So we have that
We can now, given the value of 
, propagate our state estimate from
to 
. We are not yet able, however, to propagate
our error covariance matrix. We need to look at
so that
This last step is obtained by substituting in our expression for 
, hacking away with
matrix algebra, then reexpressing in terms of .
Now, all we need is the propagation from posteriori error last turn
to a priori error this turn.
Combining these last two re-expressions, we see that
Which allows us to directly propagate our error covariance from n to n+1. If
we express as a function of 
and we'll
have our recursive estimation sequence. Combining equations 
and 
, we have:
where
This, albeit in an aethetically treasonous form, is our Discrete Time Kalman time filter.