ELE 530: Theory of Detection and Estimation

Prof. Paul Cuff, Princeton University, Spring Semester 2015-16.

Course Description

In this course we investigate how to use the tools of probability and signal processing to estimate signals and parameters and detect events from data. In many cases we can identify the optimal estimator/detector or at least bound the performance of any estimator/detector.

Instructors

Prof. Paul Cuff
Office location: B-316 E-quad

Text

We will be covering topics found in a variety of sources. If you do not wish to buy the entire library of books listed below, the main text (Kay Vol. 1) will be a useful one to have on hand.

Main text

Fundamentals of Statistical Signal Processing - Estimation Theory (Vol. 1) Steven M. Kay, Prentice Hall, 1993.

Picture of Textbook 

Other text

Topics

  • Bayesian

    • Minimum mean square-error (MMSE)

    • Linear MMSE

    • Hilbert space of random variables

    • Minimum probability of error (MAP)

  • Signals

    • Stationarity and power spectral density

    • Wiener filter

    • Kalman filter

  • Non-Bayesian Estimation

    • Sufficient Statistic

    • Bias

    • Minimum variance unbiased estimator

    • Cramer-Rao bound

    • Maximum likelihood

    • Efficient estimator

  • Non-Bayesian Detection

    • Hypothesis test

    • Neyman-Pearson lemma

    • Likelihood ratio test

    • Kullback-Leibler divergence

    • Matched filter

    • Sequential test

  • Methods of dealing with complexity

    • Expectation maximization

    • Hidden Markov model

    • Graphical models