PS7 10 - University of Minnesota Dept. of Electrical and...

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University of Minnesota Dept. of Electrical and Computer Engineering EE 8581 DETECTION AND ESTIMATION THEORY Spring 2010 Problem Set 7 Assigned March 31, 2010 Due: April 6, 2010 Readings : Read Levy Chapters 7, 8 and 9. Problem 1: Let a(t) and r(t) be two zero-mean random processes with given covariance functions K a (t,u), K ar (t,u), K r (t,u) a) Let b = 0 T f(t) a(t) dt where f(t) is a given function of time. We would like to estimate b using a linear estimator of the form b ^ = 0 T h(t) r(t) dt Find the equation that h(.) must satisfy in order to minimize the mean-squared estimation error over the class of all such linear estimators. b) Determine an expression in terms of the quantities defined above for the mean-squared estimation error for the optimum estimator in part a) For parts c) and d) we consider the special case of this problem where r(t) = a(t) + n(t). Here n(t) is a white Gaussian noise, independent of a(t), with spectral height N 0 /2. Also assume that the K-L expansion of a(t) over [0,T] is given by a(t) = i=1 x i φ i (t)
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PS7 10 - University of Minnesota Dept. of Electrical and...

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