Cell-based positioning method with single power-level of RNs
3.1 Positioning accuracy analysis in regular network structure
3.1.4 Positioning accuracy for backup reference nodes
For imperfect RNs, it will fail to work in execution stage. When a RN is failed, the entire working area cannot be covered by RNs. In this scenario, the cell-based
positioning method is failed to perform positioning in the region that without RNs’ signal coverage. Therefore, cell-based positioning method with backup RNs is discussed to avoid unexpectedly failure of RNs. As shown in Figure 3.9, a backup RN PR0 is deployed in the centroid of region that can receive thee different RNs’
(P0, P3, and P4) signal. The coverage radius of the backup RN is RR0 that can cover all type 1 regions of these three RNs (i.e. the shadowed region). In other words, each backup RN is responsible for detecting the status of three RNs so it is deployed in the region that can receive the beacon signal from them. The number of backup RNs is N/3 for N RNs.
P0
P3
P4 PR0 P1
P2
P5
P6
P7
P8
P9
P10 P11
RR0 s1
s2
s4 s3
Figure 3.9: The physical layout of cell-based positioning method with backup RNs in hexagonal structure.
A backup RN has two states: standby and active. In standby state, the backup
RN receives the heartbeats of RNs to ensure that RNs are perfect. Note that the heartbeat is a periodically message sent from RNs. In the proposed method, the periodical beacon that broadcasts location information of RNs can act as the heartbeat message. In the deployed stage of backup RNs or in the first time receiving RNs’ beacon, backup RNs store the content of beacons.
If backup RN cannot receive the heartbeat from any one of these RNs, it changes its state to active. In active state, backup RN periodically broadcasts the beacon (Sf) that contains the location of failure RN(s). In order to make the beacon format compatible for normal cell-based positioning method that we mentioned in chapter 3.1, the beacon contains the following data:
Sf = {tn, (xf r, yf r), (fa,{(xa, ya)}), . . . (fk,{(xk, yk)})}
where tn represents the type of RN’s structure (e.g. tn=3 for backup structure);
fi represents the status of RN i (e.g. fi=0 for failed RN i and fi=1 for normal RN i); (xf r, yf r) represents the location of backup RN; and (xi, yi) represents the location of RN i. Note that the location of failed RN can be obtained from the centroid of type 1 region that contained in the RN’s beacon (heartbeat). At the same time, the backup RN sends a notification message that contains the location of failed RN to the manager. After restoring failed RN, the backup RN can receive the heartbeat of RNs. If all heartbeats of RNs in its coverage area can be received by backup RNs, it changes its state to standby. The state transition diagram of backup RN is shown in Figure 3.10(a).
According to the state transition of backup RN, SN must transit its current state to corresponding state (see Figure 3.10(b)). If SN receives beacons with-out backup RN, it performs the cell-based positioning method that we proposed
Standby Active
Without heartbeats from 2 or 3 RNs Without heartbeat
from 1 RN
With heartbeats from 3 RNs
Normal Correction
Receive Sf beacon
Without Sf beacon
Receive Sf beacon
(a) (b)
Figure 3.10: The state transition diagram of backup RN and SN. (a)Backup RN has two states: standby and active (b)SN has two states: normal and correction
.
in chapter 3. If one or more RNs are failed, SN can receive the beacons form backup RN. SN transits its state from normal to correction and its position can be evaluated by the following cases:
Case 1: SN received beacons from backup RN but not from other RNs. In this scenario, SN must be located within the shadowed region (See Figure 3.11).
Considering the number of failed RNs in the backup RN’s coverage area, the location of SN can be discussed by three conditions.
a) One RN failure
As shown in Figure 3.11(a), SN is located within the shaded region that is the type 1 region of the failed RN P0. The position of SN is assigned as the location of the failed RN P0.
(x, y) = (xP0, yP0).
b) Two RNs failure
SN is located within the shaded region that is shown in Figure 3.11(b). The
position of SN can be assigned as the centroid of this region which is the midpoint of the location of these two failed RNs.
(x, y) = (xP0 + xP3
2 ,yP0 + yP3 2 ).
c) Three RNs failure
SN is located within the shaded region that is shown in Figure 3.11(c). The position of SN can be assigned as the centroid of this region which is the location of the backup RN PR0.
Case 2: SN can receive beacons from backup RN and from one or two RNs. In this scenario, SN is located within the area that includes the coverage area of backup RN PR0 and excludes the region of case 1. The location of SN is decided by the cell-based positioning method without considering the beacons of backup RN for simplicity.
This is because that it is hard to recognize the region where SN is located.
For example, RN P0 is failed and four SNs (s1, s2, s3, and s4) are located in the sensing area that is shown in Figure 3.9. We know that SN s1can receive beacons from RN P2 and backup RN PR0 and SN s2 can receive beacons from RN PR0 when RN P0 failed. However, s1 and s2 are located within the same region when P0 is not failed. On the contrary, both SN s3 and s4 can receive beacons from RN P3 and backup RN PR0 when RN P0failed. However, s3and s4 are located within different region when RN P0 is not failed. One of the possible solutions is that RN using directional antenna to provide additional information for recognizing these ambiguous regions. This solution has high system complexity and hardware cost. However, considering the simplicity of system, dropping some useful beacons that are broadcasted by backup RN will increase the positioning error. This is a tradeoff between positioning error and system complexity for designing a positioning method. In this dissertation, a simple method with slight positioning error is considered.
We evaluate the average accuracy for backup RNs by simulation. In our sim-ulation, 10,000 SNs were generated in the working area of 100× 100 square units.
Then, SNs are placed in the working area with a uniform distribution. We assume that all RNs are deployed in a regular hexagonal structure with transmission range 0.744 and their locations are known in advance. For each three neighboring RNs, one backup RN are placed in the centroid of type 3 region that formed by these three RNs. Three cases of imperfect RNs that proposed in previous section is con-sidered. That is, case 1 has a 1% of failure rate of RNs; case 2 has 5%; and case 3 has 10%. Figure 3.12 shows the average accuracy of the proposed method for imperfect RNs with and without perfect backup RNs. From Figure 3.12, note that
the proposed method for imperfect RNs with (without) backup RNs having 1%, 5%, and 10% failure rates can locate SN to within 0.3088 unit distance for 98.89%
(98.68%), 93.91% (92.74%) and 87.79% (85.6%) of measurements, respectively. In Figure 3.13, it shows the average accuracy with imperfect RNs (i.e. backup RNs are also imperfect). The number of un-located SNs with and without backup RNs is listed in Table 3.2. The proposed method with backup RNs can reduce the number of un-located SNs from 21, 121 and 236 to 1, 16, and 63 in 1%, 5%, and 10% RNs failure rate, respectively.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1% RNs failure with redundant RNs 5% RNs failure with redundant RNs 10% RNs failure with redundant RNs
Figure 3.12: The average accuracy for backup RNs in a hexagonal structure (backup RNs are perfect).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1% RNs failure with redundant RNs 5% RNs failure with redundant RNs 10% RNs failure with redundant RNs
Figure 3.13: The average accuracy for backup RNs in a hexagonal structure (RNs and backup RNs have the same failure rate).