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14: if size(positionsi ) >= 2 then {If there is enough positions.} 15: referencesi := chooseTwoBestPositions(positionsi ) 16: (xi , yi ) := mostDistantFromOrigin(intersectCircles(referencesi )); {Becomes a
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settled node.} Send position(xi , yi ) to all nj Neigi . {Becomes a reference node.} 18: end if
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Figure 11.16. Operation and possible trajectories for the localization with a mobile beacon. (a) The mobile beacon moving along the sensor eld in a straight line. (b) A less rectilinear trajectory. (c) A trajectory in spiral form.
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ALGORITHM 4. MBL Localization Algorithm Variables:
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1: positionsi = {Set of position information.}
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2: msgi = nil.
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Action: 3: if ni U then {If this node is a beacon node.} 4: StartWalking(); 5: Start posTimer. 6: end if Input:
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Action: 8: (xi , yi ) := getGpsPosition(); 9: Send position(xi , yi ) to all nj Neigi . 10: Restart posTimer. Input:
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11: msgi = position(xk , yk ) such that distk = distanceEstimation(msgi ).
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12: positionsi := positionsi {(xk , yk , distk )}; 13: if size(positionsi ) >= 3 then {If there is enough references.} 14: (xi , yi ) := positionComputation(positionsi ); 15: end if
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this scenario and three possible trajectories for the mobile beacon. Algorithm 4 details the functioning of the system. The communication cost for the WSN is null, since the nodes (except the mobile beacon) do not need to send any packets. An advantage of LMB is that the position estimates are computed based on the same node (mobile beacon) keeping the mean localization error low and preventing the propagation of this error. In addition, LMB avoids the use of nodes equipped with GPS, except for the mobile beacon. On the other hand, in this technique a sensor node can estimate its position only when the mobile beacon passes near this node, which may take a long time depending on factors as the size of the sensor eld, the beacon mobility capacity, and the node trajectory. Yet, the mobile beacon may never pass nearby some nodes, either because of the trajectory or because of a problem with the mobile beacon. An important aspect that directly in uences the position estimates is the trajectory of the mobile beacon. The less rectilinear the trajectory, the better the estimates. The reason is that the lower the collinearity among the reference points, the lower the estimate error [3]. Thus, rectilinear trajectories such as Figure 11.16a must be avoided.
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11.4.5 The Global Positioning System (GPS) The GPS [34, 50] is a system composed of 24 satellites in operation that orbit around the earth. Each satellite circles the earth at a height of 20.200 km and makes two complete rotations every day. The orbits were de ned in a way that in each region of the earth we could see at least four satellites in the sky. A GPS receiver is able to receive the information constantly sent by the satellites, estimate its distance to at least four known satellites using ToA, and, nally, compute its position using trilateration. Once these procedures are executed, the receiver is able to inform its latitude, longitude, and altitude. One of the solutions for the localization problem in WSN is to equip each one of the sensor nodes with a GPS receiver. One of the main advantages would be the relatively small (2 15 m, depending on the receiver) and precise localization error, because all nodes would have a similar error. However, this solution has many disadvantages [5, 6, 8, 48]: (a) The cost and size of the sensor nodes, are increased, (b) it cannot be used when there is no satellite visible (e.g., indoor scenarios, under water, under climatic conditions, mars exploration), and (c) the extra hardware consumes energy. Due to these disadvantages, the usage of the GPS is usually limited to a small fraction of the nodes (e.g., beacon nodes). 11.4.6 The Cricket Location Support System Cricket [47] combines active beacons and passive ultrasonic receivers to provide a localization system. Cricket is designed for mobile nodes in an indoor environment, but it may be used with static nodes. The active beacons broadcast their location information over an RF (radio frequency) channel together with an ultrasonic pulse. The other nodes use the TDoA method to estimate their distances to the beacons. When the node has enough information of positions and distances, it can compute its position through multilateration. To make it possible for the algorithm to work, a grid of beacon nodes must be previously created so that all nodes have at least three beacon nodes in their communication range. This infrastructure can be considered as a disadvantage of the system, but Cricket is very accurate and able to work in indoor scenarios. 11.4.7 Comments About the Localization Algorithm The localization algorithm is the main component of a localization system. This component de nes how the available information that is provided by the beacon nodes, by the distances estimations, and by the position computations will be manipulated in order to allow the localization information to expand from the beacon nodes to the nodes of the sensor network. As previously mentioned, the localization systems, especially the ones with multihop, had been extensively studied with the advent of the WSN. This way, a number of other localization algorithms have recently been proposed that focus on different aspects like errors, number of beacons, number of settled nodes, or GPS usage,
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