{%hackmd BJrTq20hE %}
Context
Given a system that contains $N$ unknown states, whose values at time $k$ are denoted as
$$
\mathbf{x}_k \in \mathbb{R}^N
$$
We want to know the values of $\mathbf{x}_k$, but we were unable to directly observe $\mathbf{x}_k$. What we have is a noisy observation $\mathbf{z}_k \in \mathbb{R}^N$ for any time $k$.