Presentation on theme: "University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 28: Orthogonal Transformations."— Presentation transcript:
University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 28: Orthogonal Transformations
University of Colorado Boulder Lecture quiz due at 5pm Exam 2 – Friday, November 7 2
University of Colorado Boulder Minimum Variance Conventional Kalman Filter Extended Kalman Filter Prediction Residuals Handling Observation Biases Numeric Considerations in the Kalman Batch vs. CKF vs. EKF Effects of Uncertainties on Estimation Potter Square-Root Filter Cholesky Decomposition w/ Forward and Backward substitution Singular Value Decomposition Methods 3
University of Colorado Boulder 4 Least Squares via Orthogonal Transformations
University of Colorado Boulder The method for selecting R defines a particular algorithm ◦ Givens Transformations (Section 5.4) ◦ Householder Transformation (Section 5.5) ◦ Gram-Schmidt Orthogonalization Not in the book and we won’t cover it 9
University of Colorado Boulder 10 LS Solution via Givens Transformations
University of Colorado Boulder Hence, Givens transformations give us a solution for the state 38 Home Exercise: Why is this true? Note: R is not equal to H ! Still a problem w/ P !
University of Colorado Boulder Givens uses a sequence of rotations to generate the R matrix Instead, Householder transformations use a sequence of reflections to generate R ◦ See the book for details 39
Your consent to our cookies if you continue to use this website.