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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 40: Information Filter. Announcements. No lecture quiz this week Final Exam Due December 16 B y noon for in-class students By 11:59pm for CAETE s tudents

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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 40: Information Filter

  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. Information Filter

  4. Project Kalman Filter Variance • Well, we know that the CKF has problems…

  5. Project Kalman Filter Variance • How about the Joseph formulation of the measurement update?

  6. Project Kalman Filter Variance • How about the EKF?

  7. Project Kalman Filter Variance • How about the Potter square-root filter?

  8. Project Kalman Filter Variance • What are we unable to do with Potter that we can do with the CKF?

  9. Minimum Variance as a Sequential Processor • Time Update • Measurement Update:

  10. Project Kalman Filter Variance • What if we go back to the minimum variance?

  11. Minimum Variance as Sequential Processor • If I don’t want to invert the information matrix, do I have another option?

  12. Information Filter Measurement Update • Well, that was easy. • What about the time update?

  13. Information Filter Time Update Derivation • What can we do to simplify this? (Assume Qk non-singular)

  14. Time Update of Information Matrix • Require that Qk be non-singular • Do not need to invert the information matrix Still need to maintain information matrix separate from D !

  15. Time Update of State Estimate • From the time update of the information matrix:

  16. Information Filter • Can I initialize the filter with an infinite a priori state covariance matrix? • What happens if we have very accurate measurements?

  17. State/Covariance Generation • Once the information matrix is positive definite:

  18. Why use the Information Filter? • Provides a more numerically stable solution • Stability equals that of the Batch, but in a sequential implementation • Don’t need to generate state/covariance until needed • Square-root information filter (SRIF) • Refined through extensive use in POD • Includes smoothing capabilities

  19. Information Filter with Bierman’s Problem

  20. Problem Statement

  21. Kalman Filter Result with Limited Precision

  22. Project Q&A

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