Variational Optimal Transport Methods for Nonlinear Filtering

自主系统的可靠和安全运行依赖于通过非线性滤波准确地量化不确定性和同化噪声感官数据。这一研究方案试图结合机器学习(ML)和最优运输(OT)的数学理论来创建可扩展和自适应的非线性滤波算法。研究目标包括所提出的算法的计算开发和评估、理论误差分析、扩展算法以处理用于位姿估计的几何约束，以及开发新的学习框架以适应使用输出感官数据的错误模型。通过将ML和OT相结合，本研究旨在提高自治系统的非线性滤波方法的性能和通用性。智力价值：本研究的智力价值在于创新的条件分布变分公式，在非线性滤波和机器学习之间起到了桥梁作用。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的维度诅咒的方法，为反馈粒子滤波和集成卡尔曼滤波等现有的非线性滤波算法提供见解。这反过来又为稳定性和误差分析方面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来推进从感官数据学习随机动态系统的研究，并为解决与部分观测马尔可夫决策过程(POMDP)相关的问题提供了新的机会。更广泛的影响：这项研究提案具有更广泛的社会影响，因为它为感知不确定性的自主系统奠定了基础，从而在存在不确定性的情况下显著提高了它们的安全性和效率。这对机器人等领域产生了影响，因为它们提高了在未知环境中导航、适应动态条件以及做出明智和安全决策的能力。这项研究还将通过有效管理可再生能源整合带来的不确定性来影响智能电网，从而更有效地利用现有能源。此外，该提案包括教育目标，利用华盛顿大学现有的基础设施为本科生提供研究机会，并为代表不足的少数民族提供指导。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.