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ASEN 5070 Statistical Orbit Determination I Fall 2012 Professor Jeffrey S. Parker

ASEN 5070 Statistical Orbit Determination I Fall 2012 Professor Jeffrey S. Parker Professor George H. Born Lecture 21: Exam 2 Debrief and More Fun. Announcements. Homework 9 due this week. Make sure you spend time studying for the exam Homework 10 out Thursday.

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ASEN 5070 Statistical Orbit Determination I Fall 2012 Professor Jeffrey S. Parker

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  1. ASEN 5070 Statistical Orbit Determination I Fall 2012 Professor Jeffrey S. Parker Professor George H. Born Lecture 21: Exam 2 Debrief and More Fun

  2. Announcements • Homework 9 due this week. • Make sure you spend time studying for the exam • Homework 10 out Thursday. • Give you a small reprieve to focus on HW9.

  3. Quiz 17 Review

  4. Quiz 17 Review

  5. Quiz 17 Review

  6. Quiz 17 Review The matrix of partials of one observation relative to the state parameters is identical to the other matrix.

  7. Quiz 17 Review

  8. Quiz 17 Review

  9. Quiz 17 Review

  10. Quiz 17 Review

  11. HW#9 • Due this Thursday

  12. HW#9 Tip • Try building x-hat from the data given online. If you can get that to work then you’ll have a better chance of getting your own x-hat to match the solutions! • Grab the accumulated matrices HTWH and HTWY. • Try computing inv(HTWH+P0bar)*HTWY

  13. HW#9 Tip • Your x-hat should match to at least 1 digit of precision in each parameter (hopefully 3). It will not be identical! • Different integrator • Different tolerance • Different computer • Different inverter • inv(HTWH+P0bar) is very poorly conditioned (e-34 I believe) • Matlab’s “inv” function will not produce the right answer.

  14. HW#9 Tip • inv(HTWH+P0bar) is very poorly conditioned (e-34 I believe) • R = chol( HTWH+P0bar) • Inv(R) is also poorly conditioned, but only e-1.This is far better. • If RTR = (HTWH+P0bar), what is inv( RTR )?

  15. Exam 2 Debrief • Overall, the class did well. Most everyone grasped the concepts. • Nobody got 100% - so don’t worry if your grade was lower than 90. (curve TBD)

  16. Exam 2 Debrief

  17. Exam 2 Debrief

  18. Exam 2 Debrief

  19. Exam 2 Debrief

  20. Exam 2 Debrief

  21. Exam 2 Debrief

  22. Exam 2 Debrief

  23. Exam 2 Debrief

  24. Exam 2 Debrief

  25. Exam 2 Debrief

  26. Exam 2 Debrief

  27. Exam 2 Debrief i.e., High Precision but low accuracy!

  28. Exam 2 Debrief

  29. Exam 2 Debrief

  30. Exam 2 Debrief

  31. Exam 2 Debrief Only guarantees a nonnegative definite!

  32. Exam 2 Debrief

  33. Exam 2 Debrief

  34. Exam 2 Debrief

  35. Exam 2 Debrief 4x3

  36. Exam 2 Debrief

  37. Exam 2 Debrief [3x4]*[4x3] = [3x3] (hint: it’s always nxn)

  38. Exam 2 Debrief

  39. Exam 2 Debrief 1. one observation vector includes 4 independent pieces of information. We only need 3 pieces of information.

  40. Exam 2 Debrief

  41. Exam 2 Debrief Then Phi, A, y, H-tilde x-hat, P, x-bar, P-bar

  42. Exam 2 Debrief

  43. Exam 2 Debrief X* (the reference trajectory) x-bar (the a priori deviation, nominally zero) P-bar (the a priori covariance) Y_i (the observations) omega and sigma (though that’s specific to this problem and it’s okay if you didn’t include that!

  44. Exam 2 Debrief

  45. Quick Break • Next up: Stuff. • Prediction Residual • Givens • Householder • Future: Process Noise, Smoothing

  46. The Prediction Residual

  47. The Prediction Residual

  48. The Prediction Residual

  49. The Prediction Residual This would be especially important in the case of the EKF

  50. Next: Orthogonal transformations: Givens, Householder

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