diff --git a/electives/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/amr/autonomous-mobile-robots-cheatsheet.pdf index f9e8b2d..2068a88 100644 Binary files a/electives/amr/autonomous-mobile-robots-cheatsheet.pdf and b/electives/amr/autonomous-mobile-robots-cheatsheet.pdf differ diff --git a/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex b/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex index 45fe433..abc1c98 100644 --- a/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex +++ b/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex @@ -1,6 +1,7 @@ \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 $\vec{w}_k \sim \cN(\vec{0}, \mat{Q}_k)$: diff --git a/electives/amr/parts/03_multi-sensor-estimation/06_extended-kalman-filter.tex b/electives/amr/parts/03_multi-sensor-estimation/06_extended-kalman-filter.tex index 48f4e23..afbc88e 100644 --- a/electives/amr/parts/03_multi-sensor-estimation/06_extended-kalman-filter.tex +++ b/electives/amr/parts/03_multi-sensor-estimation/06_extended-kalman-filter.tex @@ -1,9 +1,9 @@ \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}: $\mat{P}_{k | k - 1} = \mat{F}_k \mat{P}_{k - 1 | k - 1} \mat{F}_k^\top + \mat{L}_k \mat{Q}_k \mat{L}_k^\top$\\ - With $\mat{F}_k$ linearisation $\frac{\partial \vec{f}}{\partial \vec{x}}$ and $\mat{L}_k$ lin. $\frac{\partial \vec{f}}{\partial \vec{w}}$ + With $\mat{F}_k$ linearisation $\frac{\partial \vec{f}}{\partial \vec{x}}$ and $\mat{L}_k$ lin. $\frac{\partial \vec{f}}{\partial \vec{w}}$ \end{itemize} \bi{Update} Non-Linear meas.: $\tilde{\vec{z}}_k = \vec{h}(\vec{x}_k) + \vec{v}_k$: \begin{itemize}