[eru]

Though I suspect the Kalman filter only can be described as averaging, if the distributions are mono-modal?

(Or is Kalman filter defined to only work for Gaussian distributions anyway, and otherwise you call it Bayesian updating?)

[touisteur]

I think state of the art can work with something different than Gaussian distribution, either in the input data or the predicted one (which, with non linear models can be very unregular). Isn't that the point of the unscented kalman filter and all the ones that generate lots of hypotheses to check the target distribution. I probably don't use the correct vocabulary here... Sorry.