Chapter 7 TPSS
Fig. 5. Percentage of resolved nodes vs. the number of the initial beacons: the first
9 epochs.
Fig. 6. Percentage of resolved nodes vs. the number of the initial beacons: with
di?®erent network density.
beacons can cover most of the network. All the results are the average over
100 runs.
We obtain two observations from Figure 5 and 6. First, the more beacons
deployed, the more sensors get localized. Second, once more and more sensors
resolve their positions, more and more sensors get localized. Thus we can expect
that with only a small number of short-range beacons deployed, many
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sensors can be localized using our TPSS scheme. Intuitively, these two results
are reasonable since the number of beacons increases. We can give a brief statistical
analysis about why the increase of the number of beacons can result in
a better performance. Assume a network contains N nodes randomly deployed
over an area of size L by L, in which q percent of the nodes are beacons. The
transmission range of a node is R. Whether a sensor can determine its position
depends on whether it has enough beacons in the neighborhood.
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