complexity and energy consumed by the unknown sensors. Figure 14 measures the impact of different ratios of communication range to resolution on the ineffective position rate. All the trajectories have a common feature. The ineffective position rate significantly increases with increasing the ratio of communication range to resolution. When the resolution is much larger than the communication range, the value of the ineffective position rate is negligible. The ineffective position rate is affected when the communication range is much larger than the resolution (Rc d). The major reason for this is that the collinear messages are increased with the number of beacon messages broadcasted by the mobile beacon. Generally, LMAT, Circles and Hilbert cope effectively with the collinearity problem. However, Scan outperformed Circles at the beginning. As expected, RWP and Scan have a high ineffective position rate as much more collinear positions are caused for localizing the unknown sensors. The bar graph illustrated in Fig. 15, highlights a significant result in terms of the ineffective position rate for the beacon movement mechanisms where Rc =d ¼ 3=2. It compares the acquired levels of localization success and the corresponding ineffective position rate. The essential

123

issue is that the difference between the number of localized sensors and ineffective position rate should be as large as possible. As can be clearly seen, for the RWP and Scan trajectories the number of futile positions is relatively high against the localization success. In contrast, LMAT, as the most efficient method can successfully localize all 250 sensors at the expense of 102 useless positions per localized sensors. 4.3.5 Energy Power conservation and energy efficiency is arguably the hottest topic and hence has attracted a lot of attention of all WSN services such as localization [18]. Power efficiency of localization schemes is an important performance metric. Unfortunately, none of existing static path planning mechanisms proposed for mobile beacon assisted localization did emphasis on the metric. It may due to the fact that power conservation is not the primary concern of the mobile beacon as it does not have energy limitation. However, the sensor node lifetime has a strong dependence on the energy consumption of the sensor node. Hence, we evaluate the energy of the trajectories with regards to two sides, the energy consumed by the mobile beacon and the energy consumed by the unknown sensor for the localization task. It is clear that different components play a crucial role in determining the energy consumption by the mobile beacon and the unknown sensors. This set of simulations is shown in Fig. 16. Energy consumption of mobile beacon Energy consumption of the mobile beacon can be divided into two domains: the energy consumption for sending messages (Esend ) and the energy required for travelling along the trajectory (Etravell ). Thus, the total energy consumption of the mobile beacon can be calculated by:

400


350

300

250

200

150 1/2

3/4

1

5/4

3/2

7/4


2

16000

14000

12000

10000

8000

6000 RWP HILBERT SCAN CIRCLES LMAT

4000

2000 1/2

3/4

1

5/4

3/2

7/4

2


(a)

Avg. Energy Consumption per Node localization (J)

450

Avg. Energy Consumption per Node localization (µJ)

Avg. Energy Consumption per Node localization (µJ)

Wireless Netw

100 RWP

HILBERT

SCAN

CIRCLES

LMAT

90 80 70

6.9 6.7

60

6.5

50

6.3 1

40

5/4

3/2

7/4

30 20 10 0 1/2

3/4

1

5/4

3/2

7/4

2


(c)

(b)

Fig. 16 Energy consumption. a Energy consumed by the mobile beacon per node localization. b Energy spent by the unknown sensors per node localization. c Total energy spent by both mobile beacon and unknown sensors

Ebeacon ¼ Esend þ Etravell Esend ¼ Nt Etrans Etrans ¼ Ptrans

packet size data rate

ð27Þ

Etravell ¼ Lpath EP where Nt and Etrans denote the total number of transmitted messages and the energy required for sending each message, respectively. Transmit power is denoted by Ptrans . The energy required for traveling, as the second part of the total energy spent by the mobile beacon, can be derived based on the total path length of the trajectory (Lpath ) where the energy consumption for traveling per 1m is denoted by EP . It is clear that the longer the path length of the trajectory, the higher the energy consumption for traveling. We investigate the total length travelled by each path planning mechanisms in Sect. 3. So, herein, we omit the energy spent for travelling by the mobile beacon and only focus on the energy expenditure of transmitting the messages for node localization. Regardless of the employed localization technique, the energy consumption is only reflected by the number of transmitted messages. Figure 16(a) depicts the impact of various ratios of communication range to resolution on the average consumed energy by the mobile beacon per node localization. All the trajectories have a common feature where the energy consumption increases with increasing the communication range. This is due to the fact that the transmit power will be increased for larger communication ranges. Hilbert outperforms the others in terms of the energy consumption per node localization. This superiority indicates that the number of transmitted messages by the mobile beacon is lower compared with the number of successfully localized sensors than for the other path

planning schemes. RWP still has lower performance than the other deterministic trajectories. Energy consumption of unknown sensors A significant portion of energy is consumed during receiving the messages by the unknown node. Therefore, energy consumption is related to the number of received bits. Let Esensor denote the energy consumed by the unknown sensors. The Esensor is derived by the average number of received messages (Nr ) and the energy per bit value (Erec ). Esensor ¼ Nr Erec Erec ¼ Prec

packet size data rate

ð28Þ

where Prec denotes the received power. Based on Chipcon CC1000 radio [12] current consumption for receive mode (433MHz) is 7:4mA. Figure 16(b) shows the results of the energy spent by the unknown sensor for localization for different ratios of communication range to resolution. It shows that energy consumption significantly reduces for all the trajectories where (Rc d). The intuition behind this behavior is that the shorter the communication range, the lower the required value of signal strength. The Hilbert approach still resulted in lowest energy consumption. On the contrary, with increasing the communication range (Rc [ d) energy required for localization is quite large. LMAT outperforms the other path planning schemes for Rc ¼ 2d. However, most of the time Hilbert has better performance. To provide more reliable evaluation of energy consumption, Figure 16(c) shows total energy spent by both the mobile beacon and unknown sensors per successfully localized nodes. In other words: Etotal ¼

Ebeacon þ Esensor #localized sensors

ð29Þ

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Wireless Netw

0.1

6000

0.08

5000

0.06

4000

0.04

3000

0.02

2000

RWP

HILBERT

SCAN

CIRCLES

LMAT

Number of Localized Sensors

7000

Avg. Energy Consumption (µJ)


0.12

Localization Success Energy Consumption per Node Localization

7000 250

6000

200

5000

150

4000

100

3000

50

2000

0

1000

RWP

HILBERT

Trajectories

SCAN

CIRCLES

LMAT

Avg. Energy Consumption (µJ)

8000

8000 Localization Error (APT Technique) Energy Consumption per Node Localization

1000

Trajectories

(a)

(b)

Fig. 17 Energy efficiency of unknown sensors. a Energy efficiency versus localization accuracy. b Energy efficiency versus localization success

Table 3 Performance summary of path planning mechanisms for mobile beacon assisted localization when the trajectories are evaluated in level-3 and Rc ¼ d ¼ 12:5. The velocity of mobile beacon is set to v ¼ 2m/s

Trajectory

Accuracy

Success

Collinearity

Energy

Time

Path length

RWP [9]

1.27

199

40

7,680

202

1,512.3

Scan [27]

0.53

225

26

3,600

89.6

775

Hilbert [27]

0.46

239

14

2,320

70.8

787.5

Circles [24]

0.82

208

20

5,600

114

756

LMAT [17]

0.43

245

16

2,960

77.6

1,045.41

In this result, we also include the energy consumed for traveling the path by the mobile beacon. The unit of energy is Joule and the energy consumption for traveling per 1mðEP Þ is 2J [11]. It is expected that it imposes an additional energy cost. As Fig. 16(c) shows, the total energy expended per successfully localized sensors first decreases and then tends to stabilize when Rc d. This is due to the impact of the length travelled by the mobile beacon in different trajectories. It means that the longer the path the higher the energy consumption. The second factor is the number of successfully localized sensors for various trajectories. However, the latter factor has less impact on the energy efficiency of the trajectories. We have further evaluated the energy spent by the trajectories at the expense of localization accuracy and localization success which is plotted in Fig. 17. In this set of simulations, we keep Rc ¼ d where the lowest amount of energy is spent by the unknown sensors for localization. The energy efficiency of the sensors is measured by a trade-off between energy and localization success or localization accuracy. Figure 17(a) shows the efficiency of the LMAT trajectory while it provides a highly precise localization around 0:03R at the expense of approximately 2,960 lJ energy by sensors per node localization. Although, relying on the energy consumption, the efficiency of Hilbert is distinguished.

123

The results for localization success and the corresponding values of energy consumption for the trajectories are shown in Fig. 17(b). This result measures the energy efficiency of the path planning schemes considering the localization success. We observe that Hilbert is able to localize 248 sensors from all 250 sensors with the lowest amount of energy than the others. It means that Hilbert provides higher success at the expense of lower energy consumption. As a brief review, Table 3 compares the performance of the static path planning schemes for mobile beacon assisted localization. Since the simulation setting and channel model used in evaluating the various trajectories are consistent, the results and evaluations conduct a fair and reliable comparison among them. In this set of results, APT localization is employed. The unit of accuracy is m and localization success denotes the number of successfully localized nodes. Collinearity interprets the average number of collinear triple sort of received messages per localized nodes. The unit of energy and time are lJ and s, respectively. Energy spent for localization by unknown node is addressed in the table. The total distance travelled by the trajectories was measured by m.

5 Conclusion In this paper, we have evaluated the efficiency of five existing path planning schemes for mobile beacon assisted

Wireless Netw

localization, namely RWP, Scan, Hilbert, Circles and LMAT. We analyze their localization accuracy, success, time, energy consumption and collinearity. A significant finding shows that any deterministic trajectory can guarantee the efficiency of localization in terms of the mentioned metrics, as opposed to a random movement. Our performance results show that among the trajectories, LMAT offers the best performance regarding the localization success, ineffective position rate and localization accuracy. However, Hilbert has lower energy consumption. In terms of the time required for localization, Circles outperforms the other trajectories, but at the cost of lower accuracy. Considering all the evaluations and results, it is essential to develop a deterministic trajectory tailored for mobile beacon assisted localization to improve localization time and accuracy with lower consumed energy and ineffective positions. Beside, none of the evaluated static path planning schemes considered obstacle-resistant trajectory to handle the obstacles in the sensing field. Furthermore, it is interesting to investigate the trade off in transmission power control of mobile beacon and the distance with unknown nodes to allow energy efficiency and accuracy of estimated coordination as well the non-collinear positions.

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Javad Rezazadeh is currently working toward the Ph.D. degree in the department of Computer Science at the Faculty of Computing, Universiti Teknologi Malaysia (UTM). He received his B.Sc. and M.Sc. degrees both in Software Engineering in 2005 and 2008, respectively. He is member of the IEEE and Pervasive Computing Research Group (PCRG), UTM. His previous roles include being a lecturer more than five years and a software design engineer for industrial applications around ten years. His research interests include mobile localization, location tracking algorithms, mobility model, performance evaluation and mathematical modeling issues in wireless sensors and ad hoc networks.

Wireless Netw Marjan Moradi received her M.Sc. degree in Computer Science from the Faculty of Computing, Universiti Teknologi Malaysia (UTM), in 2013. She holds B.Sc. in ScientificApplied Computer Software Engineering in 2009. She is currently working as an active researcher in the Pervasive Computing Research Group (PCRG), UTM. She received the Excellent Researcher Award by the Faculty of Computing, UTM, in 2013. She is member of the IEEE and IEEE Women in Engineering (WIE). Her research interests include mobile localization, location tracking algorithms, mobility model, performance evaluation and mathematical modeling for underwater and terrestrial wireless sensors and medical body area networks.

Eryk Dutkiewicz received his B.E. degree in Electrical and Electronic Engineering from the University of Adelaide in 1988, his M.Sc. degree in Applied Mathematics from the University of Adelaide in 1992 and his Ph.D. in Telecommunications from the University of Wollongong in 1996. His industry experience includes management of the Wireless Research Laboratory at Motorola in early 2000s. He is currently a Professor of Wireless Communications and the Director of the WiMed Research Centre at Macquarie University, Sydney, Australia. He has held visiting professorial appointments at several institutions including the Chinese Academy of Sciences, Shanghai JiaoTong University and Coventry University. His current research interests cover medical body area networks and cognitive radio networks.

Abdul Samad Ismail is a professor at Faculty of Computing, Universiti Teknologi Malaysia. He graduated from University of Wisconsin Superior and Central Michigan University. He obtained his Ph.D. from University of Wales Swansea. Currently he is the Director of the Centre for Quality and Risk Management at the University. He is also member of the IEEE Computer Society and Pervasive Computing Research Group, UTM. He is working on several research related to computer networks, especially on Wireless Sensor Networks, Mobile Ad-hoc Networks, Grid Computing, Network Security, and Collaborative Virtual Environments.

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