\subsection{Particle Filter}
Is a bayes filter approximating the state distribution with a set of random samples.
Update step:
\begin{itemize}
    \item Apply Bayes rule $w'_{k, s} = \P[\vec{z}_i \divider \vec{x}_{k, s}] w_{k - 1, s}$
    \item Renormalize: $w_{k, s} = w'_{k, s} \div \sum_{s} w'_{k, s}$
    \item Resample: rand. sel. $S$ particles acc. to weights and $w_{k, s} = S^{-1}$
\end{itemize}
