- tags
- Velocity Motion Model, Odometry Motion Model

Often, we are given map \(m\) of the environment, giving us further
information about the robot pose \(x_t\). In general,

\begin{equation}
p\left(x_{t} | u_{t}, x_{t-1}\right) \neq p\left(x_{t} | u_{t}, x_{t-1}, m\right)
\end{equation}

And the map-based motion model should give better results. Computing
this motion model in closed form is difficult. An approximation via
factorization works well where the distance \(x_{t-1}\) and \(x_t\) is
small.

\begin{equation}
p\left(x_{t} | u_{t}, x_{t-1}, m\right)=\eta p\left(x_{t} | u_{t}, x_{t-1}\right) p\left(x_{t} | m\right)
\end{equation}

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