data fusion and multiple models filtering for launch vehicle tracking and impact point prediction:...

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Data Fusion and Multiple Models Filtering Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara CasePoint Prediction: The Alcântara Case

Julio Cesar Bolzani de Campos FerreiraJulio Cesar Bolzani de Campos FerreiraProfessional Master Dissertation – 15/12/2004Professional Master Dissertation – 15/12/2004

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

ContentsContents

Introduction

Kalman Filter

ProposedApproach

Reference CoordinateTransformations

Multiple HypothesisTesting

Data FusionProcess

Comparison ofData Fusion Methods

Impact PointPrediction

Target Models

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

IntroductionIntroduction

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

IntroductionIntroduction

Addressed Technology Potential ApplicationsAddressed Technology Potential Applications

Air Traffic Control (ATC)Air Traffic Control (ATC)

Robot GuidanceRobot GuidanceAir and Ground SurveilanceAir and Ground Surveilance

Remote SensingRemote Sensing

Launch Vehicle TrackingLaunch Vehicle Tracking

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

ProposedApproach

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Proposed ApproachProposed Approach

Problem OverviewProblem Overview

PropelledPropelledFlightFlight

Free FlightFree Flight

ParachuteParachuteDeployedDeployed

Long DistanceLong Distance

Short DistanceShort Distance

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Proposed ApproachProposed Approach

CI FusionCI Fusion

ADOUR

ATLAS

CIFUSION

OUTPUT

Exploits the complementary characteristics of SHORT and LONG range radars.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Proposed ApproachProposed Approach

Kalman FilteringKalman Filtering

ADOUR

ATLAS

CIFUSION

OUTPUT

KalmanFilter

KalmanFilter

Provides position, velocity, and acceleration estimates and

their corresponding covariance.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

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.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

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.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Proposed ApproachProposed Approach

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

CIFUSION

OUTPUT

KFBALLISTIC

KFPROPELLED

MHT

KFBALLISTIC

KFPROPELLED

MHT

ADOUR

ATLAS

Cartesian coordinates are appropriate to accomplish the

necessary rotation and translation transformations.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

ReferenceReferenceCoordinateCoordinate

FramesFrames

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Reference Coordinate FramesReference Coordinate Frames

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

Subtracting the bias…

)1(sin

)1(sincos

)1(coscos

2/

2/2/

2/2/

22

2222

2222

eer

eer

eer

z

y

xDe-biased

transformation

BiasedTransformation

sin

sincos

coscos

r

r

r

z

y

xPURE GEOMETRICAL

TREATEMENT

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Reference Coordinate FramesReference Coordinate Frames

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

Target distance and signal-to-noise ratio (SNR) affect the slant range variance.

2 2 2, ,radar rdiag R

2

22 2 2 60 1, , 50.10

2radar cte

cdiag D

SNR

R

SNR data

D

Transforming from uncorrelated spherical measurement errors into de-biased cartesian ones gives rise to correlated measurement errors.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Reference Coordinate FramesReference Coordinate Frames

Radar Frame to Launch-Pad Frame TransformationRadar Frame to Launch-Pad Frame Transformation

Rotação +

Translação

Z

Y

X

(1,1)

Y

X

Z

(2,2)

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Reference Coordinate FramesReference Coordinate Frames

Radar Frame to Launch-Pad Frame TransformationRadar Frame to Launch-Pad Frame Transformation

11 radar radar

radar radar

1 0 0

0 cos( ) sin( )

0 -sin( ) cos( )

R

lp radar lp radar

21

lp radar lp radar

cos( - ) 0 -sin( - )

0 1 0

sin( - ) 0 cos( - )

R

12 lp lp

lp lp

1 0 0

0 cos( ) -sin( )

0 sin( ) cos( )

R

12 21 11radarlp D R R R

xy

z

xy

z

xy

z

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Reference Coordinate FramesReference Coordinate Frames

Radar Frame to Launch-Pad Frame TransformationRadar Frame to Launch-Pad Frame Transformation

Tx y z x y z x y zX

, ,lp radar radar radarradar lp lp lpdiag D D DD

0 0 0 0 0 0Tradar

lp x y z T

radar radarlp lp radar lp X D X T

radar radar radarTlp lp radar lpP D P D

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

TargetTargetModelsModels

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Target ModelsTarget Models

Singer’s Classical ModelSinger’s Classical Model

PMAX PMAX

-AMAX AMAX0

P0

p(a)

a

01 2

2MAX

MAX

P P

A

00

1 2

2MAX

MAX MAX MAX MAXMAX

P Pf x P x A P P x A

A

xf x dx

22 x f x dx

2

201 4

3MAX

MAX

AP P

= 0

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Target ModelsTarget Models

Singer’s Classical ModelSinger’s Classical Model

22 2

11 11 ( 1 )1 ( 1 ) 1 ( 1 )

1 1 10 1 (1 ) , 0 1 (1 ) , 0 1 (1 )

0 00 0 0 0

yx z

yx z

zxy

TT Tyx z

yx z

TT T

x y z

TT T

T T eT T e T T e

diag e e e

ee e

Φ

Tx x x y y y z z zX

T

T

n

Tn

n

n

n

n

n

e

e

eTT

T

00

)1(1

10

)1(1

1

),(

2

State Transition MatrixState Transition Matrix

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Target ModelsTarget Models

Singer’s Adapted ModelsSinger’s Adapted Models

Singer’s Classical ModelSinger’s Classical Model

Single Side p.d.f.Single Side p.d.f.

Propulsion

Ballistic

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

Propulsion

Ballistic

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Target ModelsTarget Models

Single Side P.D.F. / Shifted Gate P.D.F.Single Side P.D.F. / Shifted Gate P.D.F.

PMAX

AMAX0

P0

p(a)

a

01 MAX

MAX

P P

A

012MAX

MAX

AP P

2

2 20 01 2 1

3MAX

MAX MAX

AP P A P

PMAX

A0

p(a)

a

1 MAX

MAX MIN

P

A A

AMAXAMIN

2 21( )

2 2MAX MAX MIN

MAXMAX MIN

P A Ax AP

A A

3 3

2 2 21

3 3MAX MAX MIN

MAXMAX MIN

P A AA P

A A

Since acceleration mean for both models is non-zero it must be considered in the target equation of motion. Thus, an inhomogeneous driving input must be calculated.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Target ModelsTarget Models

Inhomogeneous Driving Input for Biased ModelsInhomogeneous Driving Input for Biased Models

1 Taccu k e

2

( 1)

1 ( 1) 1 1 1 exp 10

0 1 1 1 exp 1 0

10 0 exp 1

k T

kT

k T k T k T

k k T w d

k T

u

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

KalmanKalmanFilterFilter

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

State VectorState Vector

Tx y z x y z x y zX

Used for coordinate frame transformations, implementing rotations through a 9x9 block

diagonal matrix.

Used for coordinate frame transformations, implementing rotations through a 9x9 block

diagonal matrix.

Tx x x y y y z z zX

Used for filtering, also through a 9x9 block diagonal matrix.

Used for filtering, also through a 9x9 block diagonal matrix.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

Singer’s Classical Model – ParametersSinger’s Classical Model – Parameters

0.05 PMAX=0.05

-10m/s2 AMAX=10m/s20

P0=0.1

p(a)

a

0.04

HorizontalHorizontalAxisAxis

0.05 PMAX=0.05

-50m/s2 AMAX=50m/s20

P0=0.1

p(a)

a

0.008

VerticalVerticalAxisAxis

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

Single Side P.D.F. – ParametersSingle Side P.D.F. – Parameters

PropulsionPropulsionModelModel

0.05 PMAX=0.05

-10m/s2 AMAX=10m/s20

P0=0.1

p(a)

a

0.04

0.7

80m/s20

p(a)

a

0.0038

VerticalVerticalChannelChannel

Horizontal Horizontal ChannelChannel

BallisticBallisticModelModel

VerticalVerticalChannelChannel

Horizontal Horizontal ChannelChannel

0.05 PMAX=0.05

-5m/s2 AMAX=5m/s20

P0=0.1

p(a)

a

0.04

-10m/s2 0

1

p(a)

a

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

Single Side P.D.F. – Parameter AdjustmentSingle Side P.D.F. – Parameter AdjustmentA

tla

s R

ad

ar

Atl

as

Ra

da

rA

do

ur

Rad

ar

Ad

ou

r R

ada

r

Propelled PhasePropelled Phase Ballistic PhaseBallistic Phase

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Kalman FilterThe Kalman Filter

Shifted Gate P.D.F. – Parameter AdjustmentShifted Gate P.D.F. – Parameter AdjustmentA

tla

s R

ad

ar

Atl

as

Ra

da

rA

do

ur

Rad

ar

Ad

ou

r R

ada

r

Propelled PhasePropelled Phase Ballistic PhaseBallistic Phase

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

MultipleMultipleModelsModels

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

ConceptConcept

Applicability of model 3

Applicability of model 1

Applicability of model 2

State space of interest

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

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

Sensors

Filter 1

Filter 2

Filter n

ProbabilityCalculation

CombineEstimates Output

estimate

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

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

11

22

1 1exp | 1

22 det | 1

Ti i i im

i

k k k k kk k

r S rS

1

ˆ ˆ|n

i iik k k

y y

,1ˆ ˆ ˆ ˆ| | | | | |

Tn

yy i i yy i iik k k k k k k k k k k k k

P P y y y y

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

MHT Probability Along TrajectoryMHT Probability Along Trajectory

Radar AdourRadar Adour Radar AtlasRadar Atlas

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

MHT Covariance Output AnalysisMHT Covariance Output AnalysisMultiple ModelsMultiple Models

MHT Covariance Output AnalysisMHT Covariance Output Analysis

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

Switching ModelsSwitching Models

11 1 when 1 211 0 when 1 2

1 1 1

Propelled

Propelled

Ballistic Propelled

Output Propelled

Output Propelled

Output Output

k k

k k

k k

Radar AdourRadar Adour Radar AtlasRadar Atlas

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

MHT Covariance Output AnalysisMHT Covariance Output Analysis

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Multiple ModelsMultiple Models

MHT Vertical Acceleration ResultsMHT Vertical Acceleration Results

Radar AdourRadar Adour Radar AtlasRadar Atlas

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

DataDataFusionFusionProcessProcess

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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 AssuredConsistency Assured

Consistency NOT AssuredConsistency NOT Assured

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

Covariance Intersection – Geometric InterpretationCovariance Intersection – Geometric Interpretation

Kalman Filter(independence between

Paa and Pbb)

CovarianceIntersection

Pcc for many choices of Pab

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

Covariance Intersection EquationsCovariance Intersection Equations

CI EquationsCI Equations

1 1 11 ... n

1 1 n ncc a a a aP P P

1 1 11 1 ...

n nn n 1 1cc a a a aP c P a P a

11 ini

The The nn 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.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

CI Results – Singer’s Classical ModelCI Results – Singer’s Classical Model

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

CI Results – Singer’s Classical ModelCI Results – Singer’s Classical Model

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

CI Results – Singer’s Classical ModelCI Results – Singer’s Classical Model

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

CI Results – Singer’s Classical ModelCI Results – Singer’s Classical Model

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

CI Results – Singer’s Classical ModelCI Results – Singer’s Classical Model

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

The Data Fusion ProcessThe Data Fusion Process

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison ofComparison ofData FusionData Fusion

MethodsMethods

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Measurement FusionMeasurement Fusion

Fusion

xk-1|k-1 xk|k-1 xk|k

Kalman Filtering

Prediction Correction

z-1

zk1 zk

2

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Measurement FusionMeasurement Fusion

ADOUR

ATLAS

Spherica-to-cartesian transformation

rotation andtranslation

Spherical-to-cartesian transformation

Kalman Filtering

(Singer’s Classical)

rotation andtranslation

MeasurementFusion

FusedEstimate

11 1 1 2 2 1k k k k k k kz z R R R z z

11 11 2

k k kR R R

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Measurement Fusion ResultsMeasurement Fusion Results

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Measurement Fusion ResultsMeasurement Fusion Results

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Track-to-track FusionTrack-to-track Fusion

Fu

sio

n

xk-1|k-1 xk|k-1 xk|k

Kalman Filter #2

Prediction Correction

z-1

xk-1|k-1 xk|k-1 xk|kPrediction Correction

z-1

Kalman Filter #1

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Track-to-track FusionTrack-to-track Fusion

11 1 12 1 2 12 21 2 1| | | | | | | | | |ˆ ˆ ˆ ˆk k k k k k k k k k k k k k k k k k k kx x P P P P P P x x

12 1 1 12 2 2 1 1 2 2| 1 1| 1 1 1 1 1

T TT Tk k k k k k k k k k k k k k k k kP I K H F P F I K H I K H Q I K H

ADOUR

ATLAS

Spherical-to-cartesian transformation

Kalman filtering(Singer’s Classical)rotation and translation

Spherical-to-cartesian transformation

Kalman filtering(Singer’s Classical)

rotation and translation

Track-to-track Fusion

Fused Estimate

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Track-to-track Fusion ResultsTrack-to-track Fusion Results

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Track-to-track Fusion ResultsTrack-to-track Fusion Results

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Comparison of Data Fusion MethodsComparison of Data Fusion Methods

Computational EffortComputational Effort

Measurement Fusion

Fusion and filteringTotal:19.2s

Cost:1.019.2s

Track-to-track Fusion

KFAdour KFAtlas Fusion Total:30.5s

Cost:1.62.0s 3.8s 24.7s

Multiple Models and

CI

KFAdour

Ballistic

KFAdour

PropulsionMHTAdour Fusion

Total:71.3s

Cost:3.7

3.5s 3.6s 3.9s

60.0sKFAtlas

Ballistic

KFAtlas

PropulsionMHTAtlas

3.5s 3.6s 4.2s

NOTE: These CPU times consider a 500s tracking period for radar Atlas instead of 963s since raw data for both radars shall correspond to a same time interval in order to be fused.

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact PointImpact PointPredictionPrediction

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Reference System TransformationReference System Transformation

' ' '

' ' '

' '

ˆsin cos sin cos cos

ˆsin sin cos cos sin

ˆcos sin

x y z

x y z

x z

X X X

X X X

X X

AX x

y

z

ˆ ˆ ˆcos cos cos sin sinTR BR x y z

ˆ' sin cos sin sin cos '

ˆsin cos '

ˆcos cos cos sin sin '

x y z

x y

x y z

X X X

X X

X X X

X x

y

z

NED > Earth FrameNED > Earth Frame

When Transforming Position RB shall be addedWhen Transforming Position RB shall be added

Earth Frame > NEDEarth Frame > NED

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Impact Point CalculationImpact Point Calculation

Mi

Ni

Mti

Ri

i

ti

Rti

O (centro da Terra)

Vi

dRi

dt

Ri didt

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance Ellipsoids

1P

( )-1Position Covariance

( )-1Velocity CovarianceCovariance

Eigeinvalues providesellipsoid axis

Eigeinvectors providesellipsoid orientation

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance Ellipsoids

2

23

2( )

2

kkP k erf ke

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance EllipsoidsVelocityVelocityEllipsoidEllipsoid

AccelerationAccelerationVectorVector

Velocity Vector

Velocity Vector

121 vertices per ellipsoid

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

PositionPositionEllipsoidEllipsoid

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Covariance EllipsoidsCovariance Ellipsoids

PositionPositionEllipsoidEllipsoid

VelocityVelocityEllipsoidEllipsoid

AccelerationAccelerationVectorVector

Velocity Vector

Velocity Vector

Total of 121 impact pointson Earth’s surface

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Effect of Neglecting Position CovarianceEffect of Neglecting Position Covariance

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Impact Point Maximum UncertaintyImpact Point Maximum Uncertainty

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Impact Area – Propelled FlightImpact Area – Propelled Flight

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Impact Point PredictionImpact Point Prediction

Impact Area – TrajectoryImpact Area – Trajectory

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

Data Fusion and Multiple Models Filtering for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case – Julio Cesar Bolzani de Campos Ferreira 15/12/2004

Obrigado