Variational Optimal Transport Methods for Nonlinear Filtering

University Of Washington, Seattle WA

Investigators

Abstract

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 various 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 of students. 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.