Transcript Lecture 41
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 41: Information Filter University of Colorado Boulder Exam 3 ◦ In-class Students: Due Friday by 5pm ◦ CAETE Students: Due 11:59pm (Mountain) on 12/13 Final Project Due December 14 by noon University of Colorado Boulder 2 Project Q&A University of Colorado Boulder 3 Information Filter University of Colorado Boulder 4 Negative Values University of Colorado Boulder Well, we know that the CKF has problems… 5 Negative Values University of Colorado Boulder How about the Joseph formulation of the measurement update? 6 How about the EKF? How about the Potter square-root filter? University of Colorado Boulder 7 Time Update Measurement Update: University of Colorado Boulder 8 University of Colorado Boulder What if we go back to the minimum variance? 9 If I don’t want to invert the information matrix, do I have another option? University of Colorado Boulder 10 Well, that was easy. What about the time update? University of Colorado Boulder 11 What can we do to simplify this? (Assume Qk-1 non-singular) University of Colorado Boulder 12 Still need to maintain information matrix separate from D ! Require that Qk-1 be non-singular Do not need to invert the n×n information matrix University of Colorado Boulder 13 From the time update of the information matrix: University of Colorado Boulder 14 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 15 Once the information matrix has a sufficiently small condition number: University of Colorado Boulder 16 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 17 Information Filter with Bierman’s Problem University of Colorado Boulder 18 University of Colorado Boulder 19 University of Colorado Boulder 20 University of Colorado Boulder 21 Monte Carlo Analysis University of Colorado Boulder 22 There are many unknowns in orbit determination. What are some? University of Colorado Boulder 23 There are many unknowns in orbit determination ◦ ◦ ◦ ◦ Dynamics Model Dynamics Errors (systematic and stochastic) Measurement Model Measurement Noise Many of these may be characterized using covariance analysis (CH. 6, StatOD 2) Given the large number of random inputs, how would we characterize the possible OD performance when covariance analysis is limited? University of Colorado Boulder 24 Consider many different types of models and model errors What about the accuracy of input models? ◦ Example: Gravity Field ◦ Our best estimate of the gravity field still has a variance. How do we consider the filter performance with such errors? University of Colorado Boulder 25 University of Colorado Boulder 26 University of Colorado Boulder 27 3 2.5 2 1.5 1 0.5 0 −0.5 −1 −4 University of Colorado Boulder −2 0 2 4 6 28