New Model and Methodology for Signal Estimation and Decoding

这个项目旨在将非线性动力学应用于(迭代)统计推理的研究，迭代统计推理是一类重要的算法，在通信、信号处理和人工智能中得到了广泛的应用。现有的迭代分析模型和方法主要是从信息论的角度出发的，不足以预测和控制大维度和高动态信号序列的个体(而不是集合平均)时间演化行为。另一方面，估计非线性动力系统，特别是具有挑战性的混沌情况，几乎没有充分利用统计推理这一强大的工具。计划开展一系列广泛的活动，将这两个领域的重要思想和工具结合在一起，相互提供新的视角和新的方法，并有望产生一种全新的工程方法来统一经典信号和混沌信号。具体内容将集中在理解统计推理中混沌行为的原因和影响，开发控制混沌和瞬时混沌的方法，以及在适当的模型上使用统计推理，如马尔可夫随机场和因子图，以预测和同步混沌系统。鉴于统计推断算法和非线性动力学理论在实际应用中的广泛应用，在所提出的方向上的研究工作将具有重大的社会和科学影响。它的潜在应用非常广泛，包括许多通信系统和离散动力系统，如蜂窝网络、无线传感器和自组织网络、数字数据记录系统、雷达系统、天气和龙卷风预报、生态学和人口估计。拟议的研究还纳入了有意义的教育和宣传部分，其中包括开设一系列研讨会，向本科生和研究生提供这些项目，开发一门新的研究生课程，并让代表人数不足的学生参与研究。

This project aims to apply nonlinear dynamics to the study of (iterative) statistical inference, an important class of algorithms with well-proven applications in communications, signal processing and artificial intelligence. Existing models and methodologies for iterative analysis, coming largely from an information theoretical perspective, are inadequate in predicting and controlling the individual (rather than the ensemble-average) time-evolution behavior of a large-dimension and highly-dynamic signal sequence. On the other hand, estimating nonlinear dynamical systems, especially the challenging case of chaos, has not taken advantage of the powerful tool of statistical inference nearly as much as it could have. A wide spectrum of activities are planned to bring together the important ideas and tools from these two fields, to supply each other with new perspectives and new approaches, and to hopefully generate a whole new engineering methodology for unifying classical signals and chaotic signals. Specific focus will be set on understanding the cause and impact of chaotic behavior in statistical inference, developing ways to control chaos and transient chaos, and using statistical inference on appropriate models, such as Markov random fields and factor graphs, to predict and synchronize chaotic systems. In view of the very pervasive scope of the practical applications associated with statistical inference algorithms and nonlinear dynamical theory, the research work in the proposed direction will have significant societal and scientific impacts. The potential application is broad, including many communication systems and discrete dynamical systems, such as cellular networks, wireless sensor and ad-hoc networks, digital data recording systems, radar systems, weather and tornado prediction, ecology, and population estimation. The proposed research also integrates a meaningful education and outreach component, which includes opening a series of seminars, supplying undergraduate and graduate students with theses projects, developing a new graduate level course, and engaging under-represented students in research.