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学植物，从电网到机器人导航）都需要计算机算法，以跟踪以不确定性建模和测量的动态系统的状态。 粒子过滤器是一种跟踪许多颗粒（候选状态）的技术，以达到最佳估计值，即均值或平均值状态的平均值或平均值。 该项目认为对最佳估计值（而不仅仅是单个粒子）的限制提供了一种新的方法来确保建模的正确性和基础系统的安全性。 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是具有挑战性的。该项目的新方法将约束结合到估计过程本身中，避免了浪费时间，并保证以前所不可能的方式融合。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。通过提供其就职班来在罗恩大学的课程。这项研究（i）开发了一种连续的蒙特卡洛方法，该方法迭代地构造了一组近似状态后密度并满足非线性约束的颗粒。 ii）建立此方法的误差界限和收敛属性； iii）得出了传统方法承认有限估计错误的必要条件； iv）应用并评估理论结果以解决现实世界中的应用，并具有线性和非线性约束，包括控制手肢体的控制，通信和生物学中的时变稀疏网络的估计以及电力电网中的新兴应用。