I'm struggling with a problem that I just can't seem to get a grasp of. I'm supposed to calculate an estimate for state $x(k)$ at times $k=1,2,3$ from the state-space
$ \begin{align} x(k+1) &= A x(k) + B u(k) + w(k) \\ y_1(k) &= x(k) + v1_(k) \\ y_2(k) &= x(k-1) + v_2(k) \\ \end{align} $
where the covariances of the noises are given as
$E[w(k)w(k)']$ , $E[v_1(k)v_1(k)']$, $E[v_2(k)v_2(k)']$
and
$u(k)$ is given for $k=1,2,3$
$y_1(k)$ is given for $k=1,2,3$
$y_2(k)$ is given for $k=2,3$
What kind of technique am I supposed to use? Information Kalman filter?