EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 4 Issued: September 18, 2009, Due: September 25, 2009 (in class) Note: Your work for the questions with [0 pt] are not to be turned in. Problem 1. Show tha
March 5, 2008
Spring 2008
Optimal Estimation (EGM 6934, Sec 4159 ) University of Florida Mechanical and Aerospace Engineering Instructor: Prabir Barooah
Midterm 1 Duration: 50 minutes
There are three problems that are worth 26, 14, and 20 points, respecti
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 9 Issued: November 3, 2009, Due: November 9, 2009 (in class)
Problem 1. Consider a Poisson distributed r.v. X, whose p.m.f is given by pX (k|a) = P (X = k|
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 8 Issued: October 23, 2009, Due: October 30, 2009 (in class)
Problem 1. Prove that if X and Y are independent random variables, fX|Y (x|y) = fX (x) and fY
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 7 Issued: October 12, 2009, Due: October 19, 2009 (in class)
Problem 1. [30 pt] write a MATLAB script to simulate and perform a recursive least squares est
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 6 Issued: October 5, 2009, Due: October 9, 2009 (in class) MLE with a single observation Problem 1. [10 + 5 = 15 pt] Determine the max-likelihood estimates
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering HW 10 Issued: November 20, 2009, Due: December 2, 2009 (in class)
Problem 1 (Use the definitions from Handout # 2 when answering this question). Consider the
Notes on differentiation involving vectors
Prabir Barooah October 26, 2009
We always follow the convention: A vector, by default, is a column vector. Therefore, a n-dimensional vector x is represented as x1 x2 x= . . . xn The derivative of a scalar functi
Optimal Control
Assignment #5
For the problems given in Assignments #3 and #4, implement the following direct methods:
The standard shooting method
The multiple-shooting method
In implementing the multiple-shooting method, you will need to break the int
Optimal Control
University of Florida
Anil V. Rao
Question 1
Solve Problem 5-1 in Kirk.
Question 2
Solve Problem 5-2 in Kirk.
Question 3
Solve Problem 5-5 in Kirk.
Question 4
Solve Problem 5-6 in Kirk.
Question 5
Solve Problem 5-8 in Kirk.
Question 6
Solv
Optimal Control
Assignment #5
For the problems given in Assignment #3, implement the following indirect methods:
The standard shooting method
The multiple-shooting method
In implementing the multiple-shooting method, you will need to break the interval
Optimal Control
Assignment #4
Question 1
Solve Problem 5-3 in Kirk.
Question 2
Solve Problem 5-7 in Kirk.
Question 3
Solve Problem 5-10 in Kirk.
Question 4
Solve Problem 5-14 in Kirk.
Question 5
Solve Problem 5-15 in Kirk.
Question 6
Consider the followin
Optimal Control
University of Florida
Anil V. Rao
Objective of Assignment
The objective of this assignment is to learn how to use the sparse nonlinear programming problem (NLP) solver SNOPT. SNOPT solves NLPs of the following form:
min f (z)
subject to th
Optimal Control
University of Florida
Anil V. Rao
Question 1
Using the approach for calculus of variations developed in class (not the approach used in Kirks
book), derive the necessary conditions for optimality that minimize the integral
tf
J=
L[x(t), x(
EML 6934
Fall 2009
Optimal Estimation University of Florida Mechanical and Aerospace Engineering Solution to HW 4
Problem 1.
[5 pt] Show that var(aX) = a2 var(X) (a is a deterministic parameter).
var(aX) = E[(aX - E[aX])2 ] = E[(aX - aE[X])2 ] = E[a2 (X -
April 4, 2008
Spring 2008
Optimal Estimation (EGM 6934, Sec 4159 ) University of Florida Mechanical and Aerospace Engineering Instructor: Prabir Barooah Midterm 2 Due: in class on Monday, April 7, 2008 Points will be awarded for clarity and completeness o
Notes on Probability and Random Variables Optimal Estimation (EML 6934, Section 6385) Fall 2009
University of Florida, Mechanical and Aerospace Engineering
Prabir Barooah
1
1.1
Probability
Random Experiment
Everything is based on a random experiment, whic
1
Recursive Weighted Least Square
Z k = Hk + k (1.1)
The estimate of can be obtained based on measurements available at time k :
by using the least squares technique described earlier in class. Suppose additional measurements are obtained at time k + 1: k
Schedule for nal project presentation EML 6934, Fall 2009 Instructor: Dr. Prabir Barooah
Please note that the following important instructions: Project presentation on Nov 30 and Dec 7 will be held at MCCA 2196, not in the usual class meeting place. Pleas
688
~ E E E RANSACTIONS T
O N A TJTON.~IC CONTROL, VOL.
AC-16, NO. 6,
DECEMBER
1971
A Tutorial Introduction to Estimation and Filtering
Absiracf-In this tutorial paper t he basic principles of l east squares propert,ies of t hisestimatorare derived i n Se
Hnadout #2 : supplemental notes for Application of Kalman filtering to Track a Moving Object
Optimal Estimation (EML 6934, Section 6385), Fall 2009 University of Florida, Mechanical and Aerospace Engineering
Prabir Barooah
1
1.1
Object Moving with Constan
50
^
40
3^
30
20
10
0 0.8
0.9
a ^d
1
1.1
1.2
Figure 5: Histogram of the estimated ad 's. Estimated mean = 0.996408 and estimated standard deviation = 0.057748.
Suppose E = cfw_^ < 1. ad
recall (ad = eaT )
We can estimate P (E), the probability of E from