Multilateration: Methods For Clustering Intersection Points For Wireless Sensor Networks Localization With Distance Estimation Error

In this paper we describe three methods for localizing a wireless sensor network node, using anchor nodes in its neighbourhood, when there is an error in distance estimation present. We use the intersection points of the circles formed with the estimated distances from each anchors and we apply different methods to form clusters. We then use the cluster points to calculate the final position. demand the presence of location information include wild- fire detection, target tracking and battlefield observation net- works. Each of the above list requires the network to per- form tasks that are based on physical locations within the network. The feedback from the network will also include position information so an initialization step is critical be- fore these can function properly. The location of a single node in a wireless sensor network can be obtained using sev- eral methods. The simplest of them is using a GPS chip, which have become significantly smaller, more energy effi- cient and less expensive than in the past, to a point that in- cluding one is no longer a costly decision, both in terms of energy consumption and of actual cost of the device. The GPS system provides location information using a network of satellites that orbit the earth, so even a single node with no neighbouring nodes can be localized. Traditionally, only a few nodes in a network, called anchors or beacons, were equipped with a GPS chip, and several methods were used to take advantage of their position information to localize the rest of the network. Some of these techniques can be found in (SGL05),(GG05),(AHSK05).Although now we are in a posi- tion to equip many more nodes with similar technology, these techniques are far from obsolete. The reason is that the GPS has a few drawbacks that make its use less than ideal in cer- tain circumstances. Two examples can be use of wireless sen- sor networks in other planets, losing the advantage of having the satellite network that provides the GPS information in- stalled and indoors where the satellite signal is weak at best and non existent typically. In these cases, among others, lo- calization techniques that use anchor nodes are very much relevant. Localization techniques can provide a node with ei- ther an approximation of its absolute position or even coor- dinates in a new system, which is useful only this particular network (TM04)(CA04)(DMNJ04). In the first case, the goal is of course to provide an approximation as close as possible to the real location. The assessment of such algorithms counts exactly that, the error between the approximated location and the real location of the nodes.