[AMR] Fix errors

electives/amr/parts/00_basics/02_trigonometry.tex

@@ -5,3 +5,5 @@
 \shortdefinition[Orthogonal vec] $v^\top w = 0$
 
 \shortdefinition[Determinant] $ad - bc$ for mat $[a, b; c, d]$
+
+\shortdefinition[Vec Line Eq] $\vec{p} + \lambda \vec{d}$

electives/amr/parts/00_basics/03_error-propagation.tex

@@ -1,3 +1,4 @@
 \subsection{Error Propagation}
+\label{sec:error-propagation}
 For functions $\vec{f}(\vec{x}) = \mat{A}\vec{x}$, the \bi{linear error propagation}
 is given by $\Sigma^f = A \Sigma^x \A^\top$, with $\Sigma^x$ the uncertanty of $\vec{x}$ (covariance mat.)

electives/amr/parts/02_Sensors-Actuators/00_intro.tex

@@ -1,7 +1,8 @@
 \label{sec:sensors}
 \bi{Meas. Model}: $\vec{z} = \vec{h}(\vec{x}) + \vec{v} + \vec{o}$, with $\vec{h}(\vec{x})$ determ. mean,
 $\vec{v}$ zero-mean noise, $\vec{o}$ unmodelled effects, $\vec{x}$ true state.
-$\vec{h}(\vec{x})$ describes how to compute $x$ from known values.
+$\vec{h}(\vec{x})$ describes how to compute $x$ from known values (e.g. Intercept-Theorem).
+Probabilistic M.M: use rand var in def, and s. \ref{sec:error-propagation}
 
 \bi{Motor encoders} Typ. 64-2048 incrm. per rev; Estim. rot
 

electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex

@@ -1,4 +1,5 @@
 \subsection{Depth and Range sensing}
+Typ. derive D.M. with sensor dir param (as vec line eq)
 \subsubsection{Triangulation-based}
 \bi{Struct. Light} Single cam, single projector: {\color{ForestGreen}Spatial acc}, {\color{red} no worky in bright light, interference with other IR depth cams}
 

electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex

@@ -9,7 +9,6 @@ $\vec{x}_k = \mat{F}\vec{x}_{k - 1} + \mat{G}\vec{u}_k + \mat{L}\vec{w}_k$ with
     \item \bi{Covariance} $\mat{P}_{k | k - 1} = \mat{F} \mat{P}_{k - 1 | k - 1} \mat{F}^\top + \mat{L} \mat{Q}_{k} \mat{L}^\top$
 \end{itemize}
 \bi{Update} Lin. meas.: $\tilde{\vec{z}}_k = \mat{H}\vec{x}_k + \vec{v}_k$ with $\vec{v_k} \sim \cN(\vec{0}, \mat{R}_k)$:
-\newpage
 \begin{itemize}
     \item \bi{Meas. residual}: $\vec{y}_k = \tilde{\vec{z}}_k - \mat{H} \hat{\vec{x}}_{k | k - 1}$
     \item \bi{Resid. Cov}: $\mat{S}_k = \mat{H}\mat{P}_{k | k - 1} \mat{H}^\top \mat{R}_k$

electives/amr/parts/04_vision/00_keypoints.tex

@@ -1,6 +1,6 @@
 \subsection{Keypoints}
 \bi{Corner det.} $SSD(\Delta x, \Delta y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$
-with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15;
+with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15;\\
 $\mat{R} = \det(M) - \kappa \cdot \text{TR}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$;\\
 $M = \sum_{x, y \in P}
     {\scriptsize

electives/amr/parts/04_vision/03_mapping.tex

@@ -1,4 +1,3 @@
-\newpage
 \subsection{Mapping}
 \bi{Problem Formulations} \textit{Localisation} {\scriptsize (always static given map)}:\\
 $\vec{x}^*_{R, k} = \text{argmax}\; \P(x_{R, k} \divider \vec{x}_M, \vec{z}_{1 : k}, \vec{u}_{1 : k})$ (recursive)\\