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

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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 for Launch Vehicle Tracking and Impact Point Prediction: The Alcântara Case Julio Cesar Bolzani de Campos Ferreira Professional 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 15/12/2004Contents Introduction Kalman Filter Proposed Approach Reference Coordinate Transformations Multiple Hypothesis Testing Data Fusion Process Comparison of Data Fusion Methods Impact Point Prediction 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 Introduction

Introduction Addressed Technology Potential Applications Air Traffic Control (ATC) Robot Guidance Air and Ground Surveilance Remote Sensing Launch 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 parametersIntroduction Payload 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 15/12/2004Introduction Impact 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 Proposed Approach

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 Approach Problem Overview PropelledFlight Free Flight ParachuteDeployed Long Distance Short 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 Approach CI Fusion ADOURATLAS CI FUSION 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 Approach Kalman Filtering ADOURATLAS CI FUSION OUTPUT Kalman Filter Kalman Filter 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 CI FUSION OUTPUT Proposed Approach Multiple Hypothesis Testing ADOURATLAS KF BALLISTIC KF PROPELLED MHTMHT KF BALLISTIC KF PROPELLED MHTMHT 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 Approach Reference Frame Transformations CI FUSION OUTPUT KF BALLISTIC KF PROPELLED MHTMHT KF BALLISTIC KF PROPELLED MHTMHT 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 Approach De-biased Spherical-to-Cartesian Transformation CI FUSION OUTPUT KF BALLISTIC KF PROPELLED MHTMHT KF BALLISTIC KF PROPELLED MHTMHT 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 ReferenceCoordinateFrames

Reference Coordinate Frames De-biased Spherical-to-Cartesian Transformation Subtracting the bias… De-biased transformation Biased Transformation PURE 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 Frames De-biased Spherical-to-Cartesian Transformation Target distance and signal-to-noise ratio (SNR) affect the slant range variance. 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 Frames Radar 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 Frames Radar Frame to Launch-Pad Frame Transformation x y z x y z x y 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 Frames Radar Frame to Launch-Pad Frame Transformation

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 TargetModels

Target Models Singer’s Classical Model P MAX -A MAX A MAX 0 P0P0 p(a) a  = 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 Models Singer’s Classical Model State 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 Models Singer’s Adapted Models Singer’s Classical Model Single Side p.d.f. Propulsion Ballistic 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 Models Single Side P.D.F. / Shifted Gate P.D.F. P MAX A MAX 0 P0P0 p(a) a P MAX A0 p(a) a A MAX A MIN 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 Models Inhomogeneous Driving Input for Biased 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 KalmanFilter

The Kalman Filter State Vector Used for coordinate frame transformations, implementing rotations 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 Filter Maneuver Excitation Covariance Matrix State Transition Matrix Measurement Matrix Measurement Vector

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 Filter The Algorithm

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 Filter Singer’s Classical Model – Parameters 0.05P MAX = m/s 2 A MAX =10m/s 2 0 P 0 =0.1 p(a) a 0.04 HorizontalAxis 0.05P MAX = m/s 2 A MAX =50m/s 2 0 P 0 =0.1 p(a) a VerticalAxis

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 Filter Single Side P.D.F. – Parameters PropulsionModel 0.05P MAX = m/s 2 A MAX =10m/s 2 0 P 0 =0.1 p(a) a m/s 2 0 p(a) a VerticalChannel Horizontal Channel BallisticModel VerticalChannel 0.05P MAX = m/s 2 A MAX =5m/s 2 0 P 0 =0.1 p(a) a m/s 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 Filter Single Side P.D.F. – Parameter Adjustment Atlas Radar Adour Radar Propelled Phase Ballistic 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 Filter Shifted Gate P.D.F. – Parameters PropulsionModel VerticalChannel Horizontal Channel m/s a m/s 2 75m/s P MAX = m/s 2 A MAX =10m/s 2 0 P 0 =0.1 p(a) a 0.04 BallisticModel VerticalChannel Horizontal Channel -10m/s p(a) a m/s 2 -15m/s P MAX = m/s 2 A MAX =5m/s 2 0 P 0 =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 Filter Shifted Gate P.D.F. – Parameter Adjustment Atlas Radar Adour Radar Propelled Phase Ballistic 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 MultipleModels

Multiple Models Concept 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 Models Multiple Hypothesis Testing (MHT) Sensors Filter 1 Filter 2 Filter n Probability Calculation Combine Estimates 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 Models Multiple Hypothesis Testing (MHT)

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 Models MHT Probability Along Trajectory Radar Adour Radar 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 Models MHT Covariance Output Analysis Multiple Models MHT 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 Models Switching Models Radar Adour Radar 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 Models MHT 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 Models MHT Vertical Acceleration Results Radar Adour Radar 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 DataFusionProcess

The Data Fusion Process Issues on System’s Statistics Linear Update and Covariance True Covariance Consistency Assured Consistency 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 Process Covariance Intersection – Geometric Interpretation Kalman Filter (independence between P aa and P bb ) Covariance Intersection P cc for many choices of P ab

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 Process Covariance Intersection Equations CI Equations The  n parameters are used to minimize the determinant of P cc 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 Process CI 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 of Data Fusion Methods

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 Methods Measurement Fusion Fusion x k-1|k-1 x k|k-1 x k|k Kalman Filtering Prediction Correction z -1 zk1zk1 zk2zk2

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 Methods Measurement Fusion ADOUR ATLAS Spherica-to-cartesian transformation rotation and translation Spherical-to-cartesian transformation Kalman Filtering (Singer’s Classical) rotation and translation Measurement 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 Methods Measurement 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 Methods Measurement 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 Methods Track-to-track Fusion Fusion x k-1|k-1 x k|k-1 x k|k Kalman Filter #2 Prediction Correction z -1 x k-1|k-1 x k|k-1 x k|k Prediction 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 Methods Track-to-track Fusion 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 Methods Track-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 Methods Track-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 Methods Computational Effort Measurement Fusion Fusion and filtering Total: 19.2s Cost: s Track-to-track Fusion KF Adour KF Atlas Fusion Total: 30.5s Cost: s3.8s24.7s Multiple Models and CI KF Adour Ballistic KF Adour Propulsion MHT Adour Fusion Total: 71.3s Cost: s3.6s3.9s 60.0s KF Atlas Ballistic KF Atlas Propulsion MHT Atlas 3.5s3.6s4.2s 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 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 Impact Point Prediction Reference System Transformation NED > Earth Frame When Transforming Position RB shall be added Earth 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 Prediction Impact Point Calculation MiMi NiNi M ti RiRi ii  ti R ti O (centro da Terra) ViVi dR i dt R i d  i dt

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 Prediction Covariance Ellipsoids (  ) -1  Position Covariance Covariance (  ) -1  Velocity Covariance Eigeinvalues provides ellipsoid axis Eigeinvectors provides ellipsoid 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 Prediction Covariance Ellipsoids

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 Prediction Covariance Ellipsoids VelocityEllipsoid AccelerationVector Velocity Vector 121 vertices per ellipsoid 14,641 (121 2 ) impact points on Earth’s surface PositionEllipsoid

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 Prediction Covariance Ellipsoids PositionEllipsoid VelocityEllipsoid AccelerationVector Velocity Vector Total of 121 impact points on 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 Prediction Effect 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 Prediction Impact 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 Prediction Impact Area – Propelled Flight Ellipsoids Magnified 1000X Impact 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 Prediction Impact Area – Trajectory Ellipsoids Magnified 1000X Impact 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