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  1. 1. 1 A2L: Angle to Landmarks Based Method Positioning for Wireless Sensor Networks Mustapha Boushaba1 , Abderrahim Benslimane2 and Abdelhakim Hafid1 1 Network Research Laboratory, University of Montreal CP 6128 succ Centre-Ville Montréal, QC, H3C 3J7, Canada {boushamu, ahafid}@iro.umontreal.ca 2 Laboratoire Informatique d’Avignon - CERI 339 chemin des Meinajaries BP 1228-84911 Avignon Cedex 9 benslimane@lia.univ-avignon.fr node location can be found by using extra hardware such as Abstract— Thanks to recent technological progress, GPS (Global Positioning System); however, equipping eachautonomous wireless sensor networks have experienced sensor node with GPS is very expensive in terms of energy andconsiderable development. Currently, they are used in the areas cost... A more acceptable solution would require only a subsetof health care, environment, military etc. Examples include:biomedical sensor monitoring (e.g., cardiac patient monitoring), of nodes equipped with GPS; the positions of their neighborshabitat monitoring (e.g., animal tracking), weather monitoring are computed using techniques such as trilateration and(temperature, humidity, etc.), vehicle detection, low-performance triangulation. It has been proven that the trilateration cannot beseismic sensing, movement, acoustic ranging, and natural disaster used alone for node localization within a network with a verydetection/monitoring (e.g., flooding and fire). For a number of small density of GPS nodes. Most techniques use recursivesensor-based applications, the knowledge of the positions of algorithms combining triangulation with trilateration orsensors is required or, at least, preferable. In this paper, wepropose a new method to locate a large number of nodes in multilateration.wireless sensor networks where only a subset of them are Some of the GPS based methods use estimated distancelandmarks (i.e., know their positions). Our method is AOA-based between pairs of neighbors. These methods are called Range-(Angle Of Arrival) and it is called A2L (Angle to Landmark). Based Localization Schemes (in contrast with Range-FreeCompared, via simulations, to previous methods such as APS and Localization Schemes [1, 2, 3]). The most popular methods areAHLoS, A2L considerably increases the number of located nodes RSSI (Received Signal Strength Indicator), ToA/TDoA (Timewith accurate precision while using a smaller node degree. of arrival / Time difference of arrival) and AOA (Angle of Keywords: Angle of Arrival, Localization, trilateration. arrival). In RSSI, nodes measure the power of the received signals and thus, can calculate the effective propagation loss. I. INTRODUCTION Theoretical or empirical models are used to translate this loss into distance. In ToA/TDoA, nodes directly translate the Sensor networks are becoming a standard technology in propagation time into distance if the signal propagation speedwireless communications. The development of these networks is known. The most basic localization system using ToAinvolves many different research areas, such as techniques is GPS [4]. In AOA, nodes estimate the angle atcommunication, sensing and computing. This leads to smart which signals are received and use simple geometricdisposable micro-sensors that can be deployed anywhere relationships to calculate their positions. The accuracy of theseregardless of geographic limitations. Therefore, such sensors measurements is closely related to the network environment;may be applied widely in military, national security, thus, the positions computed by the nodes may contain errors.environment monitoring, traffic surveillance, medical domains. In this paper, we propose a localization algorithm calledThese networks usually use a large number of tiny sensors. Angle to Landmark (A2L). This algorithm is based on someSensor nodes are low-cost, low-power, and communicate in existing techniques such as Angle of Arrival (AOA) andshort distances. Together, they communicate in wireless mode distance estimation for computing nodes positions. Ourand collaborate to provide information for common missions. technique is low cost, does not require expensive infrastructureA sensor node has generally embedded processing capabilities and any compass. We use a fraction of landmarks allowingand potentially has a number of sensors dedicated to sensing each node in the network to calculate its own position.different features such as acoustic, seismic, infrared (IR), and Compared to some previous methods such as APS andmagnetic elements; it can also operate as imagers and micro- AHLoS, A2L considerably increases the number of locatedradar devices. nodes with better precision. For specific applications, some nodes must know their The paper is organized as follows. Section 2 presents relatedphysical position to determine where events occur. Sensor work. Section 3 describes the proposed A2L algorithm.
  2. 2. 2Section 4 evaluates the performance of A2L using simulations.Section 5 concludes the paper and presents future work. II. RELATED WORK A large number of existing techniques attempt to solve thelocalization problem. A detailed survey can be found in [5]. We identify four categories: Fig. 2. Sample topology: 5 nodes with 3 landmarks - Infrastructure-based systems: They require infrastructureslike RADAR [6] or Cricket [7]. Other techniques are hybrid ones, it’s the case of the - Robot-based systems: They use robots to locate nodes [8]. technique described in [15] where the authors combine APS - GPS-free methods: They do not require anchors to locate with two other existing localization methods, namely MDSnodes. The authors in [9] propose a method that builds a (Multidimensional Scanning) and SDP (Semidefinitevirtual system of coordinates, and the nodes compute their Programming). MDS calculates positions using a set ofpositions in this virtual system. distances whereas SDP is a relaxation based method. - GPS-based methods: They use the positions of anchors(equipped with GPS) to determine estimated positions of non- In [11] authors propose an AHLoS system that producesanchor nodes. high quality positions. It uses ultrasound and RF techniques to The authors, in [10, 14, 2], use distance and angle deal with the ranging problem. To estimate node locations,information to compute nodes position. APS [12] use the AHLoS uses a set of nodes initially configured as Landmarksangle-of-arrival technique (AOA) for localization. All nodes in and defines several types of multilateration: atomic, iterative,APS have the capability to compute orientation and position. and collaborative. Atomic multilateration can be applied as a basic multilateration when a node has enough LandmarksIn this algorithm, nodes iteratively obtain position and neighbors. Once at least three distances to three Landmarks areorientation information starting from landmark nodes. When a known, a node may compute its own location. When a nodenon-positioned node knows at least three landmarks, it can estimates its position, it becomes a Landmark. Therefore, anapply a trilateration technique for computing its position and iterative multilateration continues until no more nodes can beits orientation to the landmarks. This information will be localized. But in some case, even after applying these twobroadcasted to neighbors for subsequent iterations. For methods there are nodes unable to compute their positions. Inlocalizing an arbitrary node A (Fig. 1 [10]), it needs to have at a collaborative fashion, nodes try to estimate their locationsleast two neighbors, B and C, which have estimates - angles or using beacons at two hops away.ranges for landmark L (B and C should to be neighbors too). The disadvantage of AHLoS is that it requires high . percentage of beacons to achieve high percentage of located nodes. For example, to resolve 90 percent of unknown nodes with an average degree of 6.28, AHLoS requires a density of 45% beacons. To improve localization rate with better accuracy, using a small set of landmarks and a small node degree, we propose A2L that locates more nodes than existing approaches, e.g., A2L allows locating D and E in the topologies shown in Fig. 2 (see Section III for more details). Fig. 1. Node A infer it’s bearing to a landmark L III. ANGLE TO LANDMARK ALGORITHM Let us consider the topology shown in Fig.2; nodes A, B, C In this Section, we present a new method that allowsare landmarks and D, E are not positioned nodes. With APS, localizing a high percentage of nodes in wireless sensorthe landmarks A, B and C start the localization mechanism. In networks by using a minimum number of landmarks. It isa recursive way, nodes E and D try to compute their positions AOA-based where each node computes the difference betweenand their orientations towards landmarks. Node E needs to two AOA: incoming angle from landmark neighbors and fromhave two neighbors that know the coordinates or the non-positioned neighbors (Figure. 3). These angles are used toorientation towards landmark C; this is not the case in the compute distances between nodes and landmarks within twotopology shown in Fig. 2. Thus, no quadrilateral can be hops. We assume that each node (e.g., Medusa node [13]) isformed between node D and the landmark C; the same applies able to measure its distance from its immediate neighbors andfor localizing node E. In this topology, APS cannot locate has an antenna array enabling it to compute the incomingnodes D and E. signals angles (AOA). In Figure 3, let us suppose that A, D, and F are the landmarks. B, C, E and N are the non-positioned nodes. Plain lines are the links between two immediate neighbors and
  3. 3. 3dashed line are the links between nodes at two hops away. graph G = (NR, E), where NR represents the set of sensor nodes and E the set of links between nodes. A link between two nodes exists if each node is within the transmission range of the other. We classify nodes into two sets: (1) NL: the set of landmarks (i.e., know their positions using GPS for example); and (2) NnL: the set of non-positioned nodes. All nodes in NL and NnL are randomly placed in a geographic area using a uniform distribution . The goal of our proposed protocol is to locate a maximum number of nodes in NnL by using a minimum of landmarks. Our protocol requires that nodes exchange two messages called INIT and POSITION: Fig. 3. Localization nodes using A2L algorithm - INIT message It is broadcasted once by NL nodes (landmarks) to their To compute its position, node N needs to know the distances immediate neighbors (one hop). The INIT message structure isand the coordinates of the Landmarks A, D, F and G.. When defined by two fields < idL, CoordL >, where idL is thenode N receives all useful information, it applies a identifier of the sending node and CoordL its coordinatestriangulation to compute distances to Landmarks at two hops. (x,y).As an example, let θN be the incoming angle from node N and - POSITION Message:θF the incoming angle from F, When the message POSITION is broadcasted, a receiver When N knows the angle θ = | θN – θF |, it becomes easy to node K can extract information of interest from A2L records.compute dNE distance by applying the formula: This will help a node K trying to locate itself. This message is dNF=dNE+dEF-2.dNE.dEF.cos(θ) (2) broadcasted by each node I, in NnL, having at least one Let us assume a 2-D space, (x,y) is the unknown position, neighboring landmark J and another neighboring node Kand (xi,yi) are the coordinate of the ith Landmark for i=1,…,n. which is not a landmark. When node K receives this message,The coordinates and the estimated distance (di), distance it can compute its distance towards landmark J by applying thebetween the ith Landmark and (x,y), are related by the triangulation mechanism using equation (2). The format of thefollowing set of equations: message POSITION is defined as: <idS, CoordS, A2L1, A2L3, …, A2Ln> ( x1 − x )2 + ( y1 − y )2   d 12  where idS is the identifier of the node which broadcasts the      M  = M  (3) POSITION message and CoordS are the coordinates (x,y) of (xn − x)2 + ( yn − y )2  dn2      the sender node broadcasting the message POSITION., A2Lk is defined as <idLj, idlk, CoordL, DistL, Angle>, where idLj To resolve this set of equations, we transform (3) into a is the identifier of landmark J, idlk is the identifier of node klinear system of equations by subtracting the nth equation (the to which the message A2L is destined, CoordL are coordinates (x, y) of landmark J, and Angle is the anglelast line in (3)) from each other equation (lines 1 to n-1 in (3)). between landmark J, transmitter I and the receiver K of A2LThe linear system is written in the form Ax = b, where message. This angle will be computed by node I; it is the difference between two AOAs (AOA from nodes J and K).  2 ( x1 − x n ) 2 ( y1 − y n )    A =  M M , B. A2L algorithm 2( x 2 ( y n −1 − y n )   n −1 − x n )  Initially, every landmark initializes A2L positioning  x 12 − x n + y 12 − y n + d n2 − d 12 2 2  (4) algorithm by broadcasting a message INIT. For each node, the   b =  M  MAC Layer can provide information for building Neighbors x 2 2 2 2 2 2  table, called TN, shown in Fig.10. For each node I, each entry  n −1 − x n + y n − 1 − y n + d n − d n −1  of TN includes: (1) id: node’s identifier from incoming signal; When range (di in (4)) measurements are noisy resolving (2) AOA: incoming angle from node id; and (3) Distance: thedifferent equations (lines in (4)) would not yield the same distance between node id and node I.results. To solve this, we use a least-squares solution (5) which id AOA Distanceis a technique borrowed from linear algebra that is often usedin applications that consists of over-determined system with Fig.4. Neighbors table structurenoisy measurements. x = ( AT A) −1 AT b (5) ˆ When a landmark’s neighbor I receives INIT messages, it updates its landmarks table, called TL (Fig.5), and tries toA. Message exchanges by A2L nodes resolve the corresponding trilateration system by using We consider an adhoc network R modeled by a bidirectional equation (5). Node I must have at least three non-aligned
  4. 4. 4landmarks in its TL table. For each node I, each entry of TL Landmarks coordinates and distances (i.e., messageincludes: (1) idL: the landmark identifier; (2) Coord: POSITION). By receiving message POSITION, node Ncoordinates (x,y) of landmark idL; (3) Distance: the distance computes distances dND, dNA and dNF, updates its TL andbetween landmark idL and node I; it is retrieved from TN or applies a trilateration for computing its position. The TTLcomputed by triangulation; and (4) nextHop: the sender of the value in this case is equal 2. When N is localized, it broadcastsmessage POSITION. If its value is equal to idL then the its message POSITION containing its position and A2L fieldslandmark idL is neighbor; otherwise, they are two hops away. serving nodes B, C, E to be located. Thus, all nodes are Node I builds a list of A2L by combining the TL and TN located with TTL maximum value equal to 3.records; the Angle in each element of the list corresponds tothe difference between the AOA landmark J and the AOA Algorithm. 1. Angle to Landmark Algorithm: processfrom node K. This information allows node I to build the when node i receives a message POSITION.POSITION message to be broadcasted toward its neighbors. Input: message POSITIONAs an example, let us consider a node I (with identifier equal Output: node i coordinates and message POSITION Variables:to 3), that maintains two tables: (1) TN with 3 entries <4, 2.3, - nb2L is the number of landmarks at two hops from node i.10; 5, 1.1, 12 ; 6, 3.2, 10>; and (2) TL with one entry < 5, - nbL is the number of landmarks at one hop (immediate(850,200), 12, 5> . The information in TL means that the node neighbors for node i).5 is a Landmark and it is one hop away from node I (3). The - TL table is a landmarks tablemessage POSITION will include two A2L fields: - TN table is a neighbors table A2L4 = <5, 4, (850, 200), 12, 1.2) Functions: - Receive (POSITION): it is used to check the A2L fields in the A2L6 = <5, 6, (850, 200), 12, 2.1) message POSITION which are intended for node I and updates the Thus, POSITION=<3, , A2L4, A2L6>. In this example, the Landmarks table (TL) that node i maintains.field CoordS is null; this means that node 3 (I) cannot be - Positioning (TL): it is used to compute node position bylocalized; it broadcasts its message POSITION to help nodes 4 applying a least-squares technique and builds messageand 6 to compute their location. POSITION. - Broadcast (POSITION): it broadcasts the message POSITION to the neighbors of node i. idL Coord distance nextHop ---------------- Algorithm ----------------- Fig.5. Landmarks table structure 1 For (i є NnL){ 2 Receive (POSITION); Upon receipt of a POSITION message, a non-positioned 3 If (nb2L+nbL ≥ 3) {node J checks whether the message contains A2L; if the 4 POSITION = Positioning(TL); 5 Broadcast (POSITION);response is yes, it applies triangulation to compute the 6 If (localized) Sleep();}distances towards other landmarks at two hop neighbors and 7}updates its table TL. Node J consults its table TL to computeits position. It must have at least three non aligned landmarks. IV. EXPERIMENTAL RESULTSTherefore, to compute its position, J takes into considerationlandmarks at one hop then landmarks at two hops. This In order to evaluate the performance of A2L, we developedtechnique allows node J to compute its position with a better our own JAVA-based simulator. We assume that all messagesdegree of accuracy by reducing errors caused by AOA broadcasted by nodes during simulation are reliably deliveredmeasurement. If the least-squares system is resolved, node J to their neighbors. We generate many random sensor networkbecomes a landmark and notifies its neighbors by broadcasting topologies according to the number of nodes and the numberPOSITION message; it may also turns off all the circuits going of landmarks; we use a square area where nodes are randomlyinto sleep mode to save energy. Otherwise, it simply placed using a uniform distribution. Landmarks are selectedbroadcasts POSITION messages to help other nodes to be randomly and nodes’ degrees (average number of neighbors)localized. The coordinates (x,y) sent by node J will help are controlled by specification of their radio range. We assumenodes at a TTL(Time To Live) bigger than 2 computing their that each node is equipped with an AVR microcontroller [13].positions. For our simulation, we set the radio transmission power to Let us consider the topology shown in Fig 3 to describe the 0.24mW. The simulation results represent the average of 100execution of the proposed algorithm (Algorithm 1). Initially, executions.A, F, D, G broadcast their messages INIT. None of the nodes We studied the effect of TTL and the landmark rate on theB, C, and E is located after the first iteration (TTL=1). Node E rate of nodes being positioned (percentage of non landmarksbuilds a message POSITION including information: angle θˆ able to resolve their positions) and the corresponding energy consumption. Our results were compared respectively with ˆ ˆ ˆ(where θ = θ N − θ F ) position F(x,y) and distance dEF and APS using AOA and AHLoS. We believe that it is preferablebroadcasts it. At the same time nodes B, C, and N compute the to limit the TTL value to 2 for better accuracy localization asangles to Landmarks and broadcast their values with localization errors increase with TTL. However, our
  5. 5. 5simulations covered a wide range of TTL values. In the first set of simulations (Fig 6 and Fig 7), we consider In the third set of simulations we study the relationshipa scenario with 300 nodes and 10% of landmarks. We execute between the localization rate, the amount of landmarksA2L and APS algorithms for various values of TTL (from 1 to required and the average node degree.10) and various node degrees (4.2, 6.14, 10.27) With TTL Fig. 9 shows that A2L, for a 200-nodes network (averagevalue equal to 1; only the nodes with at least three landmarks node degree is equal to 5.36), uses only 15% of landmarks tocan apply a trilateration technique to compute theirs positions. localize 98% of the network’s nodes. These results show theWith a TTL value equal to 6, A2L improves, compared to superiority of A2L over AHLoS [12] ,which requires anAPS, the localization rate by 16%, in the case the node degree average node degree equal to 6.28 to localize 90% of theis equal to 4.6, and by 21%, in the case the node degree is nodes with 45% of landmarks.equal to 6.14.. In the case of a large node degree, such as10.27, A2L locates 12% (resp. 3%) more than APS with TTLequal to 2 (resp. 6). Further the localization improvement, A2Lconverges faster than APS; indeed, ,A2L locates all the nodeswith TTL value equal to 6 while APS requires TTL valueequal to 7 (Figs. 6-7).. The force of A2L is laid in the anglesthat a node forms with its neighbors and a distant landmark.Knowing these angles, even if a node doesn’t have anyimmediate landmark neighbor, it can use its two-hop landmarkneighbors and apply trilateration to compute its position; this Fig 9. Required Landmarks for localization in networks with different sizes inis not the case for APS. Hence, A2L is more efficient than as square area 100x100APS in uniform topologies with small or large node degree. In the fourth set of simulations, we study the relationship between the amount of traffic generated - during the A2L_4,2 A2L_6,14 A2L_10,27 APS_4,2 APS_6,14 APS_10,27 localization process - by the network nodes and other 1 00 100 80 attributes, of interest, including network size, energy, etc. Coverage (%) 80 Coverage (%) 60 60 Fig. 10 shows the variation of the average number of 40 40 transmitted bytes for each network size; the number of 20 20 0 0 transmitted bytes is computed by summing the sizes of all 0 1 2 3 4 5 6 7 8 9 1 0 0 1 2 3 4 5 6 7 8 9 10 TTL TTL INIT and POSITION messages generated/broadcasted by landmarks and non landmarks to locate the maximum numberFig 6. A2L Coverage in different node Fig 7. APS Coverage in different node of nodes. Fig. 11 shows the corresponding energydegree (4.2, 6.14, 10.27) degree (4.2, 6.14, 10.27) consumption; the transmission power of the network’s In the second set of simulations, we set the TTL value to 2 (Medusa) nodes is set to 0.24mW.and vary the landmarks rate in a 300-nodes topology. The Fig. 12 shows the variation of the amount of trafficradius is set to 14. In this scenario, the average node degree is generated during the localization process with the percentage6.14. Fig. 8 shows that A2L requires only 45% of landmarks of landmarks in the network. The Figure shows that the(i.e., 45% of the network nodes are landmarks) to locate 63% number of transmitted bytes is inversely proportional to theof non-localized nodes, whereas APS requires more than 70% number of Landmarks. This can be easily explained by the factof landmarks to achieve the same goal. APS’s problem is that that increasing the number of landmarks in the network speedsit requires that each node should to form a quadrilateral with up the convergence with smaller values of TTL. Indeed, in thistwo neighbors and a landmark. This situation usually occurs in case, most of the exchanged messages are of type INIT (rathernetworks with high node degree. We conclude that A2L than POSITION) that has far smaller size than POSITION.requires fewer landmarks than APS (using AOA) to locate the 10% 20% 10% 20%same amount of nodes. 60 1 0,9 50 Energy per node (µj) Bytes Transmitted 0,8 A 2L APS 0,7 (thousand) 40 0,6 100 30 0,5 0,4 80 20 o ea e % Cv r g ( ) 0,3 60 10 0,2 0,1 40 0 0 50 100 150 200 250 300 50 100 150 200 250 300 20 Network Size Network Size 0 10 15 20 25 30 35 40 45 50 55 60 65 70 Landmarks (%) Fig.10 Traffic Vs size with 10% and Fig.11 Average energy Vs network 20% Landmarks size with 10% and 20% LandmarksFig 8. localized nodes rate Vs landmarks in 300 nodes network Fig. 13 shows the variation of the amount of traffic
  6. 6. 6generated during the localization process with the value of APS_using AoA APS_using DvDistance A2LTTL and the percentage of localized nodes; the results are as 120expected. For smaller values of TTL, the amount of generated 100traffic is smaller but the percentage of localized nodes is 80 Nodes (%)smaller too. For bigger TTL values, the amount of generated 60traffic is bigger and the percentage of localized nodes is bigger 40as well. 20 0 0 10 20 30 40 50 60 70 80 90 100 Bytes Transmitted Localized nodes 30 Position Error (% of the range) Bytes Transmitted (thousand) 30 120 25 Fig. 14 Accuracy measurement in 100 nodes networks Bytes Transmitted Percent of Localized 25 100 20 (thousand) 20 80 15 Nodes 15 60 10 40 10 V. CONCLUSION 5 5 20 0 0 0 10 20 30 40 50 60 70 80 90 In this paper, we propose a new algorithm, called A2L, to 1 2 3 4 5 6 7 8 9 TTL Percent of initial landmarks locate a large number of nodes in wireless sensor networks where only a subset of them is composed of landmarks. A2LFig. 13 Traffic Vs TTL Vs localized Fig 12 Traffic Vs Landmarks in 200-nodes in 200-nodes network with nodes network makes use of landmarks coordinates and AOA to compute the10% Landmarks distance from a node to a landmark at a maximum of 2 hops away. Then, it uses trilateration to compute the node’s position In the five set of simulations, like in [2, 10], a Gaussian in the case it knows at least 3 landmarks are 1 or 2 hops awaydistribution error (with standard deviation as a parameter) is from it.applied to AOA and a normal distribution error (with standard Simulations showed that A2L algorithm is more effective; itdeviation and the radio range as parameters) is applied to converges faster and locates more nodes. Compared to existingdistance measurement. Errors are normalised using the “real” techniques, such as APS and AHLoS, A2L considerablypositions of the nodes and the radio range (i.e., increases the number of located nodes with better precisionerror=[Euclidian distance between the estimated position and while using a smaller node degree and fewer landmarksthe “real” position]/(radio range)). Currently, we are finalizing our study of positioning errors Since A2L uses a Least-Squares technique, we need to introduced by A2L and techniques to minimize them.control the consistency of the resolution of the equations (4).Thus, we compute the residue [16]: ACKNOWLEDGMENT ∑ n 2 2 i =1 ˆ ˆ (xi - x) + ( yi − y ) − di We would like to thank Dragos Niculescu and Badri Nath Residue = for providing us APS code. n ˆ ˆ Where ( x, y ) is the position estimate.. A large residue REFERENCESmeans that the set of equations used in the least-square is [1] Tian He, Chengdu Huang, Brian M. Blum, John A. Stankovic,and Tarekinconsistent. For achieving a high accuracy, we use a small Abdelzaher. Range-free localization and its impact on large scale sensorthreshold (i.e., if the residue exceeds the threshold, the networks. IEEE Personal Communications Magazine, 2005position estimate is rejected) and we increase the TTL value. [2] Dragos Niculescu and Badri Nath. 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