Transcript Lecture 13
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 13: Probability and Statistics (Part 3) University of Colorado Boulder Lecture Quiz and Homework Due Friday University of Colorado Boulder 2 Lecture Quizzes 2 & 3 Example Problem Wrap-Up Example Distributions Moment Generating Functions Variance-Covariance Matrix University of Colorado Boulder 3 Lecture Quiz 2 Results University of Colorado Boulder 4 Percent Correct: 76% You are given an estimation problem that has nonlinear dynamics and a linear observation model. Based on the discussion so far in class: ◦ You actually don’t need to linearize since the observation model is linear ◦ You only need to use an observation deviation vector ◦ You only need to use a state deviation vector ◦ You need to use both a state and an observation deviation vector University of Colorado Boulder 5 Percent Correct: 69% Which of the following is correct nomenclature/symbology introduced in the class so far: University of Colorado Boulder 6 Percent Correct: 80% If H^T*H in the above equation is positive semi-definite, then the state estimate is a minimum of the least squares cost function. ◦ True ◦ False University of Colorado Boulder 7 Percent Correct: 51% For any matrix, we can use the eigenvalues to determine if it is full rank. ◦ True ◦ False University of Colorado Boulder 8 Lecture Quiz 3 Results University of Colorado Boulder 9 Percent Correct: 72% (76% previous) You are given an estimation problem that has nonlinear dynamics and a linear observation model. Based on the discussion so far in class: ◦ You actually don’t need to linearize since the observation model is linear ◦ You only need to use an observation deviation vector ◦ You only need to use a state deviation vector ◦ You need to use both a state and an observation deviation vector University of Colorado Boulder 10 Percent Correct: 76% (80%) If H^T*H in the above equation is positive semi-definite, then the state estimate is a minimum of the least squares cost function. ◦ True ◦ False University of Colorado Boulder 11 Percent Correct: 74% Solving for the state transition matrix via a Laplace transform is only possible when A(t) is constant ◦ True ◦ False University of Colorado Boulder 12 Percent Correct: 70% The above can be a state transition matrix. ◦ True ◦ False University of Colorado Boulder 13 Example Problem Wrap-Up University of Colorado Boulder 14 University of Colorado Boulder 15 Example Distributions University of Colorado Boulder 16 Images: Wikicommons University of Colorado Boulder 17 PDF CDF Images: Wikicommons University of Colorado Boulder 18 Images: Wikicommons University of Colorado Boulder 19 University of Colorado Boulder 20 Moment Generating Functions University of Colorado Boulder 21 University of Colorado Boulder 22 University of Colorado Boulder 23 University of Colorado Boulder 24 Variance-Covariance Matrix University of Colorado Boulder 25 Covariance provides a measure of correlation between variables University of Colorado Boulder 26 Indicates the degree of linear correlations between variables University of Colorado Boulder 27 University of Colorado Boulder 28 University of Colorado Boulder 29 University of Colorado Boulder 30 University of Colorado Boulder 31 University of Colorado Boulder 32 Symmetric University of Colorado Boulder 33