Sequential Signal Processing by Markov Chain Monte Carlo Sampling

滤波、预测和平滑是信号处理的基本操作。它们都非常重要，并且在每台收音机和电视机，CD播放机，调制解调器，电话接收器以及几乎任何通过处理数据提取信息的设备中都有实现。在过去，对这些运算的研究大多与“简单”问题有关，这些问题易于处理，并适合于良好的数学分析。然而，在现实中，有许多情况下，信号处理的标准方法不能很好地工作，需要一个完全不同的，更一般的方法。该项目正在为在这种情况下出现的各种各样的困难问题开发方法和技术。将从这项研究成果中受益的领域包括通信、雷达、声纳、地震学、机器人技术、金融工程和控制。这项研究涉及的工作与动态非线性和非高斯模型。应用的方法是贝叶斯，主要作用是由样本过滤器的概念。它们的作用是传播过滤密度，这些密度由从这些密度中提取的样本表示。该方法通过从预测密度生成样本，然后从后验中提取样本来实现。从后验中采样是具有挑战性的，将由完美的采样器来实现。这些都是基于马尔可夫链蒙特卡罗抽样和耦合的概念从过去。完美抽样是一个新概念，关于它的结果并不多。在从连续空间采样的背景下，情况更是如此。因此，研究的一个重要组成部分将是构建有效的采样器，将适合所解决的应用程序的需求。工作范围还包括对已开发的样本过滤器进行性能分析，研究案例动态模型，以及为新过滤器制定一般准则。

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.