Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Covariance Intersection-Based Sensor Fusion with Local Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Multiple Model Hypothesis Testing for Sounding Rocket

Tracking and Impact Point PredictionTracking and Impact Point Prediction

Julio Cesar Bolzani de Campos FerreiraJulio Cesar Bolzani de Campos Ferreira

Jacques WaldmannJacques Waldmann

COBEM2005 – Ouro Preto – 08 de Novembro de 2005COBEM2005 – Ouro Preto – 08 de Novembro de 2005

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

ContentsContents

Introduction

Target Models and Kalman Filter

Multiple Hypothesis Testing

Data Fusion

Impact Point Prediction

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

IntroductionIntroduction

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Poor estimates may cause payload loss

Demands accurate estimation of position and velocity for prediction of the orbit parameters

Poor estimates may cause payload loss

Demands accurate estimation of position and velocity for prediction of the orbit parameters

IntroductionIntroduction

Payload Orbital InjectionPayload Orbital Injection

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

IntroductionIntroduction

Impact Point PredictionImpact Point Prediction

IPP has a fundamental role in safety-of-flight

Relies on vehicle position and velocity estimates

IPP has a fundamental role in safety-of-flight

Relies on vehicle position and velocity estimates

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

ProposedApproach

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Proposed ApproachProposed Approach

Problem OverviewProblem Overview

PropelledPropelledFlightFlight

Free FlightFree Flight

ParachuteParachuteDeployedDeployed

Long DistanceLong Distance

Short DistanceShort Distance

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Proposed ApproachProposed Approach

CI FusionCI Fusion

ADOUR

ATLAS

CIFUSION

OUTPUT

Exploits the complementary characteristics of SHORT and LONG range radars.

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Proposed ApproachProposed Approach

Kalman FilteringKalman Filtering

ADOUR

ATLAS

CIFUSION

OUTPUT

KalmanFilter

KalmanFilter

Provides position, velocity, and acceleration estimates and

their corresponding covariance.

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

CIFUSION

OUTPUT

Proposed ApproachProposed Approach

Multiple Hypothesis TestingMultiple Hypothesis Testing

ADOUR

ATLAS

KFBALLISTIC

KFPROPELLED

MHT

KFBALLISTIC

KFPROPELLED

MHT

Multiple models cover both propelled and ballistic flight

behaviors.

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Proposed ApproachProposed Approach

Reference Frame TransformationsReference Frame Transformations

CIFUSION

OUTPUT

KFBALLISTIC

KFPROPELLED

MHT

KFBALLISTIC

KFPROPELLED

MHT

ADOUR

ATLAS

Fusion is performed in a common reference frame, demanding local-level estimates to be rotated and

translated.

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Proposed ApproachProposed Approach

De-biased Spherical-to-Cartesian TransformationDe-biased Spherical-to-Cartesian Transformation

CIFUSION

OUTPUT

KFBALLISTIC

KFPROPELLED

MHT

KFBALLISTIC

KFPROPELLED

MHT

ADOUR

ATLAS

De-biased transformation to cartesian coordinates is useful to describe the

kinematics without incurring in biased estimation errors

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

TargetTargetModelsModels

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Target ModelsTarget Models

Singer’s Adapted ModelsSinger’s Adapted Models

Singer’s Classical ModelSinger’s Classical Model

Shifted Gate p.d.f.Shifted Gate p.d.f.

Propulsion

Ballistic

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Target ModelsTarget Models

Shifted Gate P.D.F. – ParametersShifted Gate P.D.F. – Parameters

PropulsionPropulsionModelModel

VerticalVerticalChannelChannel

Horizontal Horizontal ChannelChannel

0.9

90m/s20

0

a

0.005

70m/s2 75m/s2

0.05 PMAX=0.05

-10m/s2 AMAX=10m/s20

P0=0.1

p(a)

a

0.04

BallisticBallisticModelModel

VerticalVerticalChannelChannel

Horizontal Horizontal ChannelChannel

-10m/s2 0

0.3

p(a)

a

0.07

-5m/s2-15m/s2

0.05 PMAX=0.05

-5m/s2 AMAX=5m/s20

P0=0.1

p(a)

a

0.04

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

MultipleMultipleModelsModels

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

Multiple Hypothesis Testing (MHT)Multiple Hypothesis Testing (MHT)

Sensors

Filter 1

Filter 2

Filter n

ProbabilityCalculation

CombineEstimates Output

estimate

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

Multiple Hypothesis Testing (MHT)Multiple Hypothesis Testing (MHT)

11

22

1 1exp

22

Tj j j jm

j

k

r S rS

2

1ˆ ˆ| |MHT j jj

k k k k k

z z

2

ˆ ˆ ˆ ˆ, ,1ˆ ˆ ˆ ˆ| | | | | |

T

MHT j j j MHT j MHTjk k k k k k k k k k k k k

zz zzP P z z z z

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

MHT Probability Along TrajectoryMHT Probability Along Trajectory

Radar AdourRadar Adour Radar AtlasRadar Atlas

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

MHT Covariance Output AnalysisMHT Covariance Output AnalysisMultiple ModelsMultiple Models

MHT Covariance Output AnalysisMHT Covariance Output Analysis

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

Switching ModelsSwitching Models

Radar AdourRadar Adour Radar AtlasRadar Atlas

1 1

1

2 1

1* 1 if 2* 0 otherwise

* 1 *

k k

k

k k

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Multiple ModelsMultiple Models

Covariance Output Analysis with Switching ModelsCovariance Output Analysis with Switching Models

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

DataDataFusionFusion

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Data FusionData Fusion

Issues on System’s StatisticsIssues on System’s Statistics

a bc W a+W bT T T T

acc a aa a a ab b b ba b bb bP = W P W +W P W +W P W +W P W

Linear Update and CovarianceLinear Update and Covariance

T T T Tcc a aa a a ab b b ba a b bb bP = W P W +W P W +W P W +W P W

True CovarianceTrue Covariance

0 ab abP P

0abP

Consistency assured whenConsistency assured whenPPaaaa and P and Pbbbb are consistent are consistent

Consistency NOT assured even Consistency NOT assured even when Pwhen Paaaa and P and Pbbbb are consistent are consistent

PPaaaa and P and Pbbbb are consistent if: are consistent if:

0 aa aaP P 0 bb bbP P

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Data FusionData Fusion

Covariance Intersection – Geometric InterpretationCovariance Intersection – Geometric Interpretation

Kalman Filter(independence between

Paa and Pbb)

CovarianceIntersection

Pcc for many choices of Pab

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

CI EquationsCI Equations

1 1 11 , 0,1 cc aa bbP P P

1 1 11 cc aa bbP c P a P b

Data FusionData Fusion

Covariance Intersection EquationsCovariance Intersection Equations

The The parameters are used to minimize the determinant parameters are used to minimize the determinant of Pof Pcccc and is recalculated for every update. and is recalculated for every update.

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Data FusionData Fusion

CI Results – Shifted Gate P.D.F. ModelCI Results – Shifted Gate P.D.F. Model

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Data FusionData Fusion

CI Results – Shifted Gate P.D.F. ModelCI Results – Shifted Gate P.D.F. Model

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Data FusionData Fusion

CI Results – Shifted Gate P.D.F. ModelCI Results – Shifted Gate P.D.F. Model

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Impact PointImpact PointPredictionPrediction

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance Ellipsoids

1P

( )-1Position Covariance

( )-1Velocity CovarianceCovariance

Eigeinvalues provides covariance ellipsoid axis

Eigeinvectors provides covariance ellipsoid

orientation

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

AccelerationAccelerationVectorVector

Velocity Vector

Velocity Vector

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance EllipsoidsVelocityVelocityEllipsoidEllipsoid

121 vertices per ellipsoid

14,641 (1212) impact pointson Earth’s surface

PositionPositionEllipsoidEllipsoid

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance Ellipsoids

PositionPositionEllipsoidEllipsoid

VelocityVelocityEllipsoidEllipsoid

AccelerationAccelerationVectorVector

Velocity Vector

Velocity Vector

Total of 121 impact pointson Earth’s surface

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Impact Point PredictionImpact Point Prediction

Effect of Neglecting Position CovarianceEffect of Neglecting Position Covariance

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

Impact Point PredictionImpact Point Prediction

Impact Area – Propelled FlightImpact Area – Propelled Flight

Ellipsoids Magnified 1000XEllipsoids Magnified 1000XImpact Area Magnified 20XImpact Area Magnified 20X

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction

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