Considering
the unavoidable measuring errors, such a process makes it possible to ???pass???
computation errors from resolved sensors to the others, though it does help in
reducing the number of beacons necessary for location discovery. As more and
more sensors get localized, more and more computation errors are introduced,
that is, the inaccuracy gets cumulated. However, Figures 7??“8 show that such
an error cumulation is quite slow in TPSS. For most of the resolved sensors,
the localization error is still tolerable compared with the transmission range.
188 Fang Liu et al.
Chapter 7 TPSS
(a) epoch=1, 15.94% resolved (b) epoch=3, 51.56% resolved
(c) epoch=5, 69.69% resolved (d) epoch=10, 91.25% resolved
Fig. 7. Illustration of TPSS in terms of variant epochs and resolved percentage.
The measuring errors are assumed normally distributed w.r.t. N(0, 0.05). In each
figure, ???o??? represents a beacon, ???x??? represents the estimated location of a sensor
which is linked to the real position (denoted by *), and ????·??? represents a node whose
location is not resolved yet.
Another observation from Figure 8 is that the computation errors increase
along with the TDoA measurement errors. This trend shows the impact of
measurement errors in local timers at sensors, which can be easily understood
from Equations (3)(4) and (7)(8). Thus the larger the TDoA measuring error,
the larger the position error.
6 Conclusion
In this chapter, we present TPSS, a time-based localization scheme which uses
only short-range beacons.
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