Detection and Estimation Theory Lecture 5 Mojtaba Soltanalian- UIC - PowerPoint PPT Presentation

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Detection and Estimation Theory Lecture 5 Mojtaba Soltanalian- UIC msol@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

Detection and Estimation Theory Lecture 5 Mojtaba Soltanalian- UIC msol@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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