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ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones

ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones Professor George H. Born Lecture 25: Kalman Filter Case Study. Announcements. Homework 8 Due Friday Lecture Quiz Due by 5pm on Wednesday Exam 2 – Friday, November 8

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ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones

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  1. ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones Professor George H. Born Lecture 25: Kalman Filter Case Study

  2. Announcements • Homework 8 Due Friday • Lecture Quiz • Due by 5pm on Wednesday • Exam 2 – Friday, November 8 • Covers material through the end of this week • Accumulative in the sense that some topics, e.g., probability and statistics, used in the sequential filters

  3. Kalman Filter Case Study - Introduction

  4. Example – Problem Statement • Ballistic trajectory with unknown start/stop • Red band indicates time with available observations Obs. Stations Start of filter

  5. Example – Problem Statement • Object in ballistic trajectory under the influence of drag and gravity • Nonlinear observation model • Two observations stations

  6. Example – Problem Statement

  7. Filter Characterization • What should we look at to characterize the filter performance? • Residuals (pre-/post-fit) • Covariance • State Estimate • There are different ways to visualize these • We will consider the case where we have a known truth for comparison

  8. Filter Residuals over Time Station 1 Station 2 • Blue – Range • Green – Range-Rate

  9. Observation Residual Histograms Postfits Prefits

  10. State Error and Uncertainty Velocity Position

  11. What are some of the things we may want to consider adding to our filter?

  12. Kalman Filter Case Study – Filter Saturation

  13. Process Noise • To prevent filter saturation, we add a constant term to the covariance time update to set a minimum value: • This is usually referred to as process noise • More typically based on stochastic acceleration (more on this in November)

  14. State Estimate with Process Noise Velocity Position

  15. Residuals with Process Noise Station 1 Station 2

  16. Residual Histogram with Process Noise Postfits Prefits

  17. Kalman Filter Case Study – Observation Editing

  18. Process Noise • Compute the prefit residual variance via • An observation is not processed in the filter if:

  19. Kalman Filter with Scalar Inversion

  20. Kalman Filter with Scalar Inversion

  21. Residuals with Observation Editing Station 1 Station 2

  22. Residual Histograms w/ Editing Postfits Prefits

  23. Filter Accuracy w/ Editing Velocity Position

  24. Kalman Filter Case Study – Bias Estimation

  25. Bias Estimation • To estimate the bias, we add it to the estimated state vector

  26. Residual Histograms w/o Bias Estimation Postfits Prefits

  27. Residual Histograms w/ Bias Estimation Postfits Prefits

  28. Residuals without Bias Estimation Station 1 Station 2

  29. Residuals w/ Bias Estimation Station 1 Station 2

  30. Accuracy w/ Bias Estimation Velocity Position

  31. Accuracy w/o Bias Estimation Velocity Position

  32. Filter Estimated State Correlation Proc. Noise, Editing, Bias Est. No Augmentation

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