using collective decision system support to manage error in wireless sensor fusion

8/14/2019 Using Collective Decision System Support to Manage Error in Wireless Sensor Fusion

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Using Collective Decision System Support to

Manage Error in Wireless Sensor Fusion

Arnold B. UrkenProfessor of Political Science

Stevens Institute of Technology

Hoboken, NJ [email protected]

Presented at Fusion 05, the International Conference on Information Fusion, Philadelphia, PA., July, 2005.


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Using Collective Decision System Support to

Manage Error in Wireless Sensor Fusion*

Arnold B. UrkenProfessor of Political Science

Stevens Institute of TechnologyHoboken, NJ [email protected]

Abstract When sensor fusion uses voting methods to

produce collective decisions on the basis of incomplete

and imperfect information that would be produced if

voting information were perfect and complete, the

collective outcomes will be error-resilient. Theseoutcomes will not be changed by breakdowns in wireless

network communications or decision making errors.

Error-resilient collective outcome (ERCO) analysis

makes it possible to predict how long to wait or how

many votes to reach an optimal collective decision.

ERCO analysis also provides a new framework for

gaining strategic and tactical advantages from network-

centric information sharing. This framework raises new

theoretical and empirical research opportunities for

integrating voting theory and fusion research.

Keywords: wireless sensor networks, distributeddetection, error, decision fusion, voting systems, error-resilient.

Patent pending. Portions of this work were supported bycontract DAAE30-00-D-1011 to the Stevens Wireless

Network Security Center, 2004. Approved for GeneralPublic Release.

1 Introduction

Current developments in the design and deployment of

sensors are challenging existing methodologies for

collecting data and producing useful information inwireless networks. In commercial and security

applications of sensor technology, producing precise and

accurate intelligence is being constrained by new

standards for reliability, cost, processing speed and

energy conservation. Although voting methods have

been used to address problems of sensor communications

in networks, sensor fusion techniques have not been

developed to overcome errors caused by breakdowns in

network communications and faulty decision making.

This paper outlines a new approach to wireless sensor

fusion that uses voting systems to manage these errors.

The paper is organized to explain how voting system

can be designed to provide error-resilient sensor fusion.Section 2 provides a framework that explains the

motivation for developing a new approach and

summarizes the state of the art in building error

management into voting processes. Section 3 presents

the concept of an error-resilient collective outcome

(ERCO) and explains how voting systems can be

designed to measure ERCO efficiency for complex

decision tasks in risky network environments. In these

systems, voting methods are used to answer different and

complementary questions about the same data. Section 4

applies this theoretical approach to a complex decision

task in which voter ratings are processed throughplurality, approval, and Copeland scoring methods in a

Monte-Carlo simulation to compare their ERCO

efficiency. And Section 5 discusses the simulation

results and outlines key questions for future research.

2 Sensor Design and Deployment

New sensor designs and deployment plans are driving

forces in the evolution of sensor fusion techniques. For

example, sensors that use light-scattering technology to

identify and detect more than one agent have led to

proposals [1] for deploying large sensor arrays ofmultipurpose sensors in cities to provide protection

against NBC (Nuclear, Biological, and Chemical)

attacks. These deployments could provide early

warnings that enable targeted populations to take evasive

action and permit first responders to mitigate damage.

Innovative use of materials is extending such

capabilities by creating smaller, mobile, and inexpensive

sensor systems that can increase the scope and accuracy


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of multifaceted data that can be collected to produce

knowledge [2]. By understanding the underlying

complex patterns in such artificial environments, controls

can be designed to generate precise and accurate sensor

information.

However innovations in the ability of sensors to

produce complex knowledge have not taken full account

of the problems of producing information in wireless

networks. Sensor capabilities are limited by decision-

making and transmission errors. Physical interactions

with sensed environments can degrade sensor reliability

and speed in detecting phenomena. Even if sensor

performance is not degraded by environmental

conditions, technology costs and energy constraints may

limit the feasibility of deploying enough sensors to

monitor a situation.

Moreover, when sensors are not attacked by physical or

cyber attacks, the wireless networks that are needed fortransmitting data and producing knowledge pose risks.

Data collection can be thwarted by malicious actions that

divert messages to the wrong destination or overwhelm

the processing speed and energy constraints provided by

network architecture. Although malicious attackers can

use commercial jamming devices to thwart wireless

communications, the same effect can be caused

inadvertently by environmental distortions from

background radiation from buildings.

For these reasons, decision fusion should not be

considered an afterthought in the development and

deployment of new techniques for sensor knowledge.Error should be integrated into the design of wireless

sensor architecture. Wireless systems based on such

designs will facilitate the development and deployment

of innovative sensors in two ways. First, they can remove

obstacles that limit deployment of emerging sensor

techniques for producing more complex intelligence.

And second, wireless sensor systems that are resilient to

error will enable designers of sensors to increase the

complexity of inputs that can enhance the scope and

accuracy of knowledge.

2.1 Voting, Error, and Decision Fusion

Sensor fusion models have been developed to plandecision tasks and the collection of sensor data, address

the ontological basis of fusion processes [10], use

Bayesian techniques to manage the integration of sensor

data [13], and design local sensor decision thresholds to

maximize detection performance [12]. Fusion models

that have used voting systems to achieve similar analytic

objectives [11] have drawn from voting theory as well as

theoretical insights about processing data in computer

networks [4, 5]. Each of these analytical perspectives

addresses the problem of error in different ways, though

neither perspective incorporates the concept of error-

resilient fusion into the voting process itself.

The computer science and computer engineering

literatures have used voting methods in sensor fusion

because processing of votes does not require much

bandwidth or computational overhead. With notable

exceptions [6], applications of voting systems are

confined to the use of simple methods of weighting votes

with majority rule to control sensor fusion processes. In

these studies, there is usually a focus on how to weight

the votes.

Voting systems contain subsystems that enable

individual voters to communicate information about

preferences and judgments to form a collective outcome.Each voting system contains subsystems based on rules

for the endowment of votes that can be used to express

individual information, rules for the allocation of votes,

and rules for aggregating votes to create a collective

outcome. For instance, plurality voting, commonly

used in elections in many Western democratic polities,

includes an endowment of one vote, an allocation

constraint that restricts assigning the vote to a single

choicenormally without splitting or saving the vote

and a plurality aggregation rule that recognizes the

choice with the most votes as the winner.

Computer scientists counterbalance the application ofvoting methods with techniques for managing problems

caused by breakdowns in network communication that

prevent the production of collective outcomes. For

example, statistical techniques are used to remove clutter,

cleanse data, and weight votes. These techniques depend

on the assumption that data collection satisfies

quantitative and qualitative requirements necessary for

the application of statistical methodology. These

requirements entail the creation of networks that are

computationally intensive, energy inefficient, and

dependent on sequential sharing of information [7],

In the theoretical voting literature, where elections arethe focus of analysis, the most common assumption is

that votes are collected successfully to produce a

collective outcome that reveals the group preference.

Problems in voting theory, social choice, and collective

decision making analyses focus on how to process the

voting data once it received so that collective outcomes

with particular attributes can be created. And although


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voting theorists often disagree about the properties of

these attributes, the question of what happens if votes are

missing does not normally arise in arguments for or

against the use of a voting method [9].

In pre and post-election surveys sampling and data

cleansing techniques are used to deal with missing data

by making a priori assumptions that permit the creation

of stratified samples. But voting analysts focus on

problems of preference aggregation such as paradoxical

and manipulated collective outcomes. Outside of the

preference aggregation mainstream, voting theorists who

address the problem of voter error by weighting

individual votes based on the cognitive ability or

competence of each decision maker. Neither of these

analytical traditions of voting analysis considers what to

do if and when error caused by network communications

breakdown occurs. If all of the votes cannot be

collected, group preferences cannot be inferred andindividual voter preferences cannot be weighted to

optimize group performance.

Neither the voting literature nor the computer science

literature builds error-management into the vote-

collection process itself [2]. Integrating error

management into voting process design makes it possible

leverage communication in the network applications

layer to improve wireless sensor fusion. By interpreting

network communications from the viewpoint of the

recipient of votes, incomplete and imperfect voting data

can be transformed into instantaneous and accurate

information. Understanding the complex patternsunderlying such voting transactions can be used manage

sensor decisions in risky network environments.

3. Error-Resilient Voting Analysis

This section provides a formal definition of an error-resilient collective outcome (ERCO) and explains howto analyze voting systems to compute the probability of

producing ERCOs.

3.1 What is an ERCO?

An ERCO, error-resilient collective outcome, is avoting outcome based on incomplete and imperfect

information that would be produced if information about

the voting situation were complete and perfect. Humans

make intuitive use of ERCOs in simple situations. For

example, suppose a central commander relies on ten

sensors to report whether an object is A or B and bases

an inference on the majority outcome. If the commander

has already received 6 votes in favor of A, then the

outstanding 4 votes cannot change the collective

outcome. The score in favor of A may increase or stay

the same, but the outcome cannot be changed by lack of

information caused by network communications and/or

sensor errors.

In our hypothetical convoy assessment example with

only two choices, six votes satisfied the aggregation

requirement to make choice A an ERCO. However

ERCO-based distributed inference provides a generic

form of automated decision support that enables

commanders to manage risk and uncertainty when the

collective outcome is not as clear-cut as it is in our

hypothetical example. For instance, suppose that the

commander has received 5 votes in favor of A and 2

votes in favor of B. In this case, the commander must

either wait to receive more voting information or make

an inference that might be very risky and

counterproductive. In such complex situations, it is notclear if the outstanding information has been delayed by

network traffic or if breakdowns in network

communications or sensor failures have caused the

problem. Under such conditions, without collective

decision system support, commanders may unwittingly

avoid risky choices that are reasonable and make risky

choices that are unreasonable.

For more complex, non-binary decision tasks, ERCOs

can be defined for collective decisions with two or more

choices for a fixed number of human or machine sensor

voters and an aggregation rule that determines that a

decisive collective outcome has been produced. At eachstage of data collection, the number of outstanding votes

in the network can be represented in terms of the

percentage of the total number of voters or time required

to collect a particular segment of the outstanding votes.

If at any stage of the process of collecting votes, the

number of collected votes satisfies the aggregation rule

and the collective outcome cannot be changed by receipt

of any combination of outstanding votes, then the

collective outcome is an error-resilient collective

outcome (ERCO).

ERCOs can be produced for choices on single or

multiple dimensions for collective decisions that takeplace in client-server or peer-to-peer computer

networking environments [8]. However this paper

describes ERCO production for a complex decision task

along a single dimension: the number of vehicles in a

convoy.

Regardless of the cause(s), the costs of waiting can be

significant. Lives and property will be lost and


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opportunities for redeploying resources to counterattack

or take evasive action will be missed. And emergency

responders will not receive early warnings to prepare to

care for victims.

3.2 Designing ERCO-Efficient Processes

The probability of producing an ERCO depends on the

voting system used to process voting data and produce

collective outcomes.

3.21 How Voting Systems Work

Ratings, inputs for a voting system, can be based on

ordinal or cardinal scales. These inputs are processed

according to rules for communicating the rating

information, converting this information into votes and

aggregating the results into a collective outcome. Ratingcommunication depends on vote endowment and

allocation rules that govern the expression of rating

information.

The vote endowmentfixes the number of votes that can

be used to express ratings while the vote allocation rule

sets constraints on the allocation of the endowment. The

aggregation rule determines how many votes are

required to form a winning coalition.


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The following chart illustrates the definition of these

rules for three systems.

The OPOV system, a fully-specified description of

plurality voting, reveals which choice is most

frequently top-ranked in voter ratings. Approval voting

(AV) shows which choices are approved (or disapproved)by a plurality or majority of voters. And Copeland

voting reveals the relative collective intensity of

preference that voters express in their ratings.

Although voting theorists debate which voting system

is best, each system answers different questions about the

collective outcomes produced by the same voting or

rating inputs. All voting systems may have paradoxical

attributes and do not necessarily generate consistent

collective outcomes.

Consider the processing of the following voter cardinal

ratings for three choices, A, B, and C.

When these inputs are processed in a OPOV system with

plurality rule, the allocations are

and the collective outcome is a three-way tie, a

phenomenon associated with the paradox between

individual and collective transitivity.

When the original inputs are processed in AV and

voters cast one approval vote for each choice that equals

or exceeds their average rating, the vote allocations are

Table 1Subsystems of Three Voting Systems

Table 2Hypothetical Voter Rating Scenario

Table 3Conversion of Ratings into Single Votes


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and B is the plurality winner (based on the definition of

the aggregation rule determined by the number of voters

who expressed approval (3 out of 3), which would not

satisfy the requirement of a majority of the total number

of allocated approval votes).

Under Copeland voting with plurality rule, the ratings

are first processed with Condorcet scoring, which

computes the number of times that each choice is ranked

higher than every other choice in voter preference

ratings. These Condorcet scores are

Table 5Conversion of Ratingsinto Condorcet Scores

Copeland scores are then computed by subtracting the

Condorcet scores to produce

Table 6Derivation of Copeland Scores

This illustration shows that voting systems can produce

inconsistent collective outcomes, but also generate

collective outcomes with different scores with consistent

relationships. For example, B wins under AV and

Copeland voting.

ERCO Production

The following example shows how voting systems

produce ERCOs under OPOV system; the results for AV

and Copeland voting follow the same logic and are

presented below.

In this example, ten sensors (including acoustic (AC)

and infrared (IR) sensors) provide feedback to a

commander to collectively identify the number of

vehicles in a convoy so that the commander can

determine if an attack is reasonable. The sensors report

the correct number of vehicles by rating an overlapping

set of choices (from 0 to 4 vehicles) on a 0-10 scale, as

shown below.

Table 4Conversion of Ratings into Approval Votes


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Table 7Sensor Ratings for

Convoy Assessment Task

When these ratings are converted into OPOV allocations,

as shown below in Table 8:

Table 8OPOV Allocations based on Table 7

there is no majority winner (since 4 vehicles receivesonly 4 out of 10 votes), leaving the commander, C2,

without advice about whether to attack. And if IR1s

ratings are not received, the commander would be faced

with a tied collective outcome.

In this type of decision scenario, if all of the sensors

were equally competent, ERCO analysis would focus on

the probability of satisfying the aggregation rule at any

point during the voting process. However sensors have

diverse competencies in detecting objects depending on

the manufacturers specifications and sensor limitations

caused by different operating conditions. So we will

assume that the ERCO objective is to produce acollective outcome that optimizes the group probability

of making a correct collective choice with complex

preferences and competencies. In this scenario, sensor

votes can be weighted using the Shapley-Grofman

theorem [10], which assigns weights to votes based on

sensor competence or reliability using the following

formula:


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ln(p/1-p) (10),where

p = probability of a correct choice (11)and

(1-p) = the probability of an incorrect choice (12)If p=.2 for sensors AC1-AC3, .5 for sensors AC4-

AC6, and .8 for sensors IR1-IR4 have a .8 competence,

the following chart shows the Shapley-Grofman (SG)

[10] weights that would be used to adjust the value of the

votes in Table 8:

Table 9Shapley-Grofman Weights

And the sensor votes in Table 8 would be transformed as

shown below:

Table 10Sensor OPOV Allocations

Based on Tables 8 & 9

with the 4 vehicles choice identified as the winner

under plurality or majority rule.

Table 11Example of an ERCO

In this scenario, if the votes of AC2 and AC6 are not

received, 4 vehicles would be an ERCO.

4. Monte Carlo Analysis

To investigate the probability of producing ERCOs under

OPOV, AV, and Copeland voting systems, Monte Carlo

experiments were conducted in Mat Lab. Random

variables include voter ratings (homogeneous or

heterogeneous), decision competencies, and the time

required for each set of voting information that

successfully makes it from a sensor to the commander to

form a collective outcome. Shapley-Grofman weights

are used to adjust individual votes and time is

represented by a Rayleigh distribution with a mean of 5seconds.

The following results are based on 20,000 runs for 100

sensors in a bimodal culture. In this culture, 75% of the

sensors have homogeneous ratings and a high (.9)

competence, and 25% of the sensors have heterogeneous

ratings with a competence of .48. This scenario is typical

of situations in which sensor disagreement can lead

decision makers to take unreasonable risks. In such

cases, human consumers of sensor fusion may be forced

to rely on experience or intuition to resolve sensor

disagreement. When only 1 or 2, sensors disagree,

educated guesses may be reasonable, but, as in ourscenario, when 25 out of 100 sensors disagree, additional

decision support is needed to augment human

capabilities.

In each simulation run, a group of voters are randomly

selected from a randomly chosen set of 100 voters that

are drawn from a population with the bimodal cultural

preference, competence, and vote transmission time


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attributes associated with our scenario. Then voters are

randomly selected to simulate the process of votes

arriving at C2 (Command & Control) from distributed

sensors. After a vote is received, the simulation finds the

collective outcome under OPOV, AV, and Copeland

voting methods and counts the number of times that a

given collective outcome would be produced if all of the

votes were collected. These counts are correlated with

the proportion of outstanding votes and the cumulative

vote transmission time associated with each ERCO.

Then the counts of successes and failures in ERCO

production are used to compute the probability of

producing an ERCO. This probability can be used to

compare the ERCO efficiency of voting systems under

different scenarios.

Ties can occur under all voting systems, though the

probability of generating a tie is greater under some

voting systems. For example, when preferences areheterogeneous, the probability of a tie is greater under

AV than it is under OPOV or Copeland voting systems.

The simulation results reported here are based on the

assumption that ties are randomly broken. This

assumption increases the performance of the AV system

more than it improves the ERCO-efficiency of OPOV

and Copeland systems. Ties could also be resolved

optimally by, for example, by selecting the Copeland

winner in a tied set if one existed.

Other control variables such as false positive and false

negatives are kept low and constant in the results

presented in Figures 1-4 (below). All of these scenariosare based on the same initial conditions for a simulation

run, but Figures 1 and 3 include homogeneous (similar)

ratings or preferences, while Figures 2 and 4 show what

happens when ratings or preferences are heterogeneous

(diverse).

Although all of the simulation results show that ERCO

efficiency increases monotonically as a function of the

proportion of outstanding voters or cumulative time, the

relative efficiency of voting systems varies.

For example, Figure 1 shows that the OPOV system is

most ERCO-efficient when 75% of the voters have

homogeneous preferences. As the proportion ofoutstanding voters declines, the probability of producing

an ERCO increase rapidly so that ERCO efficiency

exceeds .95 even when only half of the votes have been

received. Under the same conditions, the AV and

Copeland display an overlapping, less efficient ERCO

production pattern. Both of these voting systems are

much less ERCO efficient than OPOV even when the

proportion of outstanding voters approaches zero.

Figure 1Homogeneous Results

based on Votes Collected

In this bimodal culture, Figure 2 shows that making the

preferences of 75% of the sensors heterogeneous makes

Copeland voting, not OPOV, most ERCO efficient.

However Copeland votings ERCO efficiency increases

more slowly and achieves a lower maximum than the

OPOV system does (in Figure 1) when preferences arehomogeneous. In Figure 2, with 50% of the voters

outstanding, Copeland voting is 80% ERCO efficient and

only reaches a maximum of .9 ERCO efficiency.

Figure 2Heterogeneous Results

based on Votes Collected

Under these conditions, the OPOV and AV systems are

much less ERCO efficient and display a relatively flat,

overlapping pattern of ERCO production once 10% of

the outstanding votes have been collected.

Figures 3 and 4 present similar contrasts when

preferences in this bimodal culture become more

heterogeneous.

Figure 3Homogenous Results based on Time


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In Figure 3, when preferences are homogeneous,

OPOVs ERCO efficiency closely approaches a

maximum efficiency of more than .95 when only 250 out

of 500 seconds have elapsed. In contrast, AV and

Copeland voting display an overlapping pattern of ERCO

efficiency that increases slowly and produces a

maximum ERCO efficiency that is approximately 30%

less ERCO efficient than the OPOV maximum.

Figure 4Heterogeneous Results based on Time

In Figure 4, preferences are heterogeneous and the

Copeland method is most ERCO efficient. However the

rate of change in ERCO efficiency is slower and the

maximum ERCO efficiency is lower for Copeland voting

than they are for OPOV when preferences are

homogeneous. AV and OPOV display the same

overlapping, less-efficient, and flat ERCO production

pattern.

4. Discussion

ERCO efficiency can augment decision support forsensors by making it possible to predict how much(voting) information to collect or how long to wait toinfer that the collective inference at any point in adecision making process is actionable.

At the beginning of a sensor collective decision, C2 candetermine how long to wait or how many votes to collect

before taking action. ERCO efficiency analysis gives C2an information advantage that can be used to takeevasive action, launch a neutralizing counterattack, ordispatch first responders to mitigate the effects of anattack.

During an attack, C2 can obtain on-demandintelligence about the implications of waiting longer tomake a decision or collecting more information beforemaking an inference. ERCO-based analysis may revealif to wait for more votes to be received or time to pass orhow much longer to wait or how many more votes must

be collected to reach a distributed inference about thenumber of vehicles in the convoy.

.1 Tradeoffs among Voting Systems

In addition to revealing information about how long towait and how much information to collect beforereaching a distributed inference, ERCO analysis drawsour attention to tradeoffs between voting systems andwaiting and information collection.

Since voting systems answer different questions about

the same data set, choosing a voting system depends onwhat C2 wants to learn from the fusion process. In ourscenario, for instance, if C2s goal is only to learn whichof the five choices in the convoy assessment situation themost frequently top-rated choice is in the shortest

possible time, then, for example, the ERCO results inFigures 3 can be used with the OPOV results to reach anERCO inference that meets the time constraint. Forinstance, C2 might set a time to decide of 200 secondsinto the decision making process to achieve a high (.95)level of confidence.

However, if C2 wants to know more about thecollective assessment of the number of convoy vehicles,Figure 3 might be used to derive additional insights. For

instance, if C2 wants to know how much more each ofthe five choices was preferred to every other choice, thenFigure 3 would be used to take account of the Copelandresults to verify the results derived from the OPOV

pattern. In our scenario, the Copeland system isapproximately 30% less ERCO-efficient than the OPOVsystem, does not become significantly more ERCO-efficient as more time passes or more votes are collected,and displays volatility.. For these reasons, C2 mightdiscount the value of gaining a second opinion based onCopeland voting and consider the AV results. So C2might wait another 50 or 60 seconds to check the resultsfor AV that produces higher ERCO efficiency than can bederived from Copeland voting.

5.2 Further Research

The scenario investigated in this paper illustrates the

potential usefulness of ERCO analysis in providing

collective decision support when the network

environment includes imperfections in sensor decision

making and network communication channels. The

results of this scenario will be compared to those ERCO

efficiencies produced when a) sensors are assumed to be

perfect and communications channels are imperfect and

b) sensors are imperfect and communications channelsare perfect.

ERCO production is also being studied for peer-to-peer

scenarios and for situations in which decision tasks are

multi-dimensional. In convoy assessment task, for

example, additional dimensionality would be added by

asking about other attributes of the convoy (e.g., vehicle

shape, color, etc.) in addition to number.


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As probability results are developed for a variety of

ERCO scenarios, analytic models will be developed to

describe the effects of increasing or decreasing the

number of sensors and introducing periodic signal

interruptions into the fusion process. In addition,

situations in which the number of sensors is not known

will be investigated.

Concurrently, empirical tests will be conducted in

wireless sensor test beds.

* I would like to thank Russ Ovans and anonymous

reviewers for their comments on an earlier draft of this

paper.

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using collective decision system support to manage error in wireless sensor fusion

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