E1 244 : Detection and Estimation Theory

Instructor

Rajesh Sundaresan

Lecture Hours

Lectures: Tuesdays and Thursdays : 09:00 - 10:30
Make-up lectures and problem set discussions: Fridays : 09:00 - 10:30

Location

ECE 1.07

Course syllabus

Hypothesis testing: Neyman-Pearson theorem, likelihood ratio test and generalised likelihood ratio test, uniformly most powerful test, multiple-decision problem, detection of deterministic and random signals in Gaussian noise, detection in nonGaussian noise, sequential detection.
Parameter estimation: unbiasedness, consistency, Cramer-Rao bound, sufficient statistics, Rao-Blackwell theorem, best linear unbiased estimation, maximum likelihood estimation, method of moments.
Bayesian estimation: MMSE and MAP estimators, Wiener filter, Kalman filter, Levinson-Durbin and innovation algorithms.

Course Grade

• 20/100 : Homeworks - Fortnightly
  
• 30/100 : Mid-term - Thursday 12 February 2015 (09:00 - 10:30, 1.5 hours)
  
• 50/100 : Final - Friday 24 April 2015 (09:00 - 12:00, 3 hours)
  

Homeworks

• Problem Set 1 : Due 27 January 2015
  
• Problem Set 2 : Due 10 February 2015
  
• Problem Set 3 : Due 03 March 2015
  
• Problem Set 4 : No due date
  
• Problem Set 5 : Due 27 March 2015
  
• Problem Set 6 : No due date
  
• Problem Set 7 : No due date
  

Reference Texts

• H. V. Poor, An Introduction to Signal Detection and Estimation, Springer-Verlag, 2nd edition, 1994.
  
• G. Casella and R. L. Berger, Statistical Inference, Cengage Learning, 2nd edition, 2002.

Lecture topics

• 06/01: Lecture 1: Motivating examples
  
• 08/01: Lecture 2: Bayesian hypothesis testing (Section II-B of Poor)
  
• 13/01: Lecture 3: Minimax hypothesis testing (Section II-C of Poor)
  
• 22/01: Lecture 4: Minimax hypothesis testing continued
  
• 23/01: Lecture 5: Neyman-Pearson lemma (Section II-D of Poor)
  
• 27/01: Lecture 6: Examples
  
• 29/01: Lecture 7: Composite hypotheses
  
• 12/02: Mid-term
  
• 19/02: Lecture 8: Detector structures (Section III-B of Poor)
  
• 20/02: Lecture 9: Detector structures - dependent Gaussian noise
  
• 24/02: Lecture 10: Detector structures - signals with random parameters, stochastic signals, estimator-correlator
  
• 03/03: Lecture 11: Performance bounds (Section III-C-2 of Poor)
  
• 05/03: Lecture 12: Sequential detection: Formulation and SPRT (Section III-D of Poor)
  
• 06/03: Lecture 13: Sequential detection: Wald-Wolfowitz theorem
  
• 10/03: Lecture 14: Sequential detection: Wald's approximations
  
• 12/03: Lecture 15: Bayesian estimation
  
• 13/03: Lecture 16: Bayesian estimation
  
• 17/03: Lecture 17: Sufficiency, minimal sufficiency, examples
  
• 19/03: Lecture 18: Factorisation theorem, Rao-Blackwell theorem
  
• 20/03: Lecture 19: Complete families, examples, complete sufficient statistic
  
• 24/03: Lecture 20: Exponential families, examples, Cramer-Rao lower bound
  
• 26/03: Lecture 21: MLE, large sample asymptotics, consistency, efficiency
  
• 27/03: Lecture 22: Examples, bias-variance tradeoff
  
• 31/03: Lecture 23: Consistency, asymptotic normality of MLE, recursive algorithms
  
• 07/04: Lecture 24: Signal estimation and tracking, Kalman-Bucy filter
  
• 09/04: Lecture 25: Linear MMSE estimation, Orthogonality principle
  
• 10/04: Lecture 26: Wiener-Hopf equation, Yule-Walker equation and the Levinson algorithm
  
• 16/04: Lecture 27: Noncausal and causal Wiener-Kolmogorov filtering
  
• 24/04: Final exam: 9:00 - 12:00