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.
«IMPORTANT — read before publishing this page.
The README currently in this repo is the upstream UKF-M library’s own README. Anyone who checks will see that in about ten seconds, so the page has to be explicit about what is yours and what is the library’s.
Rewrite the paragraph below to say exactly that:
- which parts are the UKF-M library by Brossard, Barrau and Bonnabel
- what YOU implemented, modified, or ran on top of it
- what system you applied it to and what you were estimating
If the honest answer is “I used the library as-is to run experiments for my thesis”, write that. It is still a legitimate project — applying an estimation library correctly to a real problem is real work. What sinks you is letting a reader assume you wrote the filter. Also fix the repo’s README while you’re at it.»
«FILL: what you estimated, on what system, and what the results showed»
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.