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Cricket Location Support System. After that, some general comments will be made regarding this component and its methods. 11.4.1 Ad Hoc Positioning System (APS) In the APS [8], a reduced number of beacon nodes (e.g., three or more) are deployed with the unknown nodes. The author proposes, then, a localization algorithm where each node estimates its distance to the beacon nodes in a multihop way. Once these distances are estimated, the nodes can compute their positions using trilateration. Three methods of hop-by-hop distance propagation are proposed: DV-Hop, DV-Distance, and Euclidean. In the DV-Hop, the beacon nodes start the propagation of their position information (Figure 11.12a). Working as an extension of the distance vector algorithm, all nodes receive the position information of all beacon nodes as well as the number of hops to these beacons. When a beacon node receives a position information from the other beacon nodes, it has enough information to compute the average size of one hop based on its own position, on the position of the other beacon nodes, and also on the number of hops among them (Figure 11.12b). This last value is then ooded in a controlled way into the network as a correction factor. When an unknown node receives the correction, it is able to convert its distance to the beacon nodes from number of hops to meters (Figure 11.12c). The complete DV-Hop algorithm is shown in Algorithm 1. The complexity of message exchanging of this algorithm is driven by the total number of beacon and normal nodes, which is O(n (m + 1)), where n is the number of nodes and m is the number of beacon nodes. DV-Distance works like DV-Hop. But, instead of propagating the number of hops, it propagates the estimated distances (e.g., using RSSI); and each node, before forwarding the position information of the beacon nodes, adds its estimated distance to the one contained in the packet and then forwards this packet. In this case, there is
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Figure 11.12. Example and phases of the APS: DV-Hop. (a) Initially, the beacon nodes broadcast their positions and (b) Compute the average size of hop. (c) This last value is sent to the network, and the nodes receiving it compute their positions.
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LOCALIZATION ALGORITHM
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ALGORITHM 1. APS DV-HoP Localization Algorithm Variables:
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1: positionsi = ; {Set of beacon positions.} 2: correctioni = 1; {Correction computed/received by this node.}
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3: msgi = nil.
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Action: 4: if ni B then {If this node is a beacon node.} (xi , yi ) := getGpsPosition(); 5: 6: Send beaconPos(i, xi , yi , 0) to all nj Neigi . 7: end if Input:
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8: msgi = beaconPos(k, xk , yk , hk ).
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Action: 9: if k Ri then {If this node did not already receive this packet.} / 10: Ri := Ri {k}; 11: positionsi := positionsi {(xk , yk , hk )}; 12: if ni B then {If this is a beacon node, wait for more position packets} Re Start waitTimer. 14: end if 15: Send beaconPos(k, xk , yk , hk + 1) to all nj Neigi . 16: end if Input:
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17: waitTimer timeout. {Executed only by the beacon nodes.}
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18: correctioni =
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(xi xj )2 +(yi yj )2 hj
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for all (xj , yj , hj ) positionsi ;
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19: Send correctioni to all nj Neigi .
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20: msgi = correctionk .
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21: if ni U then {If this node is an unknown node.} 22: correctioni := correctionk ; 23: hj := hj correctioni for all (xj , yj , hj ) positionsi ; 24: (xi , yi ) := positionComputation(positionsi ); {Becomes a settled node.} 25: Send correctioni to all nj Neigi . 26: end if
no need for a correction factor, because the distances to the beacon nodes are already in meters. The Euclidean method works by propagating the true Euclidean distance of the unknown nodes to the beacon nodes. To allow this, a node needs at least another