Course Objectives: Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering, such as statistics, signal processing, communications, control and navigation. The techniques are used in several areas in computer science, such as bioinformatics, computer vision, image processing, machine learning, pattern recognition, and robotics. This course will focus on the design and implementation of efficient and reliable computer algorithms in this area. It will use the Global Positioning System (GPS) as an example to show how to use the techniques to solve practical problems.

Topics:

• Theory and Algorithms:
  
  • Linear algebra review and matrix factorizations;
  • Basic results of probability theory and statistics;
  • Ordinary least squares estimation;
  • Generalized least squares estimation;
  • Regularized least squares estimation;
  • Total least squares estimation;
  • Nonlinear least squares estimation;
  • Maximum-likelihood estimation;
  • Minimum mean-squared error estimation;
  • Kalman filtering;
  • Integer least squares estimation;
  • LASSO (least absolute shrinkage and selection operator) estimation.
• Applications in GPS:
  
  • GPS signals, receivers, measurements;
  • Mathematical models for positioning and position estimation

Prerequisites: COMP 350A Numerical Computing or equivalent, MATH 323 Probability Theory or equivalent, a good introductory matrix theory course. COMP 540 Matrix Computations is helpful, but not required.