I've got the following question from an exam I took a while ago.
I don't understand where the indices $(1,0), \ (1,1), \ (2,0) \ \text{and} \ (2,1)$ come from. I know that there are two prediction terms for $i$ because it's a second order system. But as far as I know $N = 1$ so the summation should stop at $i = 0$.
From the context of the question it seems that $x_{i,j|k}$ refers to the $i$th element of the state at time $j$ given measurements up until time $k$. In your case you have second order system so the size of the state is two, so $i \in \{1,2\}$.