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ARGUS II DARP: Applications of Agent-based

Information Fusion

Probabilistic Inference in Multi-Agent Systems

Steven Reece

Oxford University

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Covarianceellipse

• Estimation• Target tracking• Map building

• Decentralised estimation• Multiple observers• No central estimator• Local message passing• Inference graph can be

arbitrary

Context

agent1

agent2

agent3

agent4

Estimate

State

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Data Incest Problem

• Multiple estimates

• Correlated errors

• Maintain correlations• Centralised

• Choke network

• … or infer bounds on correlations!

agent1

agent2

agent3

agent4

x1 P11x2 P22

Estimate Covariance

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Rival Approaches

• Existing technology• Kalman filter ignores correlations. Fused

estimates can be too confident • E.g. Disaster when aircraft believe

they are sufficiently far apart to manoeuvre!

• Covariance intersection (CI) assumes all correlations are possible. Fused estimates can be uninformative

• E.g. Disaster when aircraft must manoeuvre but have insufficient information about how far apart they are. They are flying blind!

New technology Covariance inflation (CInf)

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Covariance Inflation/Deflation

• Family of 2D covariance matrices.

• Crucially, correlation is boundable.

• Fit outer or inner ellipse to family.

• Reduce risk.

agent2

agent3

agent4

x1 P11x2 P22

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Covariance Inflation

• Transmitter agent knows fraction of its own estimate that could be shared by other agents (coupling scalar).

• Agents communicate• Estimate vector

• Covariance matrix

• Coupling scalar

• Receiver determines correlation bounds by combining coupling scalars.

agent2

agent3

agent4

x1 P11x2 P22

+ couplingscalar

+ couplingscalar

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Efficiency and Computational Cost

• CInf requires only minor changes to existing data fusion code.• CInf invokes some extra computational cost for each agent but

no significant communication cost.• Along with the estimate and covariance matrix, an agent is

required to communicate an extra scalar only.

• Critical for limited bandwidth applications!

• Both the Kalman filter and Covariance intersection are special cases of CInf.

• CInf estimates are more certain than those of its nearest rival, Covariance Intersection (CI).

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EstimatedLandmark

TrueLandmark

True Vehicle Path

EstimatedVehicle Path

CorrelatedLandmark Errors

Application

• SLAM• Vehicle location is uncertain• Landmark estimates

therefore inherit common error

• Correlated errors everywhere!

• DSLAM• Multiple platforms• Limited bandwidth• Communicate sub-maps• Sub-maps are correlated!

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Simulator Details

• Simulator developed from code supplied by Eric Nettleton, now at BAE SYSTEMS

• Scenario comprises• Two agents• Each communicates a sub-map

every 10 time steps

• Compare CInf and CI• … you will see

• Individual feature location uncertainty (ellipses)

• Total uncertainty in combined agent/feature estimates

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Comparison of Covariance Inflation (CInf) and Covariance Intersection (CI)

CICInf

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Many Applications of CInf

• Applications described in this conference• Loopy communication networks

• SLAM

• Area surveillance (QinetiQ)

• Free flight (BAE SYSTEMS)

• Failure risk envelopes (Rolls-Royce)

• Data reduction (academic demonstrator)

• Also …• Multi-agent fault detection

(decorrelation of fault bids)

• Control (behaviour envelopes)

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Take Home Message

• Data incest is a significant problem for flexible multi-agent information systems.

• Covariance Inflation (CInf) offers a robust, efficient and computationally inexpensive solution to data incest problems.

• For full details, see our publication to appear at the Eighth International Conference on Information Fusion

• … and available on-line on the ARGUS web site.

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ARGUS II DARP: Applications of Agent-based

Information Fusion

Questions?