Add Continuous-Time Profile Likelihood Plots

[DanWaxman]

This is analogous to the discrete-time notebook.

[Copilot]

Pull request overview

Adds the new continuous-time LTI profile likelihood deep-dive notebook to the documentation navigation, making it discoverable alongside the existing discrete-time notebook.

Changes:

• Added deep_dives/continuous_time_lti_profile_likelihood.ipynb to the MkDocs nav under “Deep Dives”.
• Added the same notebook link to docs/tutorials.md under the Gallery list.

Reviewed changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated no comments.

File	Description
mkdocs.yml	Adds the continuous-time LTI profile likelihood notebook to the site navigation.
docs/tutorials.md	Adds a Gallery link to the new continuous-time notebook.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[mattlevine22]

Nice! Some comments:

1. I would add EnKF with perturb_measurements=True to the comparison (it is our default, and may perform better)

2. I would add the Discretizer + discrete-time Cuthbert filters to this exploration.

• Would be very informative to see changes in accuracy and speed

3. To drive home the point of Discretizer vs continuous-time filtering, perhaps do a sweep over data sample rate (still with simulator at dt0=1e-2)...we would expect that at fast sampled data, they perform similarly (and maybe Discrete-filtering w/ discretized is faster), whereas at slow sample rates, I would expect continuous-time method to do better. Probably just focus on CD-KF vs KF here.

[DanWaxman]

I would add EnKF with perturb_measurements=True to the comparison (it is our default, and may perform better)

Whoops, changed that to see if it helped, but they're about the same. Changed back to the default.

I would add the Discretizer + discrete-time Cuthbert filters to this exploration.

This is blocked by #115. I tried to look at that, but it's a bit more complicated than it seems at first.

To drive home the point of Discretizer vs continuous-time filtering [...]

Also blocked by #115.

[mattlevine22]

Submitted #199 to unblock #115 and get this back on track with including Discretizer + Filter.

[DanWaxman]

This looks good to me now, thanks @mattlevine22! Unfortunately, still can't do UKF, since it results in a time-varying covariance, not allowed by our dynamax integration.

[Copilot]

Pull request overview

Copilot reviewed 2 out of 3 changed files in this pull request and generated 2 comments.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[Copilot]

This link text says "Continuous-time" but the MkDocs nav entry uses "Continuous time". Please keep the title consistent across docs navigation and the tutorials/gallery page so users can easily recognize the same notebook.

Suggested change

	- [Continuous-time LTI profile likelihood](deep_dives/continuous_time_lti_profile_likelihood.ipynb)
	- [Continuous time LTI profile likelihood](deep_dives/continuous_time_lti_profile_likelihood.ipynb)

[mattlevine22]

changed above to use dash

[mattlevine22]

Looks good!