Sequential Signal Processing by Markov Chain Monte Carlo Sampling

摘要滤波、预测和平滑是基本的信号处理操作。它们都非常重要，应用于每一台收音机、电视机、CD播放机、调制解调器、电话接收机以及几乎任何通过处理数据提取信息的设备。过去对这些操作的大多数研究都与“简单”问题有关，这些问题易于处理，易于进行良好的数学分析。然而，在现实中，有许多情况下，标准的信号处理方法不能很好地工作，需要一个完全不同的，更通用的方法。这个项目正在开发各种方法和技术，以解决在这种情况下出现的各种各样的难题。受益于这项研究成果的领域包括通信、雷达、声纳、地震学、机器人、金融工程和控制。本研究涉及动态非线性和非高斯模型的工作。应用的方法是贝叶斯，主要作用是样本滤波器的概念。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中生成样本，然后从后验中提取样本来实现。从后验采样是具有挑战性的，将由完美采样器实现。这些都是基于马尔可夫链蒙特卡罗采样和耦合的概念从过去。完全抽样是一个新概念，关于它的研究结果并不多。在从连续空间采样的情况下更是如此。因此，研究的一个重要组成部分将是构建有效的采样器，以满足所处理的应用的需要。工作范围还包括开发的示例过滤器的性能分析，案例动态模型的工作，以及新过滤器的一般指导方针的开发。

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.