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Detection and Estimation Theory
Lecture 5
Mojtaba Soltanalian- UICmsol@uic.edu
http://msol.people.uic.edu
Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye)
The Cramer-Rao Lower Bound
---Last Lecture
• the CRLB give a lower bound on the variance of ANY UNBIASED
estimator
• does NOT guarantee bound can be obtained
• IF find an estimator whose variance = CRLB then it’s MVUE
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
Basis for CRLB
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
The Cramer-Rao Lower Bound
--- On the Regularity Condition
*
*
The Cramer-Rao Lower Bound
--- Proof (Scalar Case)
The Cramer-Rao Lower Bound
--- Proof (Scalar Case)
CRLB
The Cramer-Rao Lower Bound
--- Proof (Scalar Case)
CRLB
CRLB examples
See example 3.4
CRLB and Estimator Efficiency
Fisher Information
CRLB Derivation for Signals+WGN
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