Undergraduate - UnitECE3093 - Optimisation estimation and numerical methods

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Synopsis

This unit will introduce students to matrix decomposition methods including singular value decomposition with applications including data compression, image processing, noise filtering, and finding exact and approximate solutions of linear systems. Numerical methods for working efficiently with large matrices and handling ill-conditioned data will be discussed. Methods for unconstrained and constrained optimisation will be presented, with use of MATLAB. The second half of the unit will focus on stochastic processes inboth discrete and continuous time, with applications to time series modelling, and circuit analysis.

Outcomes

On completing this unit, students will have learned advanced mathematical techniques for working efficiently and reliably with both deterministic and stochastic systems, and their use in solving problems frequently arising in engineering applications such as solving linear systems, solving systems of differential equations, handling noise, modelling control systems, time series analysis, and studying stability in dynamical systems. Students will develop a rich set of techniques: eigenanalysis greatly simplifies the calculations for many numerical tasks; singular value decomposition and principal component analysis provide powerful tools for data compression and noise filtering; curve fitting methods for estimation, and optimization tools add to the toolkit of techniques students will learn to enable them to tackle a range of practical engineering problems. Students will also have learnt how to work with discrete and continuous random variables and some important distributions, random vectors and their covariance matrices, calculating best linear predictors, modeling using
random sequences and stochastic processes in continuous time, autocovariance functions, transfer functions, spectral density and linear filters, ARMA models and finding best linear predictors for stationary processes.

Assessment

Continuous assessment: 30%
Examination: (3 hours): 70%.
Students are required to achieve at least 45% in the total continuous assessment component (assignments, tests, mid-semester exams, laboratory reports) and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit.

Chief examiner(s)

Professor Kate Smith-Miles

Contact hours

3 hours lectures, 2 hours laboratory and practice classes and 7 hours of private study per week

Prerequisites

ECE2011, ENG2092