calculating estimate of a state for a system with two observations of the state from different times 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) &amp;= A  x(k) + B  u(k) + w(k) \\
y_1(k) &amp;= x(k) + v1_(k) \\
y_2(k) &amp;= 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?
HINT

$$ \left| \begin{array}{cc} A &amp; 0 \\ 0 &amp; 1 \end{array} \right| $$