Why Data Fusion in Sensor Networks needs a new Champion ?

Why Why Data Fusion in Sensor Networks Data Fusion in Sensor Networks needs a needs a newnew ChampionChampion? ?

Kalyan VeeramachaneniKalyan Veeramachaneni

Evo-Design GroupEvo-Design Group

CSAIL, Yumm Eye Tee CSAIL, Yumm Eye Tee

Work done at Work done at DDevelopment and evelopment and RResearch in esearch in EEvolutionary volutionary AAlgorithms for lgorithms for MMultisensor ultisensor SSmart mart NetNetworks works (DreamsNet)(DreamsNet)

Syracuse University Syracuse University

Evo-Design Group, CSAIL, MIT, September 3, 2009

AcknowledgementsAcknowledgements

Lisa Osadciw, Syracuse University Lisa Osadciw, Syracuse University Kai Goebel, NASA Ames Research Kai Goebel, NASA Ames Research Arun Ross, West Virginia University Arun Ross, West Virginia University Weizhong Yan, GE Global Research CenterWeizhong Yan, GE Global Research Center Vishwanath Avasarala, GE Global Research CenterVishwanath Avasarala, GE Global Research Center Nisha Srinivas, Syracuse University Nisha Srinivas, Syracuse University

22

Sensor Network Projects Sensor Network Projects

Biometric Security System Biometric Security System Wind Turbine Diagnostics and Prognostics Wind Turbine Diagnostics and Prognostics First Responders Sensor Network First Responders Sensor Network Pipeline Crack Detection System Pipeline Crack Detection System Airport Ground Surveillance System Airport Ground Surveillance System

33

Sensors : How big are they?Sensors : How big are they?

44

55

What are we detecting?What are we detecting?

Modern day society relies on detection or Modern day society relies on detection or determining the meaning of the presence or determining the meaning of the presence or absence of a signal absence of a signal

Digital CommunicationsDigital Communications Pipeline/Bridges crack detection Pipeline/Bridges crack detection Genuine User detection using Genuine User detection using

biometrics biometrics Presence of aircraft, ships, or motor Presence of aircraft, ships, or motor

vehicles vehicles Locating emergency personnelLocating emergency personnel Weather PhenomenaWeather Phenomena Building SecurityBuilding Security

Sensors are located in remote areas making Sensors are located in remote areas making decisions using a variety of criteriadecisions using a variety of criteria

Maximum A-Posteriori CriterionMaximum A-Posteriori Criterion Maximum Likelihood CriterionMaximum Likelihood Criterion Minimum Error CriterionMinimum Error Criterion

Systems Level View (1) Systems Level View (1) Signal Processing Signal Processing

66

Model the Probability Density Functions

Design a DetectorUsing a Likelihood Ratio

Test (LRT)

Measure PerformanceBayesian or Neyman

Pearson

Implement the detector on Hardware

Collect Experimental Data (Design of Experiments)

Da

ta

Model Operations

Per

form

ance

Hardware drives the design Ideally we would want a simple threshold on the incoming data

Systems Level View (2) Systems Level View (2) Machine Learning Machine Learning

77

Collect Data Classifier Design

Neural Networks, SVM, Decision Trees, Several other techniques

Data

Measure Performance

Code Implement on

Software

We do not have control on collection of dataData drives the entire design

Applications Applications

Signal ProcessingSignal Processing Digital communications Digital communications Wireless communications Wireless communications RadarsRadars Surveillance systemsSurveillance systems Locationing and GPS Locationing and GPS

88

Machine LearningMachine Learning Online diagnostic tools (aircrafts, Online diagnostic tools (aircrafts,

turbines etc. )turbines etc. ) Medical Diagnostics ( Cancer, Medical Diagnostics ( Cancer,

Neurological disorders, seizures Neurological disorders, seizures etc.) etc.)

Fraud detection on online systems Fraud detection on online systems

Inferencing in Sensor NetworksInferencing in Sensor Networks A mix of both problems A mix of both problems Seamless interaction of hardware and software Seamless interaction of hardware and software Applications are a mix as wellApplications are a mix as well Seamless interaction of system entities as wellSeamless interaction of system entities as well Biometrics is a classic example !! Biometrics is a classic example !!

Likelihood Ratio Test (1) Likelihood Ratio Test (1) Traditional Traditional “digital communications” “digital communications” example example Decide either a bit ‘0’ or ‘1’ has been sent Decide either a bit ‘0’ or ‘1’ has been sent Additive white Gaussian noise (AWGN) Additive white Gaussian noise (AWGN) Likelihood Ratio Test (maximizes posterior probability) Likelihood Ratio Test (maximizes posterior probability)

Optimal for Bayesian Cost Function Optimal for Bayesian Cost Function

99-3 -2 -1 0 1 2 3 4 50

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Notice this is a linear cost function

Likelihood Ratio Test (2) Likelihood Ratio Test (2)

The ratio for the The ratio for the digital communications digital communications gives us a neat gives us a neat threshold detector threshold detector

As long as As long as standard deviation standard deviation under both the Hypothesis is the same under both the Hypothesis is the same It makes the LRT It makes the LRT linearlinear and very simple to implement and very simple to implement

After taking logarithm on both sides and solving After taking logarithm on both sides and solving

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t

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Likelihood Ratio Test (3)Likelihood Ratio Test (3)

What happens when it is not digital communications ?What happens when it is not digital communications ? For example, unknown signal buried in noiseFor example, unknown signal buried in noise Standard Deviation under both the hypotheses is different Standard Deviation under both the hypotheses is different LRT becomes LRT becomes quadraticquadratic and requires two thresholds and requires two thresholds Note: Still Note: Still Gaussian Gaussian under both the Hypothesis under both the Hypothesis Solving for the roots of the quadratic we get decision regions as: Solving for the roots of the quadratic we get decision regions as:

Decide HDecide H00 : :

Decide HDecide H11 : :

1111

),( 21 ttz

],[ 21 ttz

Likelihood Ratio Test (4) Likelihood Ratio Test (4)

What about when under HWhat about when under H00 is is GaussianGaussian and under H and under H11 it is it is

ExponentialExponential, will the ratio still result in a simple detector? , will the ratio still result in a simple detector? Multimodal distributions with multiple peaks?Multimodal distributions with multiple peaks?

Summary: Summary:

When you have a When you have a linear cost functionlinear cost function, , linear system operations linear system operations (additive noise) (additive noise) you will have neat you will have neat linear operations in the detectorlinear operations in the detector. . Can we design detectors for more complicated models? Can we design detectors for more complicated models?

What happens when we have What happens when we have multiple detectors multiple detectors helping us make a helping us make a decision?decision?

1212

1313

Data Fusion (1) Data Fusion (1)

Binary Binary hypothesis testinghypothesis testing problem problem HH00 : Indicates an absence : Indicates an absence

HH11: Indicates the presence of the phenomena : Indicates the presence of the phenomena

Decisions rendered by Decisions rendered by multiple classifiers (matchers) are fusedmultiple classifiers (matchers) are fused to generate to generate a global decision a global decision

In bandwidth constrained remote processing, decisions are made locally by In bandwidth constrained remote processing, decisions are made locally by the classifier before sending them to the central nodethe classifier before sending them to the central node

1,

0,i i

ii i

xu i

x

1414

Data Fusion (2) Data Fusion (2)

Let Let xxii be the match score generated by the ibe the match score generated by the ithth classifier classifier

Each classifier applies its own threshold, , to determine if xEach classifier applies its own threshold, , to determine if x ii is a genuine or is a genuine or an impostor scorean impostor score

The variable The variable uuii records the decision made by the local classifier. records the decision made by the local classifier.

Let Let [u] [u] = (= (uu11, u, u22, …u, …unn) be the set of decisions rendered by multiple classifiers) be the set of decisions rendered by multiple classifiers The variable The variable uuff denotes the global decision as a consequence of fusing local denotes the global decision as a consequence of fusing local

decisions (udecisions (uff is 0, or u is 0, or uff is 1) is 1)

1,

0,i i

ii i

xu i

x

i

1515

Bandwidth Constrained Detection Networks Bandwidth Constrained Detection Networks

1

2

Sensor1

Sensor2

X1

X2

Fusion Rule

u1

u2

fu

Second Classifier Only

OR

AND

First SensorOnlyLikelihood density model for

a sensor

Noise only

Event

1616

Errors to be minimizedErrors to be minimized

Goal : Two errors need to be minimized. Goal : Two errors need to be minimized.

Bayesian risk function is minimized Bayesian risk function is minimized

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0 0 1 1( 1| )+ ( 0 | )FA f FR fR P C P u H PC P u H

1818

Correlated DecisionsCorrelated Decisions

Estimation of 2Estimation of 2nn-1 joint probabilities for n classifiers-1 joint probabilities for n classifiers

Numerical integration is done to estimate the joint probability integralsNumerical integration is done to estimate the joint probability integrals Bahadur-lazarfeld expansion reduces computational burdenBahadur-lazarfeld expansion reduces computational burden

0 1 1[ ]

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F P u u H P u H

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n

RR f i ij i j ijk i j ku i j i j ki

F P u u H P u H z z z z z

Correlation between normalized decisions Normalized Decisions

1919

What is the Problem?What is the Problem? Joint optimization of thresholds and fusion rule (decision level)Joint optimization of thresholds and fusion rule (decision level) The objective function is the Bayesian risk function:The objective function is the Bayesian risk function:

We incorporate the thresholds as the search variables, the search is a NP We incorporate the thresholds as the search variables, the search is a NP Complete problemComplete problem11

11 John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making and detection problems” 23and detection problems” 23 rdrd IEEE Conference on Decision and Control, 1984 IEEE Conference on Decision and Control, 1984


1 1[ ] 1

( 0 | [ ], ) ( | ) 1 ......h h h h h h h

n

RR f k ij i j ijk i j ku i j i j kk

F P u u H P u H z z z z z

Effect of fusion rule designEffect of threshold design

2020

Bandwidth Constrained Detection NetworksBandwidth Constrained Detection Networks

Two types of Errors need to be reducedTwo types of Errors need to be reduced If the entire observation value is transmitted to a central processing node, an efficient If the entire observation value is transmitted to a central processing node, an efficient machine machine

learning technique learning technique can be designed to achieve better accuracycan be designed to achieve better accuracy Shown below are 20000 samples of observations, 10000 belong to events, 10000 to noise. Shown below are 20000 samples of observations, 10000 belong to events, 10000 to noise.

9 to 32 bits required per sample if all bits are transmitted 9 to 32 bits required per sample if all bits are transmitted Reduces to 1 bit decision if decision is transmitted insteadReduces to 1 bit decision if decision is transmitted instead

Misses: Fail to detect an event

False Alarms: detecting an event that did not occur

Threshold on Sensor 1

Threshold on Sensor 2

Event is declared only in this quadrant, i.e. AND rule

Noise * Event

2121

What has been happening in this area?What has been happening in this area?

Amount of Research and Publications on Topic Indicates ComplexityAmount of Research and Publications on Topic Indicates Complexity Quick Check Research PublicationsQuick Check Research Publications

120 Journal Articles with Approximately 45 Discussing Similar Design Issues120 Journal Articles with Approximately 45 Discussing Similar Design Issues 48 Textbooks At Least Currently On Sale In This Area 48 Textbooks At Least Currently On Sale In This Area 5 Dissertations deal with same problem and provide human developed designs5 Dissertations deal with same problem and provide human developed designs

Paper Published that Addresses the Difficulty Paper Published that Addresses the Difficulty John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making

and detection problems” 23rd IEEE Conference on Decision and Control, 1984and detection problems” 23rd IEEE Conference on Decision and Control, 1984 Optimizing Distributed Detection for 2 SensorsOptimizing Distributed Detection for 2 Sensors

Independent sensors: Intractable Independent sensors: Intractable Correlated sensors: NP Complete Correlated sensors: NP Complete --

Researchers are reluctant to use EAs Researchers are reluctant to use EAs A simple architectural or a parameter change can give you literally 10 pages A simple architectural or a parameter change can give you literally 10 pages

worth of equations, fancy !! worth of equations, fancy !! Failure modes of gradient descent and other approaches are not identified Failure modes of gradient descent and other approaches are not identified

2222

Likelihood Ratio Test Based Design Likelihood Ratio Test Based Design Decouple the two problems: optimize thresholds and fusion rule separatelyDecouple the two problems: optimize thresholds and fusion rule separately

Identify optimal individual threshold that minimizes the Bayesian ErrorIdentify optimal individual threshold that minimizes the Bayesian Error

Optimal fusion rule for independent decisions Optimal fusion rule for independent decisions

Optimal fusion rule for correlated decisions Optimal fusion rule for correlated decisions

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Gradient Descent Approach Gradient Descent Approach Use gradient information to simultaneously optimize fusion rule and thresholdsUse gradient information to simultaneously optimize fusion rule and thresholds

where where

Threshold for a sensor is the solution of the likelihood ratio test given by Threshold for a sensor is the solution of the likelihood ratio test given by

where where

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2424

Particle Swarm Optimization Particle Swarm Optimization

1 2( , .......... )i i i inX Each particle is a solution

Particles are randomly initialized in the search space

Particle are moved in the search space using

( 1) tidV

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Demonstration on a test problem

2525

PSO Based Design PSO Based Design

Random Initialization of Particles

Velocity and Position Updates

Cost Evaluation

Save the best solution so far

Update Particles Memory

i<n

PSO parameters

CFA

Training Data

Output the best

solution

Convergence

PSO : Binary Search SpacesPSO : Binary Search Spaces

Using a sigmoid transformation on the velocity, the probability of Using a sigmoid transformation on the velocity, the probability of a binary variable can be determined ( Kennedy et al.)a binary variable can be determined ( Kennedy et al.)

Position update is changed toPosition update is changed to

Velocity update equation is not changed and the learning Velocity update equation is not changed and the learning

behavior of swarm is preservedbehavior of swarm is preserved

1( )

1 idid id VS sig V

e

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t t tid id id

t tgd id

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PSO : Binary Search SpacesPSO : Binary Search Spaces

Transition is now probabilisticTransition is now probabilistic

Particles try to position themselves in the velocity space such that they Particles try to position themselves in the velocity space such that they have maximum probability of having a value ‘1’, in case they have have maximum probability of having a value ‘1’, in case they have evidence from multiple neighbors/iterations about the goodness of being evidence from multiple neighbors/iterations about the goodness of being at value ‘1’ for a variable at value ‘1’ for a variable

PSO : Discrete Search Spaces PSO : Discrete Search Spaces

Many problems in real world optimization are binary, discreteMany problems in real world optimization are binary, discrete

For example, in sensor management, sensor selection, i.e., the sensor For example, in sensor management, sensor selection, i.e., the sensor

number is discrete variablenumber is discrete variable

Increased complexity due to binary transformation of a discrete variableIncreased complexity due to binary transformation of a discrete variable

The Hamming distance between two discrete values undergoes a non-The Hamming distance between two discrete values undergoes a non-linear transformation when an equivalent binary representation is used linear transformation when an equivalent binary representation is used insteadinstead

The range of the discrete variable often does not match the upper limit of The range of the discrete variable often does not match the upper limit of the equivalent binary representationthe equivalent binary representation

For example, a discrete variable of range [0,1,2,3,4,5] requires a three bit binary For example, a discrete variable of range [0,1,2,3,4,5] requires a three bit binary representation, which ranges between [0-7]representation, which ranges between [0-7]

PSO : Discrete Search Spaces PSO : Discrete Search Spaces

Modify the Sigmoid Transformation, for a M-ary system Modify the Sigmoid Transformation, for a M-ary system

The sigmoid gives the parameters of the distribution from which The sigmoid gives the parameters of the distribution from which the discrete value is generated, i.e., the discrete value is generated, i.e.,

Particles try to position themselves in the velocity space such Particles try to position themselves in the velocity space such that the probability of one or the other discrete variable is highthat the probability of one or the other discrete variable is high

1 idid V

MS

e

Using normal distribution here, Other distributions can be used

if

( ( 1) (1))id idX round S M randn

1 1id idX M then X M 0 0id idX then X if

Boundary Conditions, due to infinite support of the normal distribution

PSO : Discrete Search SpacesPSO : Discrete Search Spaces

( ( 1) (1))id idX round S M randn

1 1id idX M then X M 0 0id idX then X if

Boundary Conditions, due to infinite support of the normal distribution

0.5 0.1

3131

1

2

Sensor1

Sensor2

X1

X2

Fusion Rule

u1

u2

Human Design Solution: Likelihood Ratio Test (LRT) DesignHuman Design Solution: Likelihood Ratio Test (LRT) Design

fu

Optimize thresholds individually by keeping other thresholds and fusion rule constant

Use LRT for independent or correlated deriving fusion rule

Human Design Solution: Person-by-Person Optimal (PBPO) for Independent SensorsHuman Design Solution: Person-by-Person Optimal (PBPO) for Independent Sensors Human Competitive Result: Particle Swarm Optimization (PSO) Based DesignHuman Competitive Result: Particle Swarm Optimization (PSO) Based Design

Joint optimization of thresholds and Fusion RuleNo closed form solution exists

Sensor Suites : Homogeneous NetworkSensor Suites : Homogeneous Network

All sensors are identical in performanceAll sensors are identical in performance

Sensor Suites: Heterogeneous Network Type 1 Sensor Suites: Heterogeneous Network Type 1

Different sensors have different separation of means between the Different sensors have different separation of means between the two hypothesis two hypothesis

Sensor Suite : Heterogeneous Network Type 2 Sensor Suite : Heterogeneous Network Type 2

Different standard deviations under both hypothesis and different separation Different standard deviations under both hypothesis and different separation

of means,of means, solution to LRT is quadraticsolution to LRT is quadratic

Results- Independent Observations, Results- Independent Observations, Homogeneous NetworkHomogeneous Network

Number of Sensors PBPO PSO

% Improvements

3 0.22684 0.226843 0

6 0.15613 0.15613 0

9 0.11254 0.109758 2.4720

12 0.083829 0.079862 4.7322

15 0.060243 0.0586917 2.575

Probability of Error Achieved for Different AlgorithmsAveraged over 100 Trials

Results- Independent Observations, Homogeneous Results- Independent Observations, Homogeneous NetworkNetwork

Counting the evaluations to measure “time”Counting the evaluations to measure “time”

Evaluation Counts for PBPO vs. PSO Across Different Number of Sensors

0.00E+005.00E+021.00E+031.50E+032.00E+032.50E+033.00E+033.50E+034.00E+03

3 8 13

Number of Sensors

Nu

mb

er

of

Err

or

Fu

nc

tio

n E

va

lua

tio

ns

PBPO EvaluationCounts

2*exp(N/2)

N^3

PSO EvaluationCounts

Results : Independent Observations, Heterogeneous Type 1Results : Independent Observations, Heterogeneous Type 1

Number of Sensors PBPO PSO

% Improvements

3 0.0564834 0.055501 1.7384

5 0.0023426 0.0014518 38.0250

7 7.022446e-006 1.97107e-006 71.9317

9 3.539055e-009 5.2906e-011 98.5050


Preliminary Results : Independent Observations, Preliminary Results : Independent Observations, Heterogeneous Type 2 Heterogeneous Type 2

Number of Sensors

PBPO PSO(Single

Threshold)

% Benefits

3 1.4350e-004 2.7207e-005 81.04

4 8.9807e-006 7.9398e-006 11.59


3939

Result: Independent SensorsResult: Independent Sensors

Number of Number of Sensors Sensors PBPOPBPO PSOPSO

% % Improvements in Improvements in accuracy accuracy

33 0.05648340.0564834 0.0555010.055501 1.73841.7384

55 0.00234260.0023426 0.00145180.0014518 38.025038.0250

77 7.022446e-0067.022446e-006 1.97107e-0061.97107e-006 71.931771.9317

99 3.539055e-0093.539055e-009 5.2906e-0115.2906e-011 98.505098.5050

Human Design Accuracy

PSO Resulting Accuracy

PBPO-Person-By-Person Optimal

PSO – Particle Swarm Optimization

4040

Result: Correlated Sensors Result: Correlated Sensors

Probability of Error

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

8.00E-03

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Correlation Factor

Pro

ba

bili

ty o

f E

rro

r

LRT Based

PSO Based

Human Design

54% 13%

2.5%

Data Driven Design Data Driven Design

4141

no

yes

4242

Correlated Sensors: Designs for 0.1 Correlation Correlated Sensors: Designs for 0.1 Correlation For one specific cost structure For one specific cost structure

LRT (Human) Based Design: 2 thresholds on each sensor 2 Sensor only fusion rule

Region where an event is declared

PSO Based Design:Simple 1 Threshold for each sensor AND fusion ruleVery few errors

Region where an eventis declared

4343

Correlated Sensors: Designs for 0.9 Correlation Correlated Sensors: Designs for 0.9 Correlation

LRT (Human) Based Design: 2 thresholds on each sensor 2 Sensor only fusion rule

Region where an event is declared

PSO Based Design:Simple 1 Threshold for each sensor AND fusion ruleHigher number of errors, but still better

Region where an eventis declared

Comparison of Data Driven PSO Design with Other Comparison of Data Driven PSO Design with Other Approaches and Single Sensor Performance Approaches and Single Sensor Performance

4444

Varying the costs in the Bayesian Risk function and generating the designs gives the entire Receiver operating characteristic curve

Discrete Version of the Problem Discrete Version of the Problem Vendors only allow you to have access to multiple points on the ROC Vendors only allow you to have access to multiple points on the ROC The problem then becomes a The problem then becomes a combinatorial optimization combinatorial optimization problem problem Design problem is then:Design problem is then:

Operating point for each sensor Operating point for each sensor Fusion rule ( can still be solved by LRT) Fusion rule ( can still be solved by LRT)

Suppose we have three classifiers and each classifier can operate on any of Suppose we have three classifiers and each classifier can operate on any of the ‘N’ operating points, there are the ‘N’ operating points, there are 33NN choices for this problem choices for this problem

Discrete version of PSO or GA is used to identify the operating point sets. Discrete version of PSO or GA is used to identify the operating point sets. No alternative approaches existNo alternative approaches exist

4545

Multi-Objective Design Multi-Objective Design

Allows system designer to make trade-offs Allows system designer to make trade-offs Makes the Makes the fused system ROC fused system ROC available to the system designer available to the system designer

Adding a sensor, how much does it help?Adding a sensor, how much does it help? Since Since fused system ROC fused system ROC is available, area under the curve gives a metric to is available, area under the curve gives a metric to

evaluate the system evaluate the system Allows system designers to make choices when acquiring sensors from multiple Allows system designers to make choices when acquiring sensors from multiple

vendors vendors

If I have to use sensors incrementally, which ones should I focus If I have to use sensors incrementally, which ones should I focus on ? on ?

If I want to add sensors to my detection system, which sensors should I add to If I want to add sensors to my detection system, which sensors should I add to improve performance improve performance

4646

Multi-Objective Design Multi-Objective Design Homogeneous Sensor Suite Homogeneous Sensor Suite

4747

Multi-Objective Design Multi-Objective Design Heterogeneous Sensor Suite Heterogeneous Sensor Suite

4848

Multi-Objective Design Multi-Objective Design Results for Sensor Suites with 4,5 Sensors Results for Sensor Suites with 4,5 Sensors

4949

Algorithm design for generating non-dominated solutions (close to Pareto set)

• Non-Dominated Sorting PSO instead of a cost function • Continuous PSO for thresholds• Binary PSO for fusion rule, cannot use LRT for fusion rule

Multi-Objective Design Multi-Objective Design

5050

Distributed Detection Networks : Parallel and Serial Distributed Detection Networks : Parallel and Serial

S1

S3

S4

S2

S5S6

b2

b5u0

S1

S3 S4S2

Fusion Center

2 Sensor Serial Network Example 2 Sensor Serial Network Example

1

1 1

1

1

0

u

x

u

1 1

2 2

0 12 2 2 2

2 2

1 1

or

0 0

b b

b b

x x

b b

fu

Sensor2 X2

Sensor1 X1 b1

Organization of Serial Networks: Organization of Serial Networks: Who reports to Whom?Who reports to Whom?

For a homogeneous network with all the For a homogeneous network with all the sensors having same statistics, this is not sensors having same statistics, this is not a problem a problem

For a Heterogeneous network, the For a Heterogeneous network, the sequence affects the performance sequence affects the performance

As the number of sensors increase, the As the number of sensors increase, the number of possible sequences increase number of possible sequences increase exponentiallyexponentially

# Sensors # Sequences

5 120

6 720

8 40320

10 3628800

Serial Networks: Coupled Problem Serial Networks: Coupled Problem

The algorithm design for optimization and control of a distributed The algorithm design for optimization and control of a distributed serial detection network involves two steps:serial detection network involves two steps:

1:Identify the optimal sequence of sensors, ‘who reports to whom?’1:Identify the optimal sequence of sensors, ‘who reports to whom?’ 2:Identify the optimal local decision rules for sensors.2:Identify the optimal local decision rules for sensors.

A hybrid of PSO –ABC is used to control the sequence and identify A hybrid of PSO –ABC is used to control the sequence and identify the thresholds for a given sequencethe thresholds for a given sequence

Ants Identify the SequenceThe minimum error that is achieved by the sequence,

given by PSO, is used to move in the search space locating

better sequences

PSO Identifies the optimal thresholds for a sequence and feeds the minimum possible error for a given sequence

The

con

figur

atio

n

Receiver Operating Characteristic Curve: 10 Sensor Test Receiver Operating Characteristic Curve: 10 Sensor Test Bed Bed

Best PerformingSensor

Results: Serial NetworksResults: Serial Networks

% of Unique Evaluations (log plot)

-10

-8

-6

-4

-2

0

2

5 7 9 11 13 15

Number of Sensors

% E

valu

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ns

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1

2

Sensor1

Sensor2

X1

X2

Fusion Rule

u1

u2

Human Design Solution:Human Design Solution:Likelihood Ratio Test (LRT) DesignLikelihood Ratio Test (LRT) Design

1

11 arg min R

0

0

1 1

1

1log 1 log log

(2 )1j j

j j

NFAM M

j jFAj FA FA

H

P P P Cu u

P P CPH

LRT based fusion rule for independent sensors

2

22 arg min R

fu

1 1 1 1 1 1 1

0 0 0 0 0 0 0

0

0

)1

1

1 ........

log log1 ...... (1

ij i j ijk i j kFAi j i j k

FAij i j ijk i j ki j i j k

Hz z z z z

P C

z z z z z P C

H

LRT based Fusion Rule for

correlated sensors

Why Data Fusion in Sensor Networks needs a new Champion ?

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