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# HW2 - EML 6934 Fall 2009 Optimal Estimation University of...

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EML 6934 Fall 2009 Optimal Estimation University of Florida Mechanical and Aerospace Engineering Scientific questions often have a surface appearance of dumbness .... They are asked in order to prevent dumb mistakes later on. - Robert Pirsig, in Zen and the art of motorcycle maintenance HW 2 Issued: September 2, 2009, Due: September 9, 2009 (in class) Problem 1. In this homework (and all subsequent ones), correct answers must be accompanied by adequate explanation for points to be awarded. Is it the same as saying “correctness is a necessary condition for earning points but not sufficient”? Read the article http://www.themathpage.com/abooki/logic.htm to learn about valid arguments, necessary conditions, and sufficient conditions. Problem 2. Is the condition “ y ∈ R ( A )” necessary for a vector x to exist that satisfies Ax = y ? Or is it sufficient? Or both? Given an m × n matrix A and a m × 1 vector y , how would you numerically check whether y ∈ R ( A ) or not? Problem 3. We know that a for the solution to the equation Ax = y to be unique, we must have N = { 0 } . Given an m × n matrix A , how would you numerically check whether N ( A ) = { 0 } or not? Problem 4. Write a MATLAB program for simulating the parameter estimation experiment de- scribed in class with noisy inputs and outputs. Choose a = - 0 . 2, b = 10, T = 0 . 001 second, and use a sinusoidal input. See the course website for an example. 1. Estimate the two parameters a d and b d using the least squares technique described in the first two lectures of the course. 2. Repeat the estimation exercise N times (say, N = 500) and collect the N estimates. Make sure that you use distinct sequences of random numbers to simulate noise in each of these experiments.

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