Presentation on theme: "University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 24: Numeric Considerations and."— Presentation transcript:
University of Colorado Boulder ASEN 5070: Statistical Orbit Determination I Fall 2014 Professor Brandon A. Jones Lecture 24: Numeric Considerations and Introduction to Square-Root Algorithms
University of Colorado Boulder Homework 7 Due Friday Lecture Quiz Due by 5pm on Friday 2
University of Colorado Boulder 3 Filter Saturation
University of Colorado Boulder To enforce a symmetric result, we may instead use the Potter Formulation: 10 Always yields a symmetric P Assumes that the a priori covariance is positive definite, i.e., not corrupted by previous numeric errors Does not ensure a positive definite covariance matrix You will derive the above in the homework Still applied for unbiased scenarios
University of Colorado Boulder 11 Bierman Example of Poorly Conditioned System
University of Colorado Boulder 20 Potter Algorithm – Motivation and Derivation Chapter 5
University of Colorado Boulder The condition number of P may be described by 21 With p significant digits, there are estimation difficulties as If we can’t change the condition number, is there something else we can do?
University of Colorado Boulder For W above, the condition number is 22 Is there something we can do to instead operate on W ?
University of Colorado Boulder 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? 26
University of Colorado Boulder 31 Process the observations one at a time Repeat if multiple observations available at a single time More computationally expensive than Kalman, but more accurate W after the measurement update is not triangular! (Important for some algorithms) Motivates the derivation of the triangular square-root method (pp. 335-340)
University of Colorado Boulder If we are given P as a priori information, how do we get W ? If P is diagonal, this is trivial: 32 Great, but what if it isn’t diagonal? Cholesky decomposition (next week)