ENGINEERING TRIPOS PART IIB – 2012/2013

Module 4F6 - Signal Detection and Estimation

AIMS

The availability of modern digital hardware now allows for many statistical techniques to be implemented, some in real-time, and applied to data and signal processing applications. The aim of this module is to build on module I7 and to introduce some statistical modelling to data and signals analysis. These techniques will be applied to both the detection of signals and the estimation of parameters of models that can account for the observed data.

LECTURE SYLLABUS

Signal detection

• Hypothesis testing.
• Likelihood ratios.
• Probability of detection and false alarms.
• Receiver operator characteristics.
• The matched filter.

Bayes theorem and maximum a-posteriori methods

• Introduction of prior knowledge.
• Derivation of Bayes theorem.
• Joint and Marginal estimators.
• Effects of different priors.
• Model selection using evidence and other methods.
• Parameter estimation.
• Kalman Filters and tracking.

Maximum entropy

• How to assign probabilities.
• Maximum entropy and Fisher Information.
• Spectral estimation.
• Image recovery and Inverse problems.

Non-linear methods

• Examples of non-linear systems.
• Linear in the Parameters models.
• Volterra expansion and NARMAX models.

Lectures will be supported by interactive computer demonstrations using MATLAB.

OBJECTIVES

On completion of the module students should:

• Have a good understanding of detection and estimation theory and practice;
• Appreciate the shortcomings of some of the various approximations used in the subject;
• Be able to apply the methods described to a host of various problems;
• Be able to run and understand software implementations of the methods.

REFERENCES

Please see the Booklist for Group F Courses for references for this module.

Last updated: June 2012