PS2 10 - point the ladar receiver output will be a random...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 Problem Set 2 Assigned: February 10, 2010 Due: February 17, 2010 Readings : Read Levy Sections 2.1- 2.7, 5.1- 5.2. Problems : Solve problems 2.13 in Chapter 2 of Levy’s book and the following problem: Problem 4: Luke has lost his droid on Planet Alpha. To help in his search, Luke has rented from Don and Ron Electronics a Don and Ron Transistorized Handheld Laser Detection and Ranging unit (the famous DARTH LADAR). Luke has divided up a map of planet Alpha into a rectangular grid. He plans to hover over each grid point and fire off a ladar pulse. If his droid is not at that grid
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Unformatted text preview: point the ladar receiver output will be a random variable y with probability density P(y| droid absent) = 3 e -3 y u(y) where u(.) is the unit step function. If the droid is at that grid point, y will have a probability density p(y| droid present) = e -y u(y). Luke must decide based on the value of y he observes whether to land and begin a ground search. Design a hypothesis testing rule (find decision regions) for Luke such that the probability that he decides to land given that the droid is present (P Droid ) is maximized subject to the probability of landing given that the droid is absent is 0.01. Find the resulting value of P Droid ....
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This note was uploaded on 06/04/2010 for the course EE 8581 taught by Professor Staff during the Spring '08 term at Minnesota.

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