[Too]

Yes, point 2 is really the elevator pitch of Kalman filters. It enables sensor fusion, averaging a fast noisy sensor with a slow accurate sensor, or even add a model as one less confident input to the filter.

As pointed out elsewhere in this thread, demonstrating a Kalman filter with only one input doesn’t really show their real potential.

[auxym]

Regarding the model as an optional less confident input:

I mostly know KFs from the third approach, control theory, state observers, state space representation, where the model is a central concept.

Can you actually use KF without a model? I'm curious, would you point out some references?

[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.