[AMR] Layout fixes, highlights

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2026-08-02 17:35:52 +02:00
parent db048650e2
commit 515e99057b
3 changed files with 5 additions and 4 deletions
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\subsection{Kalman Filter (KF)}
Bayes Filter for Gauss. dist of R.V. \& linear meas. model.
Initial state $\vec{x}_0 \sim \cN(\hat{\vec{x}}, \mat{P}_0)$, $\mat{P}_0$ previous covariance;
Bayes Filter for Gauss. dist of R.V. \& \hl{linear meas. model.}
Initial state $\vec{x}_0 \sim \cN(\hat{\vec{x}}, \mat{P}_0)$, $\mat{P}_0$ previous covariance
\bi{Prediction} With linear state transition model ($\vec{u}_k$ odometry, $\vec{w}_k$ noise (covariance $\mat{Q}_k$)):\\
$\vec{x}_k = \mat{F}\vec{x}_{k - 1} + \mat{G}\vec{u}_k + \mat{L}\vec{w}_k$ with $\vec{w}_k \sim \cN(\vec{0}, \mat{Q}_k)$:
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\subsection{Extended Kalman Filter (EKF)}
Non-l. state trans. model $\vec{x}_k = \vec{f}(\vec{x}_{k - 1}, \vec{u}_k, \vec{w}_k)$ as above:
\hl{Non-l. state trans. model} $\vec{x}_k = \vec{f}(\vec{x}_{k - 1}, \vec{u}_k, \vec{w}_k)$ as above:
\begin{itemize}
\item \bi{Mean}: $\hat{\vec{x}}_{k | k - 1} = \vec{f}(\hat{\vec{x}}_{k - 1 | k - 1}, \vec{u}_k)$
\item \bi{Covariance}: $\mat{P}_{k | k - 1} = \mat{F}_k \mat{P}_{k - 1 | k - 1} \mat{F}_k^\top + \mat{L}_k \mat{Q}_k \mat{L}_k^\top$\\