AF: Small: THEORETICAL AND ALGORITHMIC FOUNDATIONS OF CONSTRAINED PARTICLE FILTERING

AF：小：约束粒子过滤的理论和算法基础

• 批准号: 1527822
• 负责人: Nidhal Bouaynaya
• 金额: $ 34.99万
• 依托单位: Rowan University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1527822&HistoricalAwards=false
• 关键词: AF; Small; THEORETICAL; ALGORITHMIC; FOUNDATIONS

Many modern technologies (from image stabilizations in a camera, to chemical plants, from power grids to robot navigation) require computer algorithms to track the state of a dynamical system that is both modeled and measured with uncertainty. Particle filters are a technique that track many particles (candidate states) to arrive at a best estimate, which is the mean or average of tracked state. This project considers constraints on the best estimate (and not just individual particles) giving a new way to ensure correctness of the modeling, and safety of the underlying system. Handling constraints in dynamical systems in real time is challenging when either the systems or the constraints, or both, are nonlinear. The new methods of this project incorporate the constraints into the estimation process itself, avoiding wasted time and guaranteeing convergence in ways that were not possible before. The project also includes integrated research and learning activities, and will serve as a crucial catalyst to the new Ph.D. program at Rowan University by providing its inaugurating class. This research (i) develops a sequential Monte Carlo method that iteratively constructs a set of particles that approximate the posterior density of the state and also satisfy the non-linear constraints; ii) establishes error bounds and convergence properties of this method; iii) derives necessary and sufficient conditions under which traditional approaches admit a bounded estimation error; iv) applies and assesses the theoretical results to solve real-world applications, with linear and non-linear constraints, including control of hand prostheses, estimation of time-varying sparse networks in communications and biology, and emerging applications in the electric power grid.

许多现代技术（从相机中的图像稳定到化工厂，从电网到机器人导航）都需要计算机算法来跟踪动态系统的状态，该动态系统的建模和测量都具有不确定性。 粒子滤波器是一种跟踪许多粒子（候选状态）以获得最佳估计的技术，即跟踪状态的平均值。 该项目考虑了对最佳估计（而不仅仅是单个粒子）的约束，从而提供了一种新的方法来确保建模的正确性和底层系统的安全性。 当系统或约束或两者都是非线性时，实时处理动态系统中的约束具有挑战性。该项目的新方法将约束纳入估计过程本身，避免了浪费时间并保证以以前不可能的方式收敛。该项目还包括综合研究和学习活动，并将成为新博士学位的关键催化剂。罗文大学的项目，提供其首届课程。这项研究 (i) 开发了一种顺序蒙特卡罗方法，迭代地构造一组近似状态后验密度并满足非线性约束的粒子； ii) 建立该方法的误差范围和收敛特性； iii) 导出传统方法承认有界估计误差的必要和充分条件； iv) 应用和评估理论结果来解决具有线性和非线性约束的现实世界应用，包括手假肢的控制、通信和生物学中时变稀疏网络的估计以及电网中的新兴应用。