(18)
185
Remarks:
Steps 2 and 3 are repeated once per epoch on all triple messages within each
group and all valid groups that can help S estimate its position. The final
coordinates (x, y) are obtained by averaging all the results. Once S??™s position is
known, it will become a beacon and help other sensors on location estimation.
The iteration of such processes can help more and more sensors get localized,
as shown by our simulation results in Section 5.
5 Performance Evaluation
We consider a sensor network deployed over a field of 100 by 100. The transmission
range of sensors and beacons is fixed at 10.We assume each sensor can
correctly receive from all the beacons within its transmission range. Each beacon
initiates a beacon signal once per epoch. A sensor becomes a beacon node
after its position is resolved. Since MATLAB provides procedures to randomly
deploy sensors and beacons, it is selected to perform all the simulations.
According to Equations (3)(4) and (7)(8), the coordinates (x, y) are obtained
from the measurements of ti??™s, ??ti??™s. The accuracy of ti??™s depends on
the local timers of the sensor nodes, whose measuring error is a?®ected by the
TDoA timer drift, the signal arrival time correlation error, and the reception
delays, etc. In the beacon node, ??ti is computed based on the beacon??™s local
timer and the known system delays, whose inaccuracy is determined by reception
and transmission delays, time-stamping inaccuracies, and turn-around
delay measurement errors, etc.
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