# Kalman filter and data extrapolation

Context of the situation:

I have a system set up that can give me the position of a person in a room. I also have a light that shines on this position. However, the light are lagging behind by 0.300 seconds.

sample rate for position is 33.33Hz

I want to try and predict the position of the person 0.300 seconds in the future. I understand that I can use Kalman filter to predict the next state which occurs in 0.03 seconds later. Can I use the Kalman filter and predict 0.300 seconds ahead?

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Of course you can - the predict stage in the Kalman filter accepts a time difference $dt$ which you can choose arbitrarily - it is not necessarily the sampling rate. Of course, larger $dt$ gives a larger error, but whether or not the error is acceptable is problem dependent.