1. University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 38: Information Filter

2. University of Colorado Boulder  Homework 11 due on Friday ◦ Sample solutions posted online  Lecture quiz due by 5pm on Friday  Exam 3 Posted On Friday ◦ In-class Students: Due December 12 by 5pm ◦ CAETE Students: Due 11:59pm (Mountain) on 12/14  Final Project Due December 15 by noon 2

3. University of Colorado Boulder 3 Information Filter

4. University of Colorado Boulder 4  Well, we know that the CKF has problems… Negative Values

5. University of Colorado Boulder 5  How about the Joseph formulation of the measurement update? Negative Values

6. University of Colorado Boulder 6  How about the EKF?

7. University of Colorado Boulder 7  How about the Potter square-root filter?

8. University of Colorado Boulder 8  Based on the class so far, what are we unable to do with Potter that we can do with the CKF?

9. University of Colorado Boulder  Time Update 9  Measurement Update:

10. University of Colorado Boulder 10  What if we go back to the minimum variance?

11. University of Colorado Boulder 11  If I don’t want to invert the information matrix, do I have another option?

12. University of Colorado Boulder  Well, that was easy.  What about the time update? 12

13. University of Colorado Boulder  What can we do to simplify this? 13 (Assume Q k non-singular)

14. University of Colorado Boulder  Require that Q k be non-singular  Do not need to invert the information matrix 14 Still need to maintain information matrix separate from D !

15. University of Colorado Boulder  From the time update of the information matrix: 15

16. University of Colorado Boulder 16  Can I initialize the filter with an infinite a priori state covariance matrix?  What happens if we have very accurate measurements?

17. University of Colorado Boulder  Once the information matrix is positive definite: 17

18. University of Colorado Boulder 18  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. University of Colorado Boulder 19 Information Filter with Bierman’s Problem

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23. University of Colorado Boulder 23 FCQs