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# Detection estimation - 5PMSDET0

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• #### Number of hours

• Lectures : 8.0
• Tutorials : 8.0
• Laboratory works : 4.0
• Projects : 0
• Internship : 0
ECTS : 2.0

### Goals

Fundamentals of estimation and detection theory

Contact Olivier MICHEL

Content

A. brief reminder on probability theory, random processes

B. Estimation theory : fundamentals
1. Context and motivation for estimation theory
2. Estimation of unknown deterministic parameters; definitions
3. Cramer-Rao bound
i. Scalar case
ii. Condition of existence of a MVUE (min variance unbiased estimation)
iii. Fisher information
iv. Multivariate case
4. Méthodology, Rao-Blackwell
i. Darmois Theorem
ii. Information contained in a sample, information divergence (KL divergence)
6. Maximum likelihood approach (ML)
i. Properties
ii. ML and sufficient statistics
7. Practice of ML estimation
8. Méthod of moments
9. Best linear unbiased estimator (BLUE)
10. Min square estimation (MSE)
11. Orthogonality principle

C. Estimating random parameters
1. Bayes strategy
2. Minimum variance Bayes estimate
3. Linear Gaussian models
4. Practicing Bayes estimation.

D. Fundamentals of detection theory
1. Binary hypothesis testing, MaP, ML
2. Bayes detection
3. Neyman Pearson criterion
5. Composite hypothesis testing
6. Generalized likelihood ration test
7. Uniformly or localy most powerfull test

Prerequisites

Basics of probability theory and statistics (for engineers). Random variables, random processes

Tests

Some exercices left as homework every week. (coeff 5/20)
Written final exam (2hours), no authorized lecture supports during the exam (coeff 15/20)

Examen Ecrit : 100%

Curriculum->Master TSI SIGMA->Semester 9
Curriculum->SICOM->Semester 9
Curriculum->Double-Diploma SICOM-TSI SIGMA->Semester 9
Curriculum->Master->Semester 9
Curriculum->Double-Diploma Engineer/Master->Semester 9

Bibliography

S.Kay : Fundamentals of Statistical Signal Processing-Estimation Theory. Volumes 1 and 2
Prentice Hall Signal Processing series.

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Date of update January 9, 2017

## Version française

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