“A major objective of the proposed research concerns the development of optimal control formulations of the feedback particle filter based on optimal transportation theory and mean-field games formalisms,” according to Mehta’s abstract. “The theoretical research is closely integrated with the work on computational algorithms.”
Mehta joined the MechSE Department in 2005. His research interests are at the intersection of dynamical systems and control theory.
Below is the full abstract:
Nonlinear filtering (Bayesian inference and reasoning) and optimization of non-convex (complicated) functions are closely related mathematical problems. Highly accurate solutions for these problems are important in a number of engineering applications, e.g., target tracking and surveillance where multiple sensor measurements are used to track targets, air traffic management to track airplanes, weather surveillance to track hurricanes, ground mapping, geophysical surveys, remote sensing, autonomous navigation, and robotics. Standard solution approaches to these problems include the Kalman filter algorithm and its many extensions. However, in practice, the standard approaches can yield inaccurate and erroneous solutions because of certain technical issues related to nonlinear dynamics and non-Gaussian uncertainty. In the past decade, a new class of algorithmic solution approaches to these problems has emerged referred to as the ‘feedback particle filter.’ The filter is able to better handle the technical issues related to nonlinear dynamics and non-Gaussian uncertainty. This award supports fundamental research to provide needed knowledge for the theoretical development and verification of the feedback particle filter algorithm. The proposed algorithmic and software tools can potentially be directly applied to engineering applications described above. Therefore, results from this research will benefit the U.S. economy and society.
A major objective of the proposed research concerns the development of optimal control formulations of the feedback particle filter based on optimal transportation theory and mean-field games formalisms. The theoretical research is closely integrated with the work on computational algorithms. The algorithmic objectives pertain to numerical solution of the Poisson equation, convergence analysis of the particle system with finitely many particles, and comparisons with importance sampling-based algorithms. The deliverables include efficient numerical schemes which will be implemented and demonstrated in software. To promote transitions, several educational initiatives are proposed that seek to engage undergraduate students in entrepreneurship.