SensIT Fault Tolerance

1
Value-Fusion versus Decision-Fusion for
Fault-tolerance in Collaborative Target Detection
in Sensor Networks
Thomas Clouqueur, Parmesh Ramanathan, Kewal K.
Saluja, Kuang-Ching Wang
Acknowledgments DARPA grant F30602-00-2-055.
2
Fault Tolerant Fusion
v5
v3
v1
v6
v4
v2
v7
v10
v9
v8
v13
v12
v11
3
Fault Tolerant Fusion
v5
v3
v1
v6
v4
v2
v7
v10
v9
v8
v13
v12
v11
4
Fault Tolerant Fusion
v5
1
v3
1
v1
1
v6
v4
1
1
v2
v7
1
0
v10
1
v9
1
v8
1
v13
1
v12
v11
1
1
5
Fault Tolerant Fusion (cont.)

• Goals
• Precision requirement all non faulty nodes in
  region make same decision.
• Accuracy requirement the decision is
  representative of the environment. For example
  decision is detect if there is an object in the
  region.

6
Agreement
Accuracy
Precision
7
Agreement (cont.)
A
A
0
0
0
1
B
C
B
C
1
1
B can not differentiate between 2
scenarios. Agreement requires 3m1 nodes to
tolerate m byzantine faults
8
Fault Tolerant Fusion

• Precision Exact agreement solves inconsistency
  problem
• All non faulty nodes obtain the same set of values

1
S
0
S
?
?
0
S
9
Fault Tolerant Fusion

• Precision Exact agreement solves inconsistency
  problem
• All non faulty nodes obtain the same set of values

1
1
1
1
1
1
1
0
?
1
?
1
1
0
1
1
1
1
0
1
1
10
Fault Tolerant Fusion

• Precision Exact agreement solves inconsistency
  problem
• All non faulty nodes obtain the same set of values

1,0
0
1
1
0
0
1
?
1
0
0
0
?
?
0
1,0
1
0
0
0
1,0
11
Fault Tolerant Fusion

• Precision Exact agreement solves inconsistency
  problem
• All non faulty nodes obtain the same set of values

1,0,0
0
1
0
1
0
0
?
0
0
0
?
?
0
1,0,0
0
0
1
0
0
1,0,0
12
Fault Tolerant Fusion

• Precision Exact agreement solves inconsistency
  problem
• All non faulty nodes obtain the same set of values

1,0,0,0
0
1
0
1
0
0
0
?
0
0
0
?
?
1,0,0,0
1
0
0
0
0
1,0,0,0
13
Fault Tolerant Fusion (cont.)

• Accuracy consistent outliers remain in the set
  of values
• Dropping highest and lowest values

m
S
N-2m used for decision
m
14
Two approaches for detection

• Value fusion

• Decision fusion

v1
v4
?
v2
v1
v4
?
v2
fusion
decision
S
S
?
S
1
0
?
1
decision
fusion
1
1
?
1
1
1
?
1
15
Two approaches for detection

• Value fusion
• 1. Perform exact agreement on values
• 2. Drop highest m and lowest m values
• 3. Compute average of remaining values
• 4. Compare to threshold

• Decision fusion
• 1. Compare to threshold
• 2. Perform exact agreement on decision
• 3. Drop highest m and lowest m decisions
• 4. Compute average of remaining decision and
  compare to threshold

16
Thresholds (a and ?) computation

• Assuming white noise N(0,s) with density
  and distribution
• Set for false alarm probability e 5
• Value fusion
• Decision fusion with second threshold a

17
Simulation

• Energy
• Variable number of sensors in 5x5 region
• Variable position of object
• False alarm rate.05

18
Simulation

• Energy
• Variable number of sensors in 5x5 region
• Variable position of object
• False alarm rate.05

19
Simulation

• Energy
• Variable number of sensors in 5x5 region
• Variable position of object
• False alarm rate.05

20
Simulation

• Energy
• Variable number of sensors in 5x5 region
• Variable position of object
• False alarm rate.05

21
Simulation Results detection probability
22
Simulation Results detection probability
23
Simulation Results detection probability
24
Simulation Results detection probability
25
Simulation Results detection probability without
dropping