CAREER: Detection and Estimation in Complex and Uncertain Environments

职业生涯：复杂和不确定环境中的检测和估计NSF提案#1053932PI：Jill Nelson统计信号处理在个人通信、国家安全和医学图像处理等多个领域发挥着重要作用。为了支持这些领域和许多其他领域的持续发展，需要为日益具有挑战性的检测和估计问题开发有效的近乎最佳的解决方案。这项研究的重点是解决在表现出高度复杂性和高度模型不确定性的环境中的检测和估计挑战。在这种情况下，最优检测和估计解决方案通常在计算上是不可行的，如果不是不可能的话。这项研究探索了树搜索技术的有效性，该技术最初是为顺序解码而开发的，以应对这些挑战。这项工作的智力价值在于开发了近似检测和估计算法，该算法实现了近乎最优的性能，同时大大降低了计算复杂性要求。本研究的主要技术目标有两个。第一种是通过分析作为系统特性函数的计算复杂性来表征树搜索技术为其提供竞争解决方案的检测/估计问题空间，并在竞争方法的现有结果的背景下框架结论。第二个目标是开发和评估树搜索方法来解决三个基准问题：广泛分散、快速变化的信道的信道估计和数据检测；认知无线电应用的多发射机位置估计；以及模型不确定或不存在时的动态状态估计。这项研究的教育部分的目的是设计和实施以实践电信活动为中心的初级工程课程，并开发基于问题的学习课程，通过使用概率模型将抽象概念与现实世界的问题联系起来，加深学生对概率和随机过程的理解。

CAREER: Detection and Estimation in Complex and Uncertain EnvironmentsNSF Proposal #1053932PI: Jill NelsonStatistical signal processing plays a fundamental role in fields as diverse as personal communications, national security, and medical image processing. To support the continued advancement of these fields and many others, there is a need to develop efficient near-optimal solutions to increasingly challenging detection and estimation problems. The focus of this research is addressing detection and estimation challenges in environments that exhibit high degrees of complexity and high levels of model uncertainty. In such scenarios, optimal detection and estimation solutions are often computationally infeasible, if not impossible, to determine. This research explores the effectiveness of tree search techniques, originally developed for sequential decoding, to address these challenges. The intellectual merit of the work is in the development of approximate detection and estimation algorithms that achieve near-optimal performance with dramatically reduced computational complexity requirements.There are two primary technical objectives of this research. The first is to characterize the detection/estimation problem space for which tree search techniques provide competitive solutions through analysis of computational complexity as a function of system properties, and to frame conclusions in the context of existing results for competing approaches. The second objective is to develop and evaluate tree search approaches to three benchmark problems: channel estimation and data detection for broadly dispersive, rapidly varying channels; multiple transmitter location estimation for cognitive radio applications; and dynamic state estimation under model uncertainty or absence. The aims of the education component of this research are to design and implement elementary-level engineering curriculum centered around hands-on telecommunications activities, and to develop college-level problem-based learning curriculum that deepens students' understanding of probability and random processes by connecting abstract concepts to real-world problems with probabilistic models.