# hw03 - θ away from the x-axis Let ρ 1 be the range to s 1...

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EEL 6935 Electronic Navigation Systems Homework #3 Problem 1 Calculate the Schuler frequency for an inertial navigation system on Mars. See http://www.solarsystem.nasa.gov/ for information on Mars. Problem 2 1. Show that the group refractive index, n g , can be written as n g = c dk . (1) 2. Also show that the wave number, k , can be written as a function of the phase refractive index, n p : k = n p ω c (2) 3. Substitute (2) into (1), and show that n g = n p + ω dn p . (3) Equation (3) is equivalent to equation (4.19) on page 137 of the text. 1

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Problem 3 We wish to analyze the errors associated with calculating our two-dimensional position using range measurements to two reference points located in the xy - plane, s 1 and s 2 , as shown below. θ x y s 1 s 2 Reference point s 1 is located along the x -axis, and reference point s 2 is located at an angle
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Unformatted text preview: θ away from the x-axis. Let ρ 1 be the range to s 1 , and ρ 2 be the range to s 2 . We will Fnd our position by solving the following two equations for x and y : ( x 1-x ) 2 + ( y 1-y ) 2 = ρ 2 1 , ( x 2-x ) 2 + ( y 2-y ) 2 = ρ 2 2 , where ( x 1 , y 1 ) is the position of s 1 , and ( x 2 , y 2 ) is the position of s 2 . The geometry matrix for this two-dimensional scenario is deFned as G , " ∂ρ 1 ∂x ∂ρ 1 ∂y ∂ρ 2 ∂x ∂ρ 2 ∂y # . 1. Show that for a person at the origin of the xy-plane, G =-± 1 cos θ sin θ ² . 2. Also, show that trace n ( G T G )-1 o = 2 sin 2 θ . 3. What value of θ results in the smallest 2-d rms error in position? Does your answer make intuitive sense? 2...
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## This note was uploaded on 01/15/2012 for the course EEL 6935 taught by Professor Staff during the Fall '08 term at University of Florida.

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hw03 - θ away from the x-axis Let ρ 1 be the range to s 1...

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