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

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ASEN 5070: Statistical Orbit Determination I Fall 2015

ASEN 5070: Statistical Orbit Determination I Fall 2015

ASEN 5070: Statistical Orbit Determination I Fall 2014

ASEN 5070: Statistical Orbit Determination I Fall 2015

ASEN 5070: Statistical Orbit Determination I Fall 2015

Presentation transcript:

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

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

University of Colorado Boulder 3 Information Filter

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

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

University of Colorado Boulder 6  How about the EKF?

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

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?

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

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

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

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

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

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 !

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

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?

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

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

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

University of Colorado Boulder 20

University of Colorado Boulder 21

University of Colorado Boulder 22

University of Colorado Boulder 23 FCQs