[alanbernstein]

IIRC, The kalman filter has a state-space formulation, in which it is clear that it is equivalent to an LTI filter (https://en.m.wikipedia.org/wiki/Linear_filter). However, I believe updating the statistics of the system in response to updated measurements breaks the "time invariant" part.

This is precisely the classic concept of an audio filter, which is, I believe, the inspiration for the term "filter" in other contexts. Bloom filters and selfie filters don't have much in common in a technical sense, but if you squint you can see the connection.