Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Julio Cesar Bolzani de Campos Ferreira Jacques Waldmann COBEM2005 – 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 PredictionContents 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 Introduction

 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

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

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

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Proposed Approach Problem Overview PropelledFlight Free Flight ParachuteDeployed Long Distance Short Distance

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Proposed Approach CI Fusion ADOURATLAS CI FUSION 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 Approach Kalman Filtering ADOURATLAS CI FUSION OUTPUT Kalman Filter Kalman Filter 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 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.

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

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Proposed Approach De-biased Spherical-to-Cartesian Transformation CI FUSION OUTPUT KF BALLISTIC KF PROPELLED MHTMHT KF BALLISTIC KF PROPELLED MHTMHT 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 TargetModels

Target Models Singer’s Adapted Models Singer’s Classical Model 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 Models 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

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

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

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

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Multiple Models MHT Probability Along Trajectory Radar Adour Radar Atlas

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

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

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

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

Data Fusion Issues on System’s Statistics Linear Update and Covariance True Covariance Consistency assured when P aa and P bb are consistent Consistency NOT assured even when P aa and P bb are consistent P aa and P bb are consistent if:

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Data Fusion Covariance Intersection – Geometric Interpretation Kalman Filter (independence between P aa and P bb ) Covariance Intersection P cc for many choices of P ab

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction CI Equations Data Fusion Covariance Intersection Equations The  parameters are used to minimize the determinant of P cc 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 Fusion CI 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 Fusion CI 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 Fusion CI 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 Point Prediction

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Impact Point Prediction Covariance Ellipsoids (  ) -1  Position Covariance Covariance (  ) -1  Velocity Covariance 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 AccelerationVector Velocity Vector Impact Point Prediction Covariance Ellipsoids VelocityEllipsoid 121 vertices per ellipsoid 14,641 (121 2 ) impact points on Earth’s surface PositionEllipsoid

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Impact Point Prediction Covariance Ellipsoids PositionEllipsoid VelocityEllipsoid AccelerationVector Velocity Vector Total of 121 impact points on Earth’s surface

Covariance Intersection-Based Sensor Fusion with Local Multiple Model Hypothesis Testing for Sounding Rocket Tracking and Impact Point Prediction Impact Point Prediction Effect 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 Prediction Impact Area – Propelled Flight Ellipsoids Magnified 1000X Impact Area Magnified 20X

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