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

▶
detection and estimation theory lecture 5
SMART_READER_LITE
LIVE PREVIEW

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

Jan 08, 2024 166 likes •354 views

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

slide-1
SLIDE 1

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)

slide-2
SLIDE 2

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
slide-3
SLIDE 3

The Cramer-Rao Lower Bound

slide-4
SLIDE 4

The Cramer-Rao Lower Bound

slide-5
SLIDE 5

The Cramer-Rao Lower Bound

Basis for CRLB

slide-6
SLIDE 6

The Cramer-Rao Lower Bound

slide-7
SLIDE 7

The Cramer-Rao Lower Bound

slide-8
SLIDE 8

The Cramer-Rao Lower Bound

slide-9
SLIDE 9

The Cramer-Rao Lower Bound

slide-10
SLIDE 10

The Cramer-Rao Lower Bound

slide-11
SLIDE 11

The Cramer-Rao Lower Bound

  • -- On the Regularity Condition

* *

slide-12
SLIDE 12

The Cramer-Rao Lower Bound

  • -- Proof (Scalar Case)
slide-13
SLIDE 13

The Cramer-Rao Lower Bound

  • -- Proof (Scalar Case)

CRLB

slide-14
SLIDE 14

The Cramer-Rao Lower Bound

  • -- Proof (Scalar Case)

CRLB

slide-15
SLIDE 15

CRLB examples

See example 3.4

slide-16
SLIDE 16

CRLB and Estimator Efficiency

slide-17
SLIDE 17

Fisher Information

slide-18
SLIDE 18

CRLB Derivation for Signals+WGN