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Iterated localization is considered where each node of a network needs to getlocalized (find its location on 2-D plane), when initially only a subset ofnodes have their location information. The iterated localization processproceeds as follows. Starting with a subset of nodes that have their locationinformation, possibly using global positioning system (GPS) devices, any othernode gets localized if it has three or more localized nodes in its radio range.The newly localized nodes are included in the subset of nodes that have theirlocation information for the next iteration. This process is allowed tocontinue, until no new node can be localized. The problem is to find theminimum size of the initially localized subset to start with so that the wholenetwork is localized with high probability. There are intimate connectionsbetween iterated localization and bootstrap percolation, that is well studiedin statistical physics. Using results known in bootstrap percolation, we find asufficient condition on the size of the initially localized subset thatguarantees the localization of all nodes in the network with high probability.

Bounds on Minimum Number of Anchors for Iterative Localization and its Connections to Bootstrap Percolation