In the Kalman Filter, is the one step look-ahead estimate generated before there is an observation, or after? i.e. if we have observations up until time t-1, do we use only this information to generate a prediction for time t?
Secondly, how do the one-step ahead predictions of the state differ from the one-step ahead predictions of the observation? My assumption is that the state predictions differ in that they are updated with the Kalman Gain, whereas the observation predictions are not.