This is a very educational and intuitive way of putting it, but to nitpick the Kalman filter is a very special case of this (it assumes a linear ruleset and Gau

This is a very educational and intuitive way of putting it, but to nitpick the Kalman filter is a very special case of this (it assumes a linear ruleset and Gaussian uncertainties in the sensor readings). What you're describing is in general the Bayesian filter (or Bayesian smoothing if you don't have to give the result immediately).