Download presentation

Presentation is loading. Please wait.

Published byKristopher Turner Modified over 2 years ago

1
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

2
University of Colorado Boulder Homework 7 Due Friday Lecture Quiz Due by 5pm on Friday 2

3
University of Colorado Boulder 3 Filter Saturation

4
University of Colorado Boulder 4

5
University of Colorado Boulder 5 Pitfall 2: Beware of collapsing covariance - Prevents new data from influencing solution - More prevalent for longer time-spans

6
University of Colorado Boulder 6 Pitfall 2: Beware of collapsing covariance - Prevents new data from influencing solution - More prevalent for longer time-spans

7
University of Colorado Boulder 7

8
University of Colorado Boulder 8

9
University of Colorado Boulder 9

10
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

11
University of Colorado Boulder 11 Bierman Example of Poorly Conditioned System

12
University of Colorado Boulder 12

13
University of Colorado Boulder 13 Process the first observation:

14
University of Colorado Boulder 14 Process the second observation:

15
University of Colorado Boulder Consider the implementation on a computer with a limited precision: 15

16
University of Colorado Boulder 16

17
University of Colorado Boulder 17

18
University of Colorado Boulder Exact to order ε 18

19
University of Colorado Boulder 19

20
University of Colorado Boulder 20 Potter Algorithm – Motivation and Derivation Chapter 5

21
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?

22
University of Colorado Boulder For W above, the condition number is 22 Is there something we can do to instead operate on W ?

23
University of Colorado Boulder 23

24
University of Colorado Boulder 24

25
University of Colorado Boulder 25

26
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

27
University of Colorado Boulder 27

28
University of Colorado Boulder 28

29
University of Colorado Boulder 29

30
University of Colorado Boulder 30

31
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)

32
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)

Similar presentations

Presentation is loading. Please wait....

OK

Dept. E.E./ESAT-STADIUS, KU Leuven

Dept. E.E./ESAT-STADIUS, KU Leuven

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on world war 1 Ppt on computer science department portal Ppt on data handling for class 7th Ppt on chapter 3 drainage cap Ppt on division for class 4 Ppt on bond length trends Holographic 3d display ppt online Ppt on national health mission Ppt on water resources of india Ppt on thermal conductivity of insulating powder