In the textbooks and in code examples, the Kalman filter equations usually have the prediction step first followed by the measurement updates. Specifically, inside the loop that iterates over the measurements, prediction is first and then the measurement update step. My question is the following: Is it correct to swap these two and put the measurement update first and then the prediction so at each time step I have a prediction for the next time step? What I want to achieve is that at time k I make a prediction about k+1, and then at k+1 I refine the estimates. 
Does that make sense?
Thanks.