> For the complete documentation index, see [llms.txt](https://www.learnros2.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://www.learnros2.com/probabilistic-robotics/bayes-filter.md).
# Bayes Filter
The core idea of the application of Bayes' rule is that we can update our belief based on the new data. Here is a classic example in many robotics text books that illustrates the idea:
This example might be too simple. An example with multiple doors is more interesting for the thought process but we will leave it as an exercise.
## Graph Model Representation
The Bayes Filter algorithm consists of two steps:
* prediction
* belief update
TODO
## Bayes Filter Algorithm
{% code fullWidth="true" %}
```latex
\begin{algorithm}
\renewcommand{\thealgorithm}{}
\caption{\textbf{Bayes Filter}}\label{alg:cap}
\begin{algorithmic}[1]
\Function{BayesFilter}{$bel(x_{t-1}), u_t, z_t$}
\ForAll{$x_t$}
\State $\overline{bel}(x_t) = \int{p(x_t|u_t, x_{t-1})bel(x_{t-1})dx_{t-1}}$
\State $bel(x_t) = \eta{}p(z_t|x_t)\overline{bel}(x_t)$
\EndFor
\State \textbf{return} $bel(x_t)$
\EndFunction
\end{algorithmic}
\end{algorithm}
```
{% endcode %}
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