Transcript Lecture 26
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 26: Potter Algorithm University of Colorado Boulder Homework 8 Due Friday (10/30) Lecture Quizzes ◦ Due by 5pm Friday Exam 2 – Friday, November 6 Out of town Nov. 16-17 ◦ Guest lecture planned on the 16th University of Colorado Boulder 2 Potter Algorithm – Motivation and Derivation Chapter 5 University of Colorado Boulder 3 The condition number of P may be described by General rule of thumb: In additional to existing errors in filtering, we can lose p significant digits where: If we can’t change the condition number, is there something else we can do? University of Colorado Boulder 4 For W above, the condition number is Is there something we can do to instead operate on W ? University of Colorado Boulder 5 University of Colorado Boulder 6 University of Colorado Boulder 7 University of Colorado Boulder 8 We must process the observations one at a time If we have multiple observations at a single time, this requires that R be diagonal. What can we do if the observations at a single time have a non-zero correlation? University of Colorado Boulder 9 University of Colorado Boulder 10 University of Colorado Boulder 11 University of Colorado Boulder 12 Process the observations one at a time Repeat if multiple observations available at a single time University of Colorado Boulder More computationally expensive than Kalman, but reduces numeric error W after the measurement update is not triangular! (Important for some algorithms) Motivates the derivation of the triangular square-root method (pp. 335-340) 13 If we are given P as a priori information, how do we get W ? If P is diagonal, this is trivial: Great, but what if it isn’t diagonal? Cholesky decomposition (next week) University of Colorado Boulder 14 Cholesky Decomposition University of Colorado Boulder 15 Provides improved numeric stability Method defined by Atilde Potter algorithm assumed the processing of one measurement at a time University of Colorado Boulder 16 If we are given P as a priori information, how do we get W ? If P is diagonal, this is easy: Great, but what if it isn’t diagonal? Cholesky decomposition University of Colorado Boulder 17 Cholesky Decomposition of p.d. matrix: MATLAB: University of Colorado Boulder 18 Algorithm found in book Eq. 5.2.6 Implementations readily available in most high-level languages: MATLAB: Be sure to check the documentation for default behavior (lower or upper) University of Colorado Boulder 19