hw01 - 1 Problem 4 Use the perturbation methods given in...

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EEL 6935 Electronic Navigation Systems Homework #1 Problem 1 Show that for any orthonormal matrix A , | A | = ± 1 HINT: Use A T A = I . Problem 2 Show that for any orthonormal matrix A , k x k = k A x k HINT: Express x as a weighted sum of columns of A , then calculate x T x . Problem 3 Suppose that the random vector X has covariance matrix C = ± σ 2 1 0 0 σ 2 2 ² . Show that 1 2 π | C | 1 / 2 e - 1 2 ( x - μ ) T C - 1 ( x - μ ) = ³ 1 2 πσ 1 e - ( x 1 - μ 1 ) 2 / (2 σ 2 1 ) ´ ³ 1 2 πσ 2 e - ( x 2 - μ 2 ) 2 / (2 σ 2 2 ) ´ What is the relationship between the covariance of a Gaussian random vector and independence of the individual random variables comprising the vector?
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Unformatted text preview: 1 Problem 4 Use the perturbation methods given in class to develop an iterative algorithm to solve the following system of non-linear equations: y = sin 2 x y = x 3 Problem 5 Show that the minimum, ˆ x , of the cost function J (ˆ x ) = ( z-H ˆ x ) T W ( z-H ˆ x ) is given by ˆ x = ( H T W H )-1 H T W z . 2...
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  • Fall '08
  • Staff
  • random vector, Electronic Navigation Systems, Gaussian random vector, individual random variables, orthonormal matrix

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hw01 - 1 Problem 4 Use the perturbation methods given in...

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