PS7 10

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

This preview shows pages 1–2. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/04/2010 for the course EE 8581 taught by Professor Staff during the Spring '08 term at Minnesota.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online