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Statistical Orbit Determination: Exam 1 Review and Concepts Overview

This document serves as a comprehensive review for Exam 1 in the Statistical Orbit Determination course (ASEN 5070). It covers key topics such as the Flat Earth Problem, Linearization Procedure, State Transition Matrix, and methods of Least Squares including weighted and unweighted approaches. The material also discusses the dimensions of state and observation vectors, the relationships between various parameters, and different cases for the number of observations and equations. This review is essential for mastering the fundamental concepts in statistical orbit determination.

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Statistical Orbit Determination: Exam 1 Review and Concepts Overview

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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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