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University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 41: Information Filter
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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 2
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University of Colorado Boulder 3 Project Q&A
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University of Colorado Boulder 4 Information Filter
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University of Colorado Boulder 5 Well, we know that the CKF has problems… Negative Values
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University of Colorado Boulder 6 How about the Joseph formulation of the measurement update? Negative Values
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University of Colorado Boulder How about the EKF? How about the Potter square-root filter? 7
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University of Colorado Boulder Time Update 8 Measurement Update:
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University of Colorado Boulder 9 What if we go back to the minimum variance?
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University of Colorado Boulder 10 If I don’t want to invert the information matrix, do I have another option?
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University of Colorado Boulder Well, that was easy. What about the time update? 11
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University of Colorado Boulder What can we do to simplify this? 12 (Assume Q k-1 non-singular)
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University of Colorado Boulder Require that Q k-1 be non-singular Do not need to invert the n×n information matrix 13 Still need to maintain information matrix separate from D !
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University of Colorado Boulder From the time update of the information matrix: 14
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University of Colorado Boulder 15 Can I initialize the filter with an infinite a priori state covariance matrix? What happens if we have very accurate measurements?
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University of Colorado Boulder Once the information matrix has a sufficiently small condition number: 16
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University of Colorado Boulder 17 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
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University of Colorado Boulder 18 Information Filter with Bierman’s Problem
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University of Colorado Boulder 22 Monte Carlo Analysis
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University of Colorado Boulder There are many unknowns in orbit determination. What are some? 23
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University of Colorado Boulder 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? 24
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University of Colorado Boulder 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? 25
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