Consider the observations x[n] = Ar" + w[n] with n = 0, ..,N – 1, where A is a parameter to be estimated, w[n] is additive white Gaussian noise of variance a² and r is a known parameter taking values larger than one (r > 1). (c) (1) Write the joint probability density function for the whole set of observations and a given value of the unknown parameter A. (i) Calculate the Cramer-Rao Lower Bound (CRLB) for A, when N = 4, r = 2 and o² = 1. (ii) Find an estimator that meets the CRLB.
Consider the observations x[n] = Ar" + w[n] with n = 0, ..,N – 1, where A is a parameter to be estimated, w[n] is additive white Gaussian noise of variance a² and r is a known parameter taking values larger than one (r > 1). (c) (1) Write the joint probability density function for the whole set of observations and a given value of the unknown parameter A. (i) Calculate the Cramer-Rao Lower Bound (CRLB) for A, when N = 4, r = 2 and o² = 1. (ii) Find an estimator that meets the CRLB.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
2c
![(c)
Consider the observations x[n] = Ar" + w[n] with n = 0, ..,N – 1, where A is a
parameter to be estimated, w[n] is additive white Gaussian noise of variance o? and
ris a known parameter taking values larger than one (r > 1).
(i)
Write the joint probability density function for the whole set of observations
and a given value of the unknown parameter A.
(i)
Calculate the Cramer-Rao Lower Bound (CRLB) for A, when N = 4, r = 2 and
o? = 1.
(ii) Find an estimator that meets the CRLB.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd190ed6-88b0-4adf-b282-a1cbba73d6eb%2F73521c21-bc7f-4cee-b07f-445873ab10fb%2F182c2vu_processed.png&w=3840&q=75)
Transcribed Image Text:(c)
Consider the observations x[n] = Ar" + w[n] with n = 0, ..,N – 1, where A is a
parameter to be estimated, w[n] is additive white Gaussian noise of variance o? and
ris a known parameter taking values larger than one (r > 1).
(i)
Write the joint probability density function for the whole set of observations
and a given value of the unknown parameter A.
(i)
Calculate the Cramer-Rao Lower Bound (CRLB) for A, when N = 4, r = 2 and
o? = 1.
(ii) Find an estimator that meets the CRLB.
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