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ASEN 5070: Statistical Orbit Determination I Fall 2013 Marco Balducci

ASEN 5070: Statistical Orbit Determination I Fall 2013 Marco Balducci Professor Brandon A. Jones Professor George H. Born Lecture 17: Exam 1 Review. Office Hours. Instead of Thursday office hours, I’ll have office hours between 12 and 5 on Wednesday. Outlines of Topics to Date.

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ASEN 5070: Statistical Orbit Determination I Fall 2013 Marco Balducci

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  1. ASEN 5070: Statistical Orbit Determination I Fall 2013 Marco Balducci Professor Brandon A. Jones Professor George H. Born Lecture 17: Exam 1 Review

  2. Office Hours • Instead of Thursday office hours, I’ll have office hours between 12 and 5 on Wednesday

  3. Outlines of Topics to Date • Flat Earth Problem • Linearization Procedure • State Transition Matrix • A(t), H(t), etc. • Least Squares (weighted and w/ and w/o a priori) • Minimum Norm • Probability and Statistics • Statistical Least Squares

  4. Review • What is n ? • Dimensions in the state vector • What is l ? • Number of observations • What is p ? • Dimensions in the observation vector • What is m ? • Number of equations m = p x l

  5. Review • What is n ? • Dimensions in the state vector • What is l ? • Number of observations • What is p ? • Dimensions in the observation vector • What is m ? • Number of equations m = p x l

  6. Review • What is n ? • Dimensions in the state vector • What is l ? • Number of observations • What is p ? • Dimensions in the observation vector • What is m ? • Number of equations m = p x l

  7. Review • What is n ? • Dimensions in the state vector • What is l ? • Number of observations • What is p ? • Dimensions in the observation vector • What is m ? • Number of equations m = p x l

  8. Review • What is n ? • Dimensions in the state vector • What is l ? • Number of observations • What is p ? • Dimensions in the observation vector • What is m ? • Number of equations m = p x l

  9. Review • The state has n parameters • n unknowns at any given time. • There are l observations of any given type. • There are p types of observations (range, range-rate, angles, etc) • We have p x l = mtotal equations. • Three situations: • n < m: Least Squares • n = m: Deterministic • n > m: Minimum Norm

  10. Review • Basic Nomenclature

  11. Review

  12. Review

  13. Review

  14. Best Estimate Solvers • Least Squares • Weighted Least Squares • Least Squares with a priori • Minimum Norm

  15. Review • Two Quick Questions

  16. Review

  17. Review

  18. Review • Application of Minimum Norm

  19. Review

  20. Review

  21. Review

  22. Review • Batch Processor Overview

  23. Review

  24. Review

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