covariance intersection-based sensor fusion with local multiple model hypothesis testing for...
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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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