A Brief Review of Theory for Information Fusion in Sensor

Networks

Xiaoling Wang

February 19, 2004

What is Information Fusion

“Information Fusion, encompasses the theory, techniques and tools conceived and employed for exploiting the synergy in the information acquired from multiple sources (sensors, databases, information gathered by human, etc.) such that the resulting decision or action is in some sense better than (qualitatively or quantitatively, in terms of accuracy, robustness and etc.) than would be possible if any of these sources were used individually without such synergy exploitation.”

- Belur V. Dasarathy, Ph.D.

Methods and Applications

Generally, information fusion methods includes: Data fusion Decision fusion

Topics of interest: Sensor fusion Classifier fusion

Representation of information from different sources

Point estimates Corresponding to the definition of concrete sensor

Interval estimates – to achieve fault tolerance Corresponding to the definition of abstract sensor

Physical value

Information Fusion Hierarchy for Target Classification in Sensor Networks

TemporalFusion

TemporalFusion…

TemporalFusion

TemporalFusion…

Multi-modality Fusion Multi-modality Fusion……

Mobile Agent FrameworkMulti-sensor Fusion

sensor sensor

node x

sensor sensor

node y

Balance redundanc

y & efficiencyMobile Agent Framework

LocalProcessing

LocalProcessing

LocalProcessing

LocalProcessing

Enabling Algorithms

Temporal fusion Majority voting

Multi-modality fusion (acoustic + seismic) Behavior-knowledge space (BKS) method

Multi-sensor fusion Multi-resolution integration (MRI) method

Temporal Fusion – Majority Voting

Objective: to reduce noise and to deal with signal non-stationarity

Majority voting – weighted average function

Consider each classifier has a function

m

jjjii dr

1

i

n

irc

1maxarg

where j – classifier

i - class

)())(()( tntxftd jiji

))(( txf ji - true class discriminant function

)(tn - noise function, zero mean

Multi-modality Fusion

Objective: to employ complementary aspects in the feature space

Treat results from multiple modalities as classifiers – classifier fusion

Majority voting won’t work

BKS method

BKS Method

Assumption: - 2 classifiers - 3 kinds of targets - 100 samples in the training setThen: - 9 possible classification combinations

c1, c2samples from each classfused result

1,1 10/3/3 11,2 3/0/6 31,3 5/4/5 1,3

…3,3 0/0/6 3

Multi-sensor Fusion

Objective: to combine the results from spatially distributed sensors

Two main points: reliability robustness - fault tolerance

Given signal inaccuracy, uncertainty, and sensor fault, interval integration methods are used in sensor fusion Marzullo, 1990 Multi-resolution integration (MRI) algorithm

Fault Tolerant Sensor Fusion

Fault tolerance concerns: how many component failures a sensor network can

tolerate and still be reliable how to separate the output of correct functioning

component from that of defective component

To solve the first question Byzantine generals problem N >= 3f+1

To solve the second question Definition: abstract sensor, interval integration

Byzantine Generals Problem

Problem description Commander-in-chief <-> messengers <-> generals

This problem is directly applicable to distributed sensor fusion This problem can be solved only if the number of traitors is

less than one third of the total number of processing elements

Every processing element must be connected directly to at least 2f+1 other processing elements

BGP Example

1

23

attack attack

Node 2 faultyretreat

1

23

attack retreat

Node 1 faulty

retreat

Mathematical Formulation for Marzullo’s Method

],[ jjj baI

],[,0

],[,1)(

jj

jjj baxif

baxifx

n

jj xxO

1

)()(

))(()( ],[ xOxS fn

}]1)(|max{},1)(|[min{ xSxxSxI p

Interval output of sensor j

Characteristic function

Overlap function

Characteristic function of the set ofall points lying in (n-f) or moreintersections of the intervals

Fused result interval

MRI Interval Fusion Method – An Example

[0.10 0.29][0.46 0.65][0.10 0.21]

[0.05 0.14][0.05 0.41][0.22 0.58]

[0.05 0.15][0.05 0.15][0.49 0.59]

[0.08 0.16][0.08 0.16][0.51 0.60]

1st node

2nd node

3rd node

4th node

Integration Results

1st node 2nd node

3rd node 4th node

Interval Generation

Generation of local confidence ranges (At each node i, use kNN for each k{5,…,15})

confidencerange

confidence level

smallest largest in this column

Class 1 Class 2 … Class nk=5 3/5 2/5 … 0k=6 2/6 3/6 … 1/6 … … … … …k=15 10/15 4/15 … 1/15

{2/6, 10/15} {4/15, 3/6} … {0, 1/6}

Reference

K. Marzullo, “Tolerating failures of continuous-valued sensors”, ACM Transactions on Computer Systems, 8(4), 1990

L. Prasad, S. S. Iyengar, R. L. Kashyap, R. N. Madan, “Functional characterization of fault tolerant integration in distributed sensor networks”, IEEE Transactions on Systems, Man, and Cybernetics, 21(5), 1991

L. Prasad, S. S. Iyengar, R. L. Rao, “Fault-tolerant sensor integration using multiresolution decomposition”, Physical Review E, 49(4), 1994

R. R. Brooks, S. S. Iyengar, “Robust distributed computing and sensing algorithm”, IEEE Computer, June, 1996