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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 15: Numerical Compensations. Announcements. Exam 1 Final Project Homework 5 is not graded…neither is the test. Homework 6 due Today

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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 15: Numerical Compensations

  2. Announcements • Exam 1 • Final Project • Homework 5 is not graded…neither is the test. • Homework 6 due Today • Homework 7 due next week (Tuesday!) • It’s okay to use Matlabto compute partials and to output them. But verify them. • Concept Quizzes to resume Monday! • Guest lecturer next week 10/25

  3. Exam 1 Debrief • Too easy? • Too short?

  4. Exam 1 Debrief

  5. Exam 1 Debrief True. The transpose of a column of zeros becomes a row of zeros. That row propagates through the whole system and the HTH matrix becomes singular.

  6. Exam 1 Debrief

  7. Exam 1 Debrief False. Consider H-tilde = [a, b, 0]^T and Phi = 1.

  8. Exam 1 Debrief

  9. Exam 1 Debrief

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  20. Exam 1 Debrief

  21. Exam 1 Debrief G(t) = z(t) is the simplest representation of the observation. If you solve the EOM for z, you can also get partials wrt z-dot and c, which is more information (optional).

  22. Exam 1 Debrief

  23. Exam 1 Debrief Can’t use a Laplace Transform because A(t) is time-dependent!

  24. Exam 1 Debrief

  25. Exam 1 Debrief

  26. Topics coming up • Conventional Kalman Filter (CKF) • Extended Kalman Filter (EKF) • Numerical Issues • Machine precision • Covariance collapse • Numerical Compensation • Joseph, Potter, Cholesky, Square-root free, unscented, Givens, orthogonal transformation, SVD • State Noise Compensation, Dynamical Model Compensation

  27. Stat OD Conceptualization • Full, nonlinear system:

  28. Stat OD Conceptualization • Linearization

  29. Stat OD Conceptualization • Observations

  30. Stat OD Conceptualization • Observation Uncertainties

  31. Stat OD Conceptualization • Least Squares (Batch)

  32. Stat OD Conceptualization • Least Squares (Batch)

  33. Stat OD Conceptualization • Least Squares (Batch)

  34. Stat OD Conceptualization • Least Squares (Batch)

  35. Stat OD Conceptualization • Least Squares (Batch)

  36. Stat OD Conceptualization • Least Squares (Batch) • Replace reference trajectory with best-estimate • Update a priori state • Generate new computed observations Iterate a few times.

  37. Stat OD Conceptualization • Least Squares (Batch) Note: the linearization assumption will gradually break down. Toward the end, the truth will begin to deviate further from the nominal. Select a measurement interval that balances the number of observations with the length of time being used.

  38. Conceptualization of the Conventional Kalman Filter (Sequential Filter)

  39. Stat OD Conceptualization • Conventional Kalman

  40. Stat OD Conceptualization • Conventional Kalman

  41. Stat OD Conceptualization • Conventional Kalman

  42. Stat OD Conceptualization • Conventional Kalman

  43. Stat OD Conceptualization • Conventional Kalman

  44. Stat OD Conceptualization • Conventional Kalman

  45. Stat OD Conceptualization • Conventional Kalman

  46. Stat OD Conceptualization • Conventional Kalman

  47. Stat OD Conceptualization • Conventional Kalman

  48. Stat OD Conceptualization • Conventional Kalman

  49. Stat OD Conceptualization • Conventional Kalman

  50. Stat OD Conceptualization • Conventional Kalman

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