Derivatives of angles

[florisvb]

Taking derivatives of a noisy time series of angles is always a huge pain (mostly because unwrapping noisy data is very hard). It would be nice if we could provide some examples (maybe helper functions?) of how to do this, which methods work best, etc. Furthermore, it could be that some methods (like the loss based methods) can be adjusted to do this in a much more elegant way by implementing an angular difference in the loss function.

Discrete action items:

1. Band-aid: provide a helper function to unwrap and then differentiate angular time series
2. Try modifying a loss based method to do angular losses, and if that works, extend to other loss based methods
3. Decide on a software architecture that would be clean. For example, would angular helper functions and modified loss methods live under their own "angulardiff" subpackage, or do we modify methods so that they have an "angular" flag?

[pavelkomarov]

What is angular differentiation? Isn't $\theta$ just a variable like $t$?

[florisvb]

If you have a time series of angles taking the derivative is really obnoxious because of wrapping issues. If the signal passes through +/- 2pi you get a discrete wrap around. If you don't deal with this you will get huge artificial spikes in the derivative. For a perfectly clean signal it isn't too hard to unwrap the signal so it does not have discontinuities. But when there is noise it is really hard. We frequently encounter this issue to estimate angular velocity from measurements of angles, and every time it requires recycling some obscure code or writing something from scratch. It would be a huge help if pynumdiff could offer a well tested and robust method. I suspect that with the right implementation the Kalman and Robust methods would do very nicely for this. For example, in the innovation step you can implement an angular difference rather than a normal euclidean difference.

…

On Tue, Nov 25, 2025 at 10:15 AM Pavel Komarov ***@***.***> wrote: *pavelkomarov* left a comment (florisvb/PyNumDiff#178) <#178 (comment)> What is angular differentiation? Isn't $\theta$ just a variable like $t$? — Reply to this email directly, view it on GitHub <#178 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAB4EPBCSSO7DKSJTG7ILRT36SMDFAVCNFSM6AAAAACNCPDVMSVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTKNZWHE2DKMBTGI> . You are receiving this because you authored the thread.Message ID: ***@***.***>

-- Floris van Breugel | http://www.florisvanbreugel.com Associate Professor of Mechanical Engineering & Graduate Program for Neuroscience University of Nevada, Reno Wildlife and Landscape Photography Galleries: http://www.ArtInNaturePhotography.com/ Blog: http://www.ArtInNaturePhotography.com/wordpress/