ECE3093 - Optimisation estimation and numerical methods

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: Eigen analysis 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.