Computational Bayesian methods for communications and control

As available computing power increases, there are now opportunities to use computational numerical methods to solve engineering problems that were once intractable. This thesis presents the application of stochastic simulation methods to areas of telecommunications and system identification. While there are many randomised algorithms available for solving problems of optimisation and integration, the focus in this work is on those based on Markov chain Monte-Carlo methods, for which it is possible to prove convergence results. This thesis provides an introduction to the Markov chain theory that is used in this area, through to the point of proving convergence properties of the algorithms developed and showing the conditions required. A method is presented for multi-user detection in code division multiple-access communications systems. The Metropolis algorithm is used to build a soft-input, soft-output detector, which provides the maximum a posteriori estimate of the symbols sent, together with the probability of error. This demonstrates the ability of stochastic algorithms to be used in high speed applications. For the second application of this thesis, the parameter estimation of dynamic systems models is considered. Not only does this provide a means of obtaining maximum a posteriori estimates of parameters in nonlinear and non-Gaussian model structures, but also provides full probability density functions of the parameters given the observed measurements. By additionally incorporating the Particle Filter, a wide class of model structures may be used. The steps required to achieve this in a computationally efficient manner are described, including a parallel implementation using Graphic Processing Units.