EECS 564: Estimation, Filtering, and Detection

University of Michigan, Winter 2012

Instructor: Clayton Scott
Classroom: 1017 Dow
Time: TTh 9-10:30
Office: 4433 EECS
Office hours: Monday 1-3 or by appointment.

Textbook: None. I'll distribute my notes.

Supplemental references, on reserve at the library:
1) Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory, Steven Kay, 1993
2) Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory, Steven Kay, 1998
3) Statistical Signal Processing, Louis Scharf, 1991
4) An Introduction to Signal Detection and Estimation, Vincent Poor, 2nd ed., 1994

Topics to be covered: Theoretical aspects of estimation, filtering, and detection. Applications of the theory to Fourier and wavelet domain signal denoising, channel estimation, object tracking, binary communication, modulation, matched filtering, Rayleigh fading channels, and functional magnetic resonance imaging. Some applications will be developed in class, and others through the homeworks.

EECS 501 or equivalent, linear algebra, signals and systems, familiarity with MATLAB.

Lecture notes:

  1. Statistical signal processing
  2. The signal subspace model, orthogonal projections, and least squares estimation
  3. Eigendecompositions and the spectral theorem
  4. The multivariate Gaussian distribution
  5. Sufficient statistics
  6. Estimation theory
  7. Minimum variance unbiased estimation
  8. The Cramer-Rao lower bound
  9. Rao-Blackwellization
  10. Maximum likelihood estimation
  11. Bayesian estimation
  12. Bayesian estimation in the Gaussian linear model
  13. Application: Wavelet denoising
  14. Linear estimation
  15. Filtering
  16. Linear prediction
  17. Wiener filtering
  18. Kalman filtering
  19. Application: Channel estimation
  20. Detection theory
  21. Bayes risk detection
  22. Neyman-Pearson detection
  23. Application: The binary symmetric channel
  24. Signal detection in Gaussian noise
  25. Uniformly most powerful tests and the Karlin-Rubin theorem
  26. Bayes factors and generalized likelihood ratios
  27. Application: The Rayleigh fading channel
  28. CFAR detectors
  29. Additional topics as time permits


The median grade for the class will be at the boundary between B+ and A-.

Cancelled lecture: Feb. 9

Make-up lecture: Monday Feb. 6, 5:30 -- 7:00 PM, EECS 1303.

Homework Policy
Homeworks are due in the 564 slot in EECS 2420 by 5 pm on the assigned due date. All homework assignments are to be completed on your own. You are allowed to consult with other students in the current class regarding the conceptualization of the problem and possible methods of solution, but you may not share details, whether in the form of scrap work, final writeups, or computer code. All written and programming work is to be generated by you working alone. You are not allowed to possess, look at, use, or in anyway derive advantage from existing solutions that you may come across.

Honor Code
All undergraduate and graduate students are expected to abide by the College of Engineering Honor Code as stated in the Student Handbook and the Honor Code Pamphlet.

Students with Disabilities
Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential.