Improving How Machines Perceive and React to the World
MIE Associate Professor Laurent Lessard was awarded a $374K NSF grant for “Optimization-Based Methods for State Estimation”.
Abstract Source: NSF
State estimation, a foundational problem in modern science and engineering, is the process of determining the internal state of a system when only indirect, noisy, or incomplete measurements are available. Nearly every intelligent technology depends on this capability, including autonomous vehicles, robotics, medical imaging, advanced manufacturing, energy networks and financial analytics. In artificial intelligence and data-driven decision systems, state estimation underlies the ability of machines to interpret data and make reliable predictions in real time. However, real-world systems often violate the ideal mathematical assumptions on which classical estimation methods are built. Measurements may contain frequent outliers or unexpected disturbances, and system dynamics may be nonlinear or poorly modeled. In these settings, existing approaches can become unreliable or computationally burdensome. This award supports research that develops a new mathematical framework that reformulates state estimation as a structured optimization problem, enabling more accurate and computationally efficient estimation even under complex and non-ideal conditions. By strengthening the reliability of intelligent technologies that depend on accurate state information, this research supports innovation, economic competitiveness, and public safety. The project will also contribute to education and workforce development by training graduate and undergraduate students, integrating research results into advanced coursework, and engaging students in hands-on research experiences.
This research reformulates state estimation as a problem of maximum a posteriori optimization problem and develops a dynamic programming recursion analogous to that used in optimal control. In the classical linear Gaussian case, this framework recovers the standard Kalman filter, providing a unified perspective. For systems with non-Gaussian noise (Aim I), the research will develop new recursive estimators by locally approximating log-likelihood functions and solving the resulting optimization problems using Newton-type and online optimization methods. The research will analyze robustness to heavy-tailed and multimodal noise distributions, develop algorithmic modifications to enhance numerical stability, and establish theoretical guarantees of convergence and stability using tools from convex optimization and nonlinear control. For systems with nonlinear dynamics (Aim II), the research aims to generalize the optimization-based recursion to nonlinear state and measurement models, exploring both perturbation-based analyses and higher-order or polynomial approximations that trade computational effort for improved accuracy. Throughout, the estimators will be evaluated on a comprehensive suite of numerical benchmarks involving nonlinear dynamical systems that arise in manufacturing and medical applications. Anticipated outcomes include computationally efficient state estimation algorithms with provable properties, stronger theoretical connections between estimation and control, and a unified optimization framework for nonlinear and non-Gaussian filtering.