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Figure 710 Illustrating triangulation
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This case when range information from more than three locations is used for the MMSE algorithm is typically referred to as multilateration The technique is illustrated in Figure 711 In this example, the system node performs ranging with four anchor points The circles drawn from each anchor point do not intersect on a single point The location is estimated by minimizing the distance from all four circles That location is shown in the middle of the four points on each circle We would also like to remark here that MMSE might also be combined with trilateration or triangulation This could be needed as the three measurements in either case might not be consistent This could result in a region estimate for the location instead of a point estimate MMSE technique could be used to get a point estimate in the estimated region 7224 Mapping (RSSI) In this approach, the quantities used for ranging, such as time of ight and signal strength, are determined at various locations during an of ine phase and a map prepared During the ranging operation of the real time phase, the system
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Figure 711 Illustration of MMSE technique
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nodes measure the quantities The measured quantities are then compared with the map prepared during the of ine phase The location that offers the best match is the estimated location This approach is typically used when using signal strengths to estimate the location 7225 Others In addition, there are other approaches, chief among them being the probabilistic approaches In this case, probability distributions are computed and the location is estimated based on the computed distributions This approach is also typically used in combination with signal strength measurement approaches 723 Attacks
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We have seen several different techniques for the ranging as well as the computation phases of localization It is clear at this point that the various ranging schemes have several vulnerabilities associated with them We summarize the various properties of the different ranging schemes and their associated vulnerabilities in Table 71 It is possible to address some of these vulnerabilities through cryptography while the other vulnerabilities would need additional tools We see from this table that it is possible to modify
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TABLE 71 Properties of Various Algorithms and Vulnerabilities of These Properties Property One-way RF time-of- ight Example Algoritms GPS Attack Threats Distance enlargement by delaying transmission of response message, by removing direct path and using multipath, false position reports and position spoo ng with GPS Distance reduction possible in restricted conditions Distance enlargement and reduction by removing direct path, by having a different node reply Distance enlargement and reduction by exploiting difference in propagation speeds Distance enlargement and reduction by removing direct path, by changing propagation loss model, by changing ambient channel noise, by changing transmission powers Distance enlargement and reduction by removing direct path and using multipath, by changing signal arrival angle Distance enlargement and reduction by modifying time synchronization Distance enlargement and reduction by jamming, by forming wormholes, by manipulating the radio range, by physically removing/displacing nodes Distance enlargement and reduction by jamming, enlarging radio region, replaying, moving locators Distance enlargement and reduction by forming wormholes, by jamming
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(both increase and decrease) the estimated distances in nearly all these techniques The computation schemes on the other hand can be in uenced indirectly by corrupting the ranging schemes, and hence we do not consider them explicitly here
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As seen from the previous section, location is an important aspect for several scenarios involving ad hoc or sensor networks Given that these infrastructureless wireless networks may be deployed in hostile environments, they would be susceptible to a variety of attacks such as wormhole or Sybil in addition to the traditional attacks such as replay and jamming that could signi cantly impact the accuracy of the localization process Hence, it is necessary to devise localization techniques that are robust even in the face of such attacks In this section we investigate how to secure the localization process We are not concerned with attacks against any other network protocol Secure localization is focused on enabling nodes in a sensor or ad hoc network to determine their location securely The secure localization problem has been solved using one of the following two approaches:
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