Variational Optimal Transport Methods for Nonlinear Filtering

自主系统的可靠安全运行依赖于对不确定性的准确量化和通过非线性滤波对噪声传感数据的吸收。本研究计划旨在结合机器学习（ML）和最优运输（OT）数学理论的最新进展，以创建可扩展和自适应的非线性过滤算法。研究目标包括所提出算法的计算开发和评估，理论误差分析，扩展算法以处理姿态估计的几何约束，以及开发新的学习框架以适应使用输出感官数据的不正确模型。通过融合机器学习和OT，本研究旨在提高自治系统非线性滤波方法的性能和通用性。智力优势：本研究的智力优势在于条件分布的创新变分公式，作为非线性滤波和机器学习之间的桥梁。这种联系促进了理论和计算工具的交流。该研究旨在探索克服粒子滤波中维数诅咒的方法，为现有的非线性滤波算法（如反馈粒子滤波和集合卡尔曼滤波）提供见解。这反过来为稳定性和误差分析的新途径铺平了道路。此外，所提出的模型自适应和学习框架具有很大的潜力，可以推进从感官数据中学习随机动态系统的研究，并为解决部分观察马尔可夫决策过程（pomdp）相关问题提供新的机会。更广泛的影响：本研究提案具有更广泛的社会影响，因为它为不确定性感知自主系统奠定了基础，导致其在不确定性存在下的安全性和效率的显着提高。通过提高机器人在未知环境中导航、适应动态条件以及做出明智和安全决策的能力，这对机器人等领域产生了影响。该研究还将通过有效管理可再生能源整合带来的不确定性，从而更有效地利用可用能源，从而影响智能电网。此外，该提案还包括教育目标，利用华盛顿大学现有的基础设施为本科生提供研究机会，并为未被充分代表的少数民族提供指导。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The reliable and safe operation of autonomous systems relies on accurately quantifying uncertainty and assimilating noisy sensory data through nonlinear filtering. This research proposal seeks to combine recent advancements in machine learning (ML) and the mathematical theory of optimal transportation (OT) to create scalable and adaptable nonlinear filtering algorithms. The research objectives encompass computational development and evaluation of the proposed algorithms, theoretical error analysis, extending the algorithms to handle geometric constraints for pose estimation, and the development of a new learning framework to adapt incorrect models using output sensory data. By merging ML and OT, this research aims to enhance the performance and versatility of nonlinear filtering methods for autonomous systems.Intellectual Merit: The intellectual merit of this research lies in the innovative variational formulation of conditional distributions, acting as a bridge between nonlinear filtering and machine learning. This connection facilitates the exchange of theoretical and computational tools. The research aims to explore ways to overcome the curse of dimensionality in particle filters, offering insights into existing nonlinear filtering algorithms like feedback particle filter and ensemble Kalman filter. This, in turn, paves the way for new avenues in stability and error analysis. Furthermore, the proposed model adaptation and learning framework holds great potential to advance the study of learning stochastic dynamic systems from sensory data and provides new opportunities in solving problems related to partially observed Markov decision processes (POMDPs). Broader Impacts: This research proposal has broader societal impacts as it lays the foundation for uncertainty-aware autonomous systems, leading to significant improvements in their safety and efficiency in the presence of uncertainty. This impacts domains such as robotics, by increasing their capability to navigate unknown environments, adapting to dynamic conditions, and making informed and safe decisions. The research would also impact the smart-grid by effectively managing the uncertainty, due to integration of renewable energy sources, leading to more efficient utilization of available energy sources. Additionally, the proposal includes educational objectives, leveraging the existing infrastructure at the University of Washington to provide research opportunities for undergraduates and mentorship for underrepresented minorities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.