ECE 6540: Estimation Theory

Course Description

Uncertainty is everywhere in engineering. Communications, radar, medical imaging, and many other applications require we estimate parameters and detect signals in the presence of high levels of uncertainty and noise. For example, in communications, we commonly want to estimate the frequency, amplitude, and phase of a sinusoid. All three of these quantities can carry important information, and there are nearly an infinite number of approaches for estimating these parameters. Yet, what approach is the ``best'' in noisy and/or uncertain conditions? Furthermore, how do we define ``best?'' What is the ``best'' way to know are even looking at a sinusoid?

In this class, we explore these types of questions. We explore optimal approaches for estimating parameters and detecting signals. We will start with discussing statistical methods for estimating the unknown parameters of a given signal. We then explore optimal approaches for detecting these signals (with or without unknown parameters).

Learning Objectives

At the completion of this course, you should be able to:

1. Understand linear models and their relationship with probability distributions
2. Compute Cramer Rao Lower Bounds
3. Estimate parameters with multiple criteria:
   1. minimum variance
   2. maximum likelihood
   3. Bayesian assumptions
4. Detect multiple types of signals:
   1. deterministic signals
   2. random signals
   3. signals with unknown parameters

Prerequisites

ECE 5510, ECE 5530, or equivalents.

Grade Distribution: