Certifiably Correct State Estimation

Abstract

Many fundamental state estimation problems in robotics and computer vision are naturally formalised as high-dimensional nonconvex optimisation problems; this class includes (for example) the fundamental problems of simultaneous localisation and mapping (in robotics) and 3D reconstruction (in computer vision). Such problems are known to be computationally hard to solve in general, with many local minima that can entrap the smooth local optimisation methods commonly applied to solve them. The result is that standard state estimation algorithms (based upon local optimisation) can be surprisingly brittle, often returning egregiously wrong estimates without warning.

In this talk, Prof. Rosen will present a class of certifiably correct estimation algorithms that are provably capable of solving challenging nonconvex state estimation problems in many practical settings. In brief, these methods directly address the problem of nonconvexity by employing convex relaxations whose minimisers provide verifiably globally optimal state estimates under mild conditions. Using representative problems in robotic spatial estimation, he will illustrate the central ideas behind this approach, and trace its development from specialised algorithms to general-purpose tools for constructing certifiable estimators. These advances substantially reduce the effort required to apply certifiable optimisation to new problems, while extending its reach to realistic challenges such as large-scale computation and corrupted measurements. Together, they provide a path toward robotic estimation systems that combine efficiency, robustness, and rigorous performance guarantees.

Speaker

Prof. David M. Rosen is an Assistant Professor in the Departments of Electrical and Computer Engineering and Mathematics at Northeastern University, where he leads the Northeastern University Robust Autonomy Lab (NEURAL). His work addresses the mathematical, computational, and algorithmic foundations of trustworthy autonomy, with a particular focus on certifiably correct algorithms for robotic perception, control, and learning.

He received a BSc in Mathematics from the California Institute of Technology in 2008, an MA in Mathematics from the University of Texas at Austin in 2010, and an ScD in Computer Science from the Massachusetts Institute of Technology in 2016. Before joining Northeastern, he was a Research Scientist at Oculus Research (now Meta Reality Labs) from 2016 to 2018 and a Postdoctoral Associate at MIT’s Laboratory for Information and Decision Systems from 2018 to 2021.

His work has been recognised with multiple honours from leading international robotics venues, including the inaugural Best Paper Award at the International Workshop on the Algorithmic Foundations of Robotics (2016), selection as an RSS Pioneer (2019), a Best Student Paper Award at Robotics: Science and Systems (2020), and the IEEE Transactions on Robotics King-Sun Fu Memorial Best Paper Award (2025).