[AMR] Start multi-sensor estimation

2026-04-28 16:19:23 +02:00 · 2026-04-03 20:15:25 +02:00
parent ec704c378d
commit 85f3ef6940
5 changed files with 17 additions and 0 deletions
@@ -61,4 +61,10 @@
 \input{parts/02_Sensors-Actuators/04_depth-range.tex}
 % \input{parts/02_Sensors-Actuators/}

+\section{Multi-Sensor Estimation}
+\input{parts/03_multi-sensor-estimation/00_linearization.tex}
+\input{parts/03_multi-sensor-estimation/01_least-squares.tex}
+% \input{parts/03_multi-sensor-estimation/02_nonlinear-least-squares.tex}
+% \input{parts/03_multi-sensor-estimation/}
+
 \end{document}
@@ -0,0 +1,7 @@
+\subsection{Linearization}
+$\vec{f}(\vec{x}) \approx \vec{f}(\vec{\overline{x}}) + \mat{J}_{\vec{f}} \big|_{x = \overline{x}}(\vec{x} - \vec{\overline{x}})$, $f'$, no vec in 1D; $\vec{\overline{x}}$ lin. p.
+
+\shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$ cols for vars of each eq.
+
+Approximation using finite differences $\frac{f(\overline{x} + h) - f(\overline{x})}{h}$,\\
+or central differences (vector of $\frac{\vec{f}(\vec{\overline{x}}) + h_i \vec{e_i}}{h_i}$, with $\vec{e_i}$ unit vec)
@@ -0,0 +1,4 @@
+\subsection{Linear Least Squares}
+\bi{Goal}: $\argmin{x \in \R^n} ||\mat{A}\vec{x} - b||^2_2$, $\mat{A}$: rows $i$-th datap. col $c$: $t_i^{c - 1}$.
+
+\bi{Man. sol.}: comp. $M = A^\top A$, $b' = A^\top b$, then $Mx = b'$