Undergraduate Teaching 2017-18

Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2017-18

Engineering Tripos Part IIB, 4F7: Statistical Signal Analysis, 2017-18

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Module Leader

Dr S.S. Singh

Lecturer

Dr S.S. Singh

Timing and Structure

Lent term. 16 lectures (including examples classes). Assessment: 100% exam

Prerequisites

3F3; Useful 3F1 and 3F8

Aims

The aims of the course are to:

  • Continue the study of statistical signal processing from the basics studied in 3F3.
  • Introduce the fundamental concepts and methods of adaptive filtering.
  • Introduce time-series models, in particular Hidden Markov Models; understand their role in applications of signal processing; develop techniques for estimating hidden signals from noisy observations.
  • Develop techniques for calibrating statistical time-series models for real data.

Objectives

As specific objectives, by the end of the course students should be able to:

  • Understand the theory and objectives of optimal filtering in an adaptive setting.
  • Recognise and describe the classes of problem where adaptive filtering might be applied.
  • Describe the implementation of the Least Mean Square and its variants, and understand their convergence properties.
  • Understand the basic principles of Kalman filtering and filtering for hidden Markov models.
  • Understand the principles of Sequential Importance Sampling with Resampling, aslo known as particle filtering, for inference in hidden Markov models.
  • Undertand Maximum Likelihood estimation for model calibration and its implementation.
  • Formulate signal processing tasks in a model-based framework, and to estimate the model parameters.

Content

This course is about fitting statistical models to data that arrives sequentially over time. Once an appropriate model has been fit, tasks like predicting future trends or estimating quantities not directly observed can be performed.  The statistical modelling and computational methodology covered by this course is widely used in many applied areas. For example, data that arrives sequentially over time is a common occurrence in Signal Processing (Engineering), Finance, Machine Learning, Environmental statistics etc.
 
The model that most appropriately describes data that arrives sequentially over time is a time-series model, an example of which is the ARMA model (studied in 3F3.) However,  this course will look at more versatile models that incorporate hidden or latent state variables as these are able to account for richer behaviour. Also, models that aim to describe how many really physical processes evolve over time often necessarily have to incorporate unobserved hidden states that form a Markov process. 
 

 

  • Optimal linear filtering: the least mean square algorithm and its variants; recursive least squares; exemplar problems in signal processing.
  • Introduction to state-space models and the recursive optimal linear filtering; the Kalman filter.
  • Introduction to hidden Markov models: definition; inference aims; exact computation of the filter.
  • Importance sampling: introduction; weight degeneracy.
  • Sequential importance sampling and resampling (also known as the particle filter): application to hidden Markov models; filtering; smoothing.
  • Calibrating hidden Markov models: maximum likelihood estimation and its implementation
  • Exemplar problems in Signal Processing
  • Examples Papers

Booklists

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

Examination Guidelines

Please refer to Form & conduct of the examinations.

UK-SPEC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

GT1

Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.

IA1

Apply appropriate quantitative science and engineering tools to the analysis of problems.

IA2

Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.

KU1

Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.

KU2

Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.

E1

Ability to use fundamental knowledge to investigate new and emerging technologies.

E2

Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.

E3

Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.

E4

Understanding of and ability to apply a systems approach to engineering problems.

P1

A thorough understanding of current practice and its limitations and some appreciation of likely new developments.

P3

Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).

P8

Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.

US1

A comprehensive understanding of the scientific principles of own specialisation and related disciplines.

US2

A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.

 
Last modified: 31/05/2018 13:01