TME filters and smoothers
Since TME can be used to approximate any expectation of the form \(\mathbb{E}[\phi(X(t)) \mid X(s)]\), it is natural to apply TME for Gaussian filtering and smoothing (Zhao, 2021).
See, a Python (Jax) implementation of TME Gaussian filters and smoothers in https://github.com/zgbkdlm/tmefs.