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

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。 粒子滤波是一种跟踪多个粒子（候选状态）以达到最佳估计的技术，该估计是跟踪状态的均值或平均值。 该项目考虑了对最佳估计（而不仅仅是单个粒子）的约束，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，在真实的时间中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纳入估计过程本身，避免浪费时间，并以以前不可能的方式保证收敛。该项目还包括综合研究和学习活动，并将作为新的博士学位的关键催化剂。在罗文大学的课程，通过提供其开创性的类。本研究（i）发展了一种序贯蒙特卡罗方法，该方法迭代构造一组粒子，这些粒子近似于状态的后验密度，并且还满足非线性约束; ii）建立了该方法的误差界和收敛性质; iii）推导了传统方法允许有界估计误差的充要条件; iv）应用和评估理论结果，以解决现实世界的应用，线性和非线性约束，包括手部假肢的控制，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。

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.