The problem is as follows: in a state space model:
\begin{align} S(t) &= A * S(t-1) + u(t) \\ Z(t) &= B * S(t) + v(t) \end{align}
where $S(t)$ is a vector process containing $4$ variables but only the last $2$ variables are unobservable, $Z(t)$ contains $6$ observable variables. I know if the $4$ variables in $S(t)$ are all unobservable, then we can use Kalman filter to estimate the model and to filter out $S(t)$. But in my setup, can I still use Kalman filter to estimate and to filter out the only $2$ unobservable variables in $S(t)$? If yes, do I need to modify the algorithm and how?
Many thanks in advance!