Monte Carlo Filters for Nonlinear and Non-Gaussian Dynamic Systems

9982846本研究关注非线性和非高斯动态系统的蒙特卡罗方法。 蒙特卡罗滤波器的基本思想是从系统当前状态的分布中顺序生成随机样本。 与传统的滤波方法相比，简单、灵活、功能强大的蒙特卡罗方法为处理复杂动态系统提供了有效的手段。 研究者在这项研究中研究了四个具体问题。 论文的第一部分研究了一种特殊的蒙特卡罗滤波器--混合卡尔曼滤波器，它适用于实际中经常遇到的一类系统--条件动态线性模型。 该过滤器利用“边缘化”操作来提高效率。 题目（II）研究了部分拒绝控制操作，这是一种在蒙特卡罗滤波器中产生更有效的随机样本的操作。 题目（三）研究了系统系数未知的动力系统的处理方法，这是一个重要而又困难的问题。 主题（IV）讨论了蒙特卡罗滤波器的几个应用，包括在杂波环境中跟踪多个机动目标，数字无线通信中的贝叶斯接收机，金融时间序列分析中市场波动的在线估计，以及非高斯新息的随机系统控制。 在雷达或声纳监视系统、移动的电信、经济和金融数据分析、计算机视觉、医疗诊断、语音识别、反馈控制和引导系统以及互联网流量监视和控制中，例子比比皆是，仅举几例。 它们大多数是非线性和非高斯的。 在处理动态系统的主要挑战之一是，他们通常需要在线（在真实的时间）的不断变化的系统特性的估计和预测（过滤），给定的观察和信息的连续流从系统。 研究和开发非线性和非高斯动态系统的蒙特卡罗滤波器。蒙特卡罗滤波器的基本思想是顺序地生成随机样本来表示系统当前状态的状态（分布）。现代计算能力的提高使蒙特卡罗方法作为滤波方法在实际应用中成为可能。 与传统的滤波方法相比，简单、灵活、功能强大的蒙特卡罗方法为处理复杂动态系统提供了有效的手段。 该研究丰富了非线性、非高斯动态系统的在线滤波工具。更快、更有效的滤波技术必将对真实的生活中广泛的重要应用产生重大影响，为推动科学技术进步做出重大贡献。 它还促进了工程和统计之间的跨学科研究。

9982846This research is concerned with Monte Carlo methods for nonlinear and non-Gaussian dynamic systems. The basic idea of the Monte Carlo filter is to sequentially generate random samples from the distribution of the current state of the system. Compared with traditional filtering methods, simple, flexible, yet powerful Monte Carlo techniques provide effective means to deal with complex dynamic systems. The investigator studies four specific topics in this research. Topic (I) studies a special Monte Carlo filter called Mixture Kalman filter for the conditional dynamic linear models, a class of widely encountered systems in practice. This filter utilizes the `marginalization' operation to improve efficiency. Topic (II) studies a partial rejection control operation, an operation aimed to generate more efficient random samples in Monte Carlo filters. Topic (III) studies methods to deal with dynamic systems with unknown system coefficients, an important but difficult problem. Topic (IV) is devoted to several applications of Monte Carlo filters, including tracking multiple maneuvering targets in a clutter environment; Bayesian receivers in digital wireless communications; on-line estimation of the market volatility in financial time series analysis; and stochastic system control with non-Gaussian innovations.Dynamic systems are widely used in almost all fields of applications. Examples abound in radar or sonar surveillance systems, in mobile telecommunications, in economic and financial data analysis, in computer vision, in medical diagnostics, in speech recognition, in feed-back control and guidance systems, and in Internet traffic monitoring and control, just to name a few. Most of them are nonlinear and non-Gaussian. One of the main challenges in dealing with dynamic systems is that they usually require on-line (in real time) estimation and prediction (filtering) of the ever-changing system characteristics, given the continuous flow of observations and information from the system. The investigator studies and develops Monte Carlo filters for nonlinear and non-Gaussian dynamic systems. The basic idea of the Monte Carlo filter is to sequentially generate random samples to represent the status (distribution) of the current state of the system. Modern computing power has made it feasible to use Monte Carlo methods as filtering methods in application. Compared with traditional filtering methods, simple, flexible, yet powerful Monte Carlo techniques provide effective means to deal with complex dynamic systems. This research enriches the toolkit of on-line filtering for nonlinear and non-Gaussian dynamic systems. Faster and more effective filtering techniques will certainly have significant impact on a wide range of important applications in real life and make significant contributions to advancing science and technology. It also promotes the interdisciplinary research between engineering and statistics.