State and Parameter Estimation on Manifolds
Unscented Kalman filtering for stochastic systems whose state lives on a Riemannian manifold.
Work from my undergraduate thesis at IIT Guwahati on state and parameter estimation for stochastic state-space systems evolving on Riemannian manifolds.
The standard Kalman machinery assumes state lives in a vector space. Plenty of real systems don’t — orientation lives on SO(3), pose on SE(3), and naively applying a linear filter to those coordinates gives you estimates that drift off the manifold entirely. The unscented Kalman filter on manifolds (UKF-M) handles this by propagating sigma points through retraction and local-chart operations instead of vector addition.
The filter itself is the UKF-M library by Brossard, Barrau and Bonnabel; my thesis work builds on it.
What I applied it to. My thesis, supervised by Prof. Budhaditya Hazra, looked at parameter and state estimation of vibrating structures equipped with geometrically consistent tuned mass dampers (GTMDs). We simulated the physical system in MATLAB and Python and used Kalman filters on Riemannian manifolds, framed through Lie algebra, as the estimation tool.
Before the thesis I spent a summer research internship with the same group (May–Jul 2023) exploring Riemannian geometry and Itô calculus: using geodesics and tensors to capture nonlinear relationships, and estimating the parameters of Gaussian and log-normal densities on curved spaces with MLE and Bayesian models.
Documents: BTP report, phase 1 · Term paper · Slides
Why it still matters to me. This is where my interest in estimation started, and it’s the thread running through what I’m reading now — how a controller behaves when the state estimate it depends on is wrong is, to me, the more interesting half of learning for control.