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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 41: Monte Carlo Sampling and Semester Review. Announcements. No lecture quiz this week Final Exam Due December 16 B y noon for in-class students

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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 41: Monte Carlo Sampling and Semester Review

  2. Announcements • No lecture quiz this week • Final Exam Due December 16 • By noon for in-class students • By 11:59pm for CAETE students • Final Project Due December 16 • By noon for in-class students • By 11:59pm for CAETE Students

  3. Monte Carlo Analysis

  4. How do I characterize the possible performance of my filter? • There are many unknowns in orbit determination. What are some?

  5. How do I characterize the possible performance of my filter? • There are many unknowns in orbit determination • Dynamics Model • Dynamics Errors (systematic and stochastic) • Measurement Model • Measurement Noise • Many of these may be characterized using covariance analysis (CH. 6, StatOD 2) • Given the large number of random inputs, how would we characterize the possible OD performance when covariance analysis is limited?

  6. Monte Carlo Analysis • Consider many different types of models and model errors • What about the accuracy of input models? • Example: Gravity Field • Estimation of the gravity field still has a variance. • How do we consider the filter performance with such errors?

  7. Monte Carlo Sampling of Multivariate Gaussian

  8. Monte Carlo Sampling of Gravity Field

  9. Example of Monte Carlo Sampling

  10. Semester Review

  11. Review Exercise • Individual Exercise: • List five things that you learned in this course • Group Exercise: • In pairs, reduce the list down to the two most important things you learned in this course • Class Exercise: • Now, let’s make a top ten list of things learned during this semester

  12. Top 10+ List • Kalman filter (and all it encompasses) • Assess the performance of filters • State, covariance, residuals, other design elements, what filter to use, etc. • The general estimation problem (difficulties) • Numeric considerations • Least squares estimation (batch processing) • Probability and Stats (probability ellipsoids) • Linearization and STM • Observability • Accurate uncertainty quantification • Process noise • LaTeX • What do we do without a truth to compare to? • Linear algebra (new elements covered in this class) • Square root filters • Sequential versus batch processing

  13. Top 10+ • Gauss Markov processes and use in process noise • Smoothing • StatOD is fun! (George’s answer) • Applicable to many different fields

  14. Wished learned more about? • Different Measurement types • Angles-only estimation • Doppler • Difficulties of such measurements • GNSS/GPS • Increased variety of problems/applications • Real data (but tough)

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