Sequential Signal Processing by Markov Chain Monte Carlo Sampling

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AbstractFiltering, prediction, and smoothing are basic signal processing operations. They are all extremely important and are implemented in every radio and TV set, CD player, modem, telephone receiver, and practically any device that extracts information by processing data. Most of the research on these operations in the past has been related to "easy" problems, which are tractable and amenable to nice mathematical analyses. In reality, however, there are many situations where the standard methods of signal processing do not work well and require an altogether different, more general approach. This project is developing methods and techniques for a very wide range of difficult problems that arise in such situations. The areas that will benefit from the results of this research include communications, radar, sonar, seismology, robotics, financial engineering, and control. This research involves work with dynamic nonlinear and non-Gaussian models. The applied methodology is Bayesian, and the main role is played by the concept of sample filters. Their role is to propagate filtering densities, which are represented by samples drawn from these densities The method is implemented by generating samples from predictive densities, followed by drawing samples from posteriors. Sampling from the posteriors is challenging and will be implemented by perfect samplers. These are based on Markov chain Monte Carlo sampling and the concept of coupling from the past. Perfect sampling is a new concept, and not many results about it are available. It is even more so in the context of sampling from continuous spaces. Therefore, a significant component of the research will be on constructing efficient samplers that will fit the needs of the addressed application. The scope of work also includes performance analyses of the developed sample filters, work on case dynamic models, and development of general guidelines for the new filters.