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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 Professional Master Dissertation – 15/12/2004. Contents. Multiple Hypothesis Testing. Introduction. Data Fusion Process. Proposed

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

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  1. 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

  2. Contents Multiple Hypothesis Testing Introduction Data Fusion Process Proposed Approach Reference Coordinate Transformations Comparison of Data Fusion Methods Impact Point Prediction Target Models Kalman Filter

  3. Introduction

  4. Introduction Addressed Technology Potential Applications Launch Vehicle Tracking Air Traffic Control (ATC) Remote Sensing Air and Ground Surveilance Robot Guidance

  5. Introduction Payload Orbital Injection • Poor estimates may cause payload loss • Demands accurate estimation of position and velocity for prediction of the orbit parameters

  6. Introduction Impact Point Prediction • IPP has a fundamental role in safety-of-flight • Relies on vehicle position and velocity estimates

  7. Proposed Approach

  8. Proposed Approach Problem Overview Free Flight Parachute Deployed Propelled Flight Long Distance Short Distance

  9. Proposed Approach CI Fusion ADOUR ATLAS CI FUSION OUTPUT Exploits the complementary characteristics of SHORT and LONG range radars.

  10. Proposed Approach Kalman Filtering Kalman Filter ADOUR ATLAS CI FUSION OUTPUT Kalman Filter Provides position, velocity, and acceleration estimates and their corresponding covariance.

  11. Proposed Approach Multiple Hypothesis Testing ADOUR ATLAS CI FUSION OUTPUT KFBALLISTIC KFBALLISTIC M H T M H T KFPROPELLED KFPROPELLED Multiple models cover both propelled and ballistic flight behaviors.

  12. Proposed Approach Reference Frame Transformations ADOUR ATLAS CI FUSION OUTPUT KFBALLISTIC KFBALLISTIC M H T M H T KFPROPELLED KFPROPELLED Fusion is performed in a common reference frame, demanding local-level estimates to be rotated and translated.

  13. Proposed Approach De-biased Spherical-to-Cartesian Transformation ADOUR ATLAS CI FUSION OUTPUT KFBALLISTIC KFBALLISTIC M H T M H T KFPROPELLED KFPROPELLED Cartesian coordinates are appropriate to accomplish the necessary rotation and translation transformations.

  14. Reference Coordinate Frames

  15. Reference Coordinate Frames De-biased Spherical-to-Cartesian Transformation Biased Transformation PURE GEOMETRICAL TREATEMENT Subtracting the bias… De-biased transformation

  16. Reference Coordinate Frames De-biased Spherical-to-Cartesian Transformation Target distance and signal-to-noise ratio (SNR) affect the slant range variance. D SNR data Transforming from uncorrelated spherical measurement errors into de-biased cartesian ones gives rise to correlated measurement errors.

  17. Reference Coordinate Frames Radar Frame to Launch-Pad Frame Transformation Y Rotação + Translação Z X (2,2) Y X (1,1) Z

  18. Reference Coordinate Frames Radar Frame to Launch-Pad Frame Transformation z z z x x x y y y

  19. Reference Coordinate Frames Radar Frame to Launch-Pad Frame Transformation

  20. Target Models

  21. Target Models Singer’s Classical Model  = 0 p(a) PMAX P0 PMAX a -AMAX 0 AMAX

  22. Target Models Singer’s Classical Model State Transition Matrix

  23. Target Models Singer’s Adapted Models Single Side p.d.f. Propulsion Ballistic Shifted Gate p.d.f. Singer’s Classical Model Propulsion Ballistic

  24. Target Models Single Side P.D.F. / Shifted Gate P.D.F. p(a) p(a) P0 PMAX PMAX a a 0 0 AMIN A AMAX AMAX 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.

  25. Target Models Inhomogeneous Driving Input for Biased Models

  26. Kalman Filter

  27. 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.

  28. The Kalman Filter Singer’s Classical Model – Parameters Vertical Axis Horizontal Axis p(a) p(a) 0.04 0.008 P0=0.1 P0=0.1 0.05 0.05 PMAX=0.05 PMAX=0.05 a a -50m/s2 -10m/s2 0 0 AMAX=10m/s2 AMAX=50m/s2

  29. The Kalman Filter Single Side P.D.F. – Parameters Propulsion Model Vertical Channel Horizontal Channel Ballistic Model Vertical Channel Horizontal Channel p(a) p(a) p(a) p(a) 0.04 0.04 0.0038 P0=0.1 P0=0.1 0.7 0.05 0.05 1 PMAX=0.05 PMAX=0.05 a a a a -10m/s2 -5m/s2 0 -10m/s2 0 0 AMAX=10m/s2 AMAX=5m/s2 80m/s2 0

  30. The Kalman Filter Single Side P.D.F. – Parameter Adjustment Adour Radar Propelled Phase Ballistic Phase Atlas Radar

  31. The Kalman Filter Shifted Gate P.D.F. – Parameters Propulsion Model Vertical Channel Horizontal Channel Ballistic Model Vertical Channel Horizontal Channel p(a) p(a) p(a) 0.04 0.04 0.9 0.3 0 P0=0.1 P0=0.1 0.005 0.07 0.05 0.05 PMAX=0.05 PMAX=0.05 a a a a -5m/s2 -10m/s2 0 -15m/s2 0 0 70m/s2 -10m/s2 AMAX=10m/s2 AMAX=5m/s2 75m/s2 -5m/s2 90m/s2 0

  32. The Kalman Filter Shifted Gate P.D.F. – Parameter Adjustment Adour Radar Propelled Phase Ballistic Phase Atlas Radar

  33. Multiple Models

  34. Multiple Models Concept Applicability of model 3 Applicability of model 2 Applicability of model 1 State space of interest

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

  36. Multiple Models Multiple Hypothesis Testing (MHT)

  37. Multiple Models MHT Probability Along Trajectory Radar Adour Radar Atlas

  38. Multiple Models MHT Covariance Output Analysis Multiple Models MHT Covariance Output Analysis

  39. Multiple Models Switching Models Radar Adour Radar Atlas

  40. Multiple Models MHT Covariance Output Analysis

  41. Multiple Models MHT Vertical Acceleration Results Radar Adour Radar Atlas

  42. Data Fusion Process

  43. The Data Fusion Process Issues on System’s Statistics True Covariance Consistency Assured Consistency NOT Assured Linear Update and Covariance

  44. The Data Fusion Process Covariance Intersection – Geometric Interpretation Pcc for many choices of Pab Covariance Intersection Kalman Filter (independence between Paa and Pbb)

  45. The Data Fusion Process Covariance Intersection Equations CI Equations The n parameters are used to minimize the determinant of Pcc and is recalculated for every update.

  46. The Data Fusion Process CI Results – Singer’s Classical Model

  47. The Data Fusion Process CI Results – Singer’s Classical Model

  48. The Data Fusion Process CI Results – Singer’s Classical Model

  49. The Data Fusion Process CI Results – Singer’s Classical Model

  50. The Data Fusion Process CI Results – Singer’s Classical Model

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