The celebrated Kalman filter has been widely applied in diverse fields to optimally estimate the state of dynamical systems. Despite this success, some challenges remain regarding its implementation in spatially distributed systems: Kalman filters are optimal under the implicit assumption that all-to-all (i.e., centralized) communications are available within the system; however, centralized communications are often infeasible in spatially distributed systems. Such a challenge motivates the design of decentralized Kalman filters, with limited communications among different spatial sites.
In this talk, I will focus on the optimal design of decentralized Kalman filters for spatially invariant systems with linear spatiotemporal dynamics described by PDEs. This is a particular instance of infinite-dimensional filtering. First, I will derive important structural characteristics of the filter in this problem set-up, showing that the filter is spatially localized and that noise properties define its degree of spatial localization. I will introduce dimensional analysis and define the Branch Point Locus as useful tools to elucidate the degree of spatial localization of the filter. Second, I will utilize such structural properties to inform a novel framework for the design of optimal distributed Kalman filters through a convex functional optimization. I will discuss the sensitivity of the performance gap between centralized and decentralized architectures to different system parameters and highlight the usefulness of dimensional analysis for this task. I will conclude the talk summarizing related on-going research directions.
Juncal Arbelaiz is a Schmidt Science Postdoctoral Fellow at Princeton University, affiliated with the Mechanical & Aerospace Engineering department and with the Center for Statistics and Machine Learning. Previously, she received her Ph.D. degree in applied mathematics from the Massachusetts Institute of Technology (MIT) in September 2022. Her research interests are in decentralized control and estimation of spatially distributed systems, inverse problems, and statistical inference.
Dr. Arbelaiz was honored as an extraordinary woman of the Basque Country through the APARTAK award in November 2023 and as a Rising Star in EECS in 2021. She was the recipient of a Hugh Hampton Young Memorial Fellowship from the Office of Graduate Education at MIT (2020 & 2021). She has been recognized as a: McKinsey Next Generation Women Leader (2020), Rafael del Pino Excellence Fellow (2019), Google Anita Borg Fellow (2018), a National Awardee for Academic Excellence of the Government of Spain (2018), a la Caixa Foundation Fellow (2017) and a MIT Presidential Fellow (2016). She was a Young Author Awardee finalist at NecSys 2022.
