54 THE DISCRETEATIME KALMAN FILTER
5.3 Prove that Bieﬂigﬂ = 0. Hint: Since at : Em] is a constant and
if," = :00 7&3; is zero-mean, we know that z 0. Given this information,
prove that = 0. From this point, use induction to complete the proof.
Solution:
T
58 THE DiSCRETE—TIME KALMAN FiLTER
Solution:
We have
an = asks? + Qk
Pic-+1 FkPEFE— FkPI:H}?(HkPk_HE+Rk)—1HkPk—FI?+ Qk
Subtracting the second equation from the first gives
Ak+1 = Ek+lipki+1
= FkAkFE+kagHE(HkPk-Hf +Rk)—1Hkp,;F,f
We note that if Ak is posit
CHAPTER 4
E
Propagation of states and covariances
Problems
Written exercises
4. 1 Prove that
Solution:
The derivative and expectation operators are both linear, therefore they can be
interchanged.
4.2 Suppose that a dynamic scalar system is given as n+1
48 PROPAcAnom OF STATES AND COVARIANCES
variance (P0 = 2)
. variance (P0 = D)
‘-».H_
Figure 4.1 Solution to Problem 4.11
Solution:
Figure 4.1 shows the solution. The steady—state value of the variance appears to be
1. Analytically, the steady-state v
56 THE DISCRETE-TIME KALMAN FILTER
c). In steady state :ckH = $16 so
Pack + Guk
(I — F)_1G1Lk
[?]m
We see that the ratio of the piranha population to the guppy population in
steady state is 2:1.
33}:
33k
5.5 The measured output of a simple moving average
52 THE DISCRETE—TIME KALMAN FILTER
the steady-state gain changes the way it does when the ratio of Q to R
changes.
Solution
93k -$k—1 + "wk—1
we 331.- + “W:
m.
5.
H
Fk—1P3:1FE_1 + Qk—l
5
H
:9
g:
F!
S
:0.
m
’7 "i
h}.
:30
5/
I
3.3
r
H
E
,L
L]
a-
H
Hu
r+
i
42 PROPAGATION OF STATES AND COVARIANCES
If Ui+1 : a: = 02 for all k, then
02 f262 + q
f2 = (02—61%ch
ll
QED
4.3 Consider the system
H 1 l 0 I
3”: _ 0 mic—1 Al” 1 TLk—l
wk N (0,1)
where mic is white noise.
a) Find all possible steady-state values of the m
44 PROPAGATION or STATES AND COVARIANCES
4.5 Two chemical mixtures are poured into a tank. One has concentration cl and
is poured at rate F1, and the other has concentration (:2 and is poured at rate F2.
The tank has volume V, and its outflow is at concen
50 PROPAGATION or STATES AND COVARlANCES
ﬂ _T 2 2 _2T —1—2
‘ e [~1—1—H3 1 2
. _ 00
:JLHSGF* iool
Q: QCT
H
l—‘Aé'l
cuo
"io
|—_J
Substituting these values int-o the discretized steady-state Lyapunov equation
P = FPFT + Q and solving for P gives
limP=[G 0]
T
46 PROPAGATION OF STATES AND COVARlANCES
Multiplying out and equating the matrix elements on the right and left side of this
equation gives
P11 2 “21311 + 2
P12 = —3P12 + 3
P22 = —4P22 + 5
Solving these equations gives
P11 = l — 6—23
P12 : 1 — E-Bt
5
P22
Week 7: Portfolio: Final
Grading Rubric
This document contains a grading rubric for this assignment.
Criteria that Submitted Assignment Meets
Total Points Possible
for Assignment
ALL REQUIRED content is present, the portfolio is logically organized
and ve
I.
II.
III.
Introduction: Gay marriage and straight marriages is the same thing as
bikinis and underwear. The same thing, but only one is acceptable in
public.how sad.
A. Their rights
B. Peoples thoughts
C. My opinion
Their rights
A. Our civil rights and
Project Name
09.04.20XX
Casey Baumer
Acme Corp
1600 Acme Parkway
Los Angeles, CA 94043
1
Overview
Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh
euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim
Running head: Apa citations
1
Name_
For this assignment, you will review materials in the DeVry library to help gain a better
understanding of APA citations.
a. Click https:/hub2.devry.edu/node/272
b. Listen to the tutorial or download and review the tran
Running Head: TITLE OF DOCUMENT
Title of Document
Your Name
DeVry University
BUSN115 Introduction to Business and Technology
Professor ZZZ
Running Head: TITLE OF DOCUMENT
2
Lemonade Stand Informal Business Report
INTRODUCTION
In this section, provide a br
BUSN115 Week 3: Lemonade Stand, Part I
Background
As you have read about in our lecture, we have used a lemonade stand to help us understand some basic
concepts of business. As we pointed out, a lemonade stand has a simple business structure, yet it can
h
Running head: CYBERBULLYING
1
Week 5 Grading - first draft (3-4 pages)
Central Idea/Focus: Topic, purpose, and thesis are clear and identifiable in the introduction; all ideas consistently address this main idea
without off-topic or irrelevant ideas.
10
S
Checklist for Course Project Peer Review
Use the checklist below as you conduct the Week 7 Peer Review.
Jamar William / Your name: Chris Styer
Name of Element:
Does the paper clearly address a
course theme?
Yes:
No:
x
Does the paper contain the
appropriat
Checklist for Course Project Peer Review
Use the checklist below as you conduct the Week 7 Peer Review.
Jamar Williams/ Your name: Jaci Scherer
Name of Element:
Does the paper clearly address a
course theme?
Yes:
No:
Comments or Suggestions
for Improvemen
Checklist for Course Project Peer Review
Use the checklist below as you conduct the Week 7 Peer Review.
Leslye Thompson/ Your name: Jaci Scherer
Name of Element:
Yes:
Does the paper clearly address a
course theme?
X
Comments or Suggestions
for Improvement
Checklist for Course Project Peer Review
Use the checklist below as you conduct the Week 7 Peer Review.
Camden McDonald/ Your name: Leslye Thompson
Name of Element:
Yes:
Does the paper clearly address a
course theme?
X
Comments or Suggestions
for Improvem
Week3AssignmentGradingRubric
Youwillhavetwoassignmentstocompleteforthecourseyoucanreadmoreabouttheseonthe
AssignmentsitemsunderWeek3andWeek6.ForWeek3assignment,youwillbegradedon
threespecificgradingcriteria.
Part
I
Earned
Points
Criteria
60
Content of yo
Week6AssignmentGradingRubric
Youwillhavetwoassignmentstocompleteforthecourseyoucanreadmoreabouttheseonthe
AssignmentsitemsunderWeek3andWeek6.ForWeek6assignment,youwillbegradedon
threespecificgradingcriteria.
Part
I
Earned
Points
Criteria
60
Content of yo
MGMT-404 Quiz Study Guide
YOU MAY WANT TO PRINT THIS GUIDE FOR QUICK REFERENCE AND CONVENIENCE
1. The Quiz is "open book, open notes." The maximum time you can spend in the exam is 2 hours,
30 minutes. If you have not clicked the Submit for Grading button
Case Analysis
Week 3
Outline and Grading Guide (150 points)
Choose a case from the textbook for this assignment from the following list.
Case 7 - United Way
Case 8 - General Motors
Case 10 - McDonalds
Case 12 - Yahoo
Case 13 - QVC
Case 17 - Readers Digest
Avery Dennison
Avery Dennison
Jamar Williams
DeVry University
Avery Dennison
2
Avery Dennison is a 6 plus Billion dollar company, they are in the consumer
goods sector and the Business equipment Industry. Avery Dennisons Mission statement is
Inspiring the
We're a pharmacy innovation company and every day we're working
to make healthcare better (CVS Health)
I remember walking into a CVS on a nice summer day. I thought it was
a walgreen until I saw how differently set up it was and made me draw my
attention
O2.0 Marketing Plan
1
Marketing Plan for O2.0
Asia Gardner, Jonathan Sladek, Vanessa Auguste, and Joaquin Iglesias
Robert Pandel
October 9, 2015
Executive Summary
O2.0 Marketing Plan
2
We are all busy people. With so many things that need to taken care of