I didn't know that -- that's very interesting! Thank you for showing me that.

I learned about Kalman filters in a mobile robotics course that made explicit Gaussian assumptions early on for the primary topic (SqrtSAM), and they brought up Kalman filters in its own lecture as kind of a "this is how they used to do SLAM" lecture. Considering the large amount of overlap in the methods, such as the use of linear covariance projections, I guess I made the assumption that Kalman filters had the same Gaussian assumption.