Inhomogeneous Kalman filter

Hi,

I was wondering if there are any plans to support the time-dependent dynamics parameters (e.g., $F_t$) and emission parameters (e.g., $H_t$) in LinearGaussian{Conjugate}SSM? The math in the LinearGaussian SSM docs suggests time dependence, but when I look at the code, it looks like they are time-independent (e.g., $F_t=F$ for all $t$).
It appears that some of the mechanics to implement time-dependence is already in place, e.g., in lgssm_posterior_sample and lgssm_smoother.
Unless I am missing something, I think what remains should be quite straightforward. Namely, instead of aggregating the statistics from different time points $t$, just keep the time index and make a separate posterior update for each $t$.
If you're interested, I can help out with a PR.

Kind regards,

Hylke

Start with the LinearGaussian{Conjugate}SSM implementation and compare its parameter handling with lgssm_posterior_sample and lgssm_smoother, which the issue identifies as already supporting time dependence. The work is complete when dynamics and emission parameters can vary by time and the corresponding posterior updates preserve each time index.