The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 5714 Robust Estimation and Filtering | ECE | Virginia Tech

### Course Information

#### Description

An introduction to the analysis and design of maximum likelihood and robust estimators and filters. Maximum likelihood estimation theory: consistency, asymptotic efficiency, sufficiency. Robust estimation theory: qualitative robustness, breakdown point, influence function, change-of-variance function. Robust estimators: M-estimators, generalized M-estimators, high-breaddown estimators.

#### Why take this course?

Robust estimation theories have undergone important developments that need to be introduced in various engineering fields such as signal processing, communications, radar systems and electric power systems, to cite a few. The cornerstones of these developments are the robustness concepts of breakdown point and influence function that enable the student to perform the analysis and design of estimators with desired requirements in view of their applications to engineering problems.

#### Prerequisites

Prerequisites: ECE 5605

This course requires a working knowledge of probability and stochastic processes as taught in 5605.

### Major Measurable Learning Objectives

• Explain maximum likelihood and robust estimation theories and methods;
• Evaluate the asymptotic efficiency, the breakdown point and the influence function of an M-estimator;
• Develop maximum likelihood and robust parameter estimation methods in regression and for ARMA models;
• Develop robust Kalman filters and evaluate their statistical properties;
• Estimate the parameters of Fractional ARIMA models for long memory processes;
• Apply maximum likelihood and robust estimation methods to engineering systems.

### Course Topics

#### Percentage of Course

Probability distribution theory 10%
Robust estimators of location and scale 10%
Maximum Likelihood estimation theory and methods 15%
Robust estimation theories and methods 20%
Robust estimators in regression and applications 15%
Robust estimation of ARMA models and applications 10%
Robust Kalman filter and applications 10%
Estimation of Fractional ARIMA models and applications 10%