If a sensor receives the same signal (originated from the
same beacon) at least three times, the location of the sensor can be readily
determined by the following two steps.
Fig. 2. Format of the Message Transferred.
4.2 Step 2: Range Detection
We only consider groups containing at least three messages originated from
the same beacon node. In each group, select three where the involved beacons
are non-colinear.
We first assume the beacon signal is relayed without loss, that is, the
signal from the initiator as well as from all the intermediate relay nodes can
182 Fang Liu et al.
Chapter 7 TPSS
successively reach the sensor S. Figure 3 shows one such example. Beacon A
starts a message M =(A, 3,??’,??’) which arrives at S and beacon B at time t1
and tb, respectively. B modifies M as M
???
=(A, 2,B,??tb) and re-broadcasts it
at time t
???
b, where t
???
b = tb + ??tb. M
???
arrives at S and beacon C at time t2 and
tc, respectively. C modifies M
???
as M
??????
=(A, 1,B,??tb,C,??tc) and broadcasts
M
??????
at time t
???
c, where t
???
c = tc+??tc. Finally, M
??????
arrives at S at time t3. Assume
all the nodes transfer the signals at the same speed v. Let dsa, dsb, dsc represent
the distances from the sensor S to beacons A,B,C, respectively. Let dab, dac
denote the distance between beacons A and B, A and C, respectively.
A B C S
t1
t2
t3
(A, 3, -, -)
(A, 2, B,
)
(A, 1, B,
, C,
)
Time Time
Fig.
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