# What information is used to make predictions in the kalman filter, and how do the state predictions differ from the measurement predictions?

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.

• Before. First you predict than you use the observation to update your belief. Hope this video helps you: youtube.com/watch?v=Qa8YMP9dQYo – xboard Sep 18 '17 at 14:46
• thanks, very helpful. I have a few more questions: (1) What statistical tests should we run to test the performance of the Kalman Filter? (2) Should I expect the difference between the forecast estimates and the observations to converge to zero over time? (3) Should I expect the difference between the posterior estimate and the observations to converge to zero? – user5211911 Sep 18 '17 at 17:08
• Closely related: stats.stackexchange.com/questions/272736 – Juho Kokkala Sep 20 '17 at 5:52