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Figure 75 Hop count-based scheme The shaded node determines the hop count from the three anchors and uses this to determine its location
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72121 Hop Count-Based Schemes Hop count-based localization techniques use a mechanism similar to classical distance vector routing An illustrative example of this technique is the DV-hop localization scheme [150] Several anchor nodes are assumed to exist in the network, as shown in Figure 75 An anchor node broadcasts a beacon, which will be ooded in the entire network The beacon contains the location of the anchor node and also has a parameter called the hop count, which is initialized to one Each node that receives this beacon will copy the value of the hop count from the source of the beacon into its own database while also incrementing the hop count value The beacon is then further transmitted Beacons from the same source that are received with a higher hop count value than that maintained by the node are ignored As a result all the nodes in the network will receive the shortest distance to multiple anchor nodes in terms of number of hops In order to convert the hop count into physical distance, the system estimates the average distance per hop The anchors in the network estimate the average distance per hop by making use of the location and the hop count information for all the anchors inside the network Using the average distance per hop and the number of hops to a locator, a node can calculate the estimated distance to an anchor Once a node has the estimated distance from three or more anchors, it uses trilateration (see next section) to estimate its own location It is obvious here that obtaining the correct hop counts between the system nodes and every anchor node is critical The more anchors that a node can hear from, the more precise the localization can be A similar approach is also taken in [151] The latter proposes a scheme called amorphous localization In this case each system node uses a mechanism similar to DV-hop to obtain the hop distance A different approach using mathematical formulae is proposed for estimating the average distance of a single hop An adversary (who can be either an external attacker or an internal attacker) can try to either manipulate the hop count measurement or the translation from hop count to physical distance Note that manipulating the hop count measurement will also result in an incorrect translation from hop count to physical distance The hop count measurements can be manipulated using physical layer attacks such as increasing/decreasing the transmission power or using network layer attacks such as jamming the area between two nodes (this might result in beacons taking a longer route), forming a wormhole (this will result in
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Figure 76 Neighbor location where the node estimates its location as the centroid of the locations of anchors that it hears
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shortening the path and hence a much smaller hop count), removing or displacing some nodes (this will modify the path), and so on 72122 Neighbor Location This is a range-independent, proximity-based technique based on leveraging the location of neighbors [152] In this case, given a set of locator nodes, a wireless device can localize by calculating the centroid of the locations of anchors that they hear The implicit assumption here is that the various nodes are uniformly distributed The main advantages of this scheme are its simplicity, low overhead and ease of implementation The drawback is that it can lead to very coarse-grained location determination The accuracy of localization can be improved using different power levels, thereby changing the transmission range of the locators This will change the set of locators in the neighborhood of a system node This approach has been proposed in [153] Note that an adversary can modify the effective radio region In addition, the adversary can make use of jammers placed strategically to bias the location estimate 72123 Region Inclusion A representative example here is APIT (approximate point in triangle) This is a range-independent scheme [154] In this case the area is divided into several triangular regions with anchor nodes forming the vertices of the triangles The anchor nodes transmit beacons A system node that seeks to determine its location determines the triangles in which the node resides using the transmitted beacons The test used to determine this is called the APIT test In this test, a node chooses three anchors from the list of anchors whose beacons it could hear and tests whether it is inside the triangle formed by connecting these three anchors The test consists of the node checking the signal strengths at all its neighbors of the three locators that form the vertices of the triangle A node is determined to be further away if its signal strength is smaller Now in APIT, if no neighbor of the node is further from/closer to all the three anchors simultaneously, then the node assumes that it is inside the triangle Otherwise, the node assumes that it is outside the triangle We illustrate the working of APIT in Figure 77 In (a) node M assumes that it is inside the triangle since none of its neighbors
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