Distributed, Non-linear Signal Processing for Large Scale Engineering Applications

该研究项目位于电气和计算机工程的三个领域的交叉点，即信号处理、控制理论和优化。将这三个领域结合在一起的首要主题是为多代理系统开发智能、高效和健壮的分布式信号处理算法。虽然线性应用的信号处理具有丰富的理论框架，但非线性、分布式信号处理缺乏一套通用的分析和设计工具。该计划的目标是统一对一大类非线性信号处理算法的研究，这些算法来自高维和分布式动力系统的统计估计原理，其中潜在的信号来自非高斯过程。最近实现的卡尔曼滤波、随机有限集方法、顺序蒙特卡罗方法和粒子流方法的变体已经显示出在状态空间具有相对低维的场景中的前景。随着维度的增加，状态空间维度的诅咒和相关的高计算成本导致其性能迅速恶化。*该研究计划将为大规模、非线性、分布式应用程序开发通用蒙特卡罗方法的实用实现，并展示其在实际工程问题上的有效性。作为大规模、非线性信号处理系统的代表，我们将集中于以下相互关联的研究问题：(A)高维蒙特卡罗方法的扩散融合；(B)基于事件的分布式信号处理和控制；(C)大数据集的加权图信号处理；以及(D)我们提出的算法的收敛性质和性能界的推导。这些信号处理算法将应用于实际工程应用，包括多目标监视(用于联合估计目标的数量及其状态)、分布式摄像网络(用于跟踪移动对象)和电力智能电网(用于实时估计智能电网的运行状态)。在信号处理领域，这项研究将导致开发一套通用的工具和设计原则，用于以计算高效的方式分析大数据集和处理关键任务系统，同时尊重底层过程的非线性物理特性。在整个研究资助期限内，通过HQP培训6名博士和6名硕士学生(此外还有15名本科生将构建原型作为顶峰项目)，在非线性信号处理领域实现社会影响，开发设计下一代技术所需的一系列技术技能。**

The research program lies at the intersection of three domains within Electrical and Computer Engineering, namely, signal processing, control theory, and optimization. The overarching theme that brings these three areas together is to develop smart, efficient, and robust, distributed signal processing algorithms for multi-agent systems. While signal processing for linear applications has a rich theoretical framework, non-linear, distributed signal processing lacks a universal set of tools for analysis and design. The objective of the program is to unify the study of a broad class of non-linear signal processing algorithms that emerge from statistical estimation principles for high-dimensional and distributed dynamical systems, where underlying signals arise from non-Gaussian processes. Recently implemented variants of the Kalman filter, random finite set methods, sequential Monte Carlo approaches, and particle flow methods have shown promise though for scenarios where the state space has a relatively low dimension. As the dimensions grow, the curse of state-space dimensionality and the associated high computational cost lead to a rapid deterioration in their performance. ******The research program will develop practical implementations of generic Monte Carlo methods for large-scale, non-linear, distributed applications and demonstrate their efficacy on real-life engineering problems. We will focus on the following inter-connected research problems in the context of geographically-distributed agent networks as representatives of large-scale, non-linear signal processing systems: (a) Diffusive fusion for large dimensional Monte Carlo approaches; (b) Event based distributed signal processing and control; (c) Weighted graph signal processing for large data sets; and (d) Derivation of the convergence properties and performance bounds of the algorithms we propose. These signal processing algorithms will be applied to practical engineering applications, including multi-target surveillance (for jointly estimating the number of targets and their states), distributed camera networks (for tracking moving objects), and electric smart grids (for estimating the operating status of smart grids in real-time).******Within the signal processing community, this research will result in the development of a universal set of tools and design principles for analyzing large data sets and processing mission critical systems in a computationally efficient manner while respecting the non-linear physics of the underlying processes. Over the length of the research grant, the societal impact is achieved through HQP training of six PhD and six Masters students (in addition to fifteen undergraduate students who will build prototypes as capstone projects) in the area of non-linear signal processing, developing a range of technical skills needed to design the next generation technologies. **