diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf index 90d7a1f..af77608 100644 Binary files a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf and b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf differ diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex index 8887366..f43787e 100644 --- a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex +++ b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex @@ -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} diff --git a/electives/others/amr/parts/03_multi-sensor-estimation/00_linearization.tex b/electives/others/amr/parts/03_multi-sensor-estimation/00_linearization.tex new file mode 100644 index 0000000..915052c --- /dev/null +++ b/electives/others/amr/parts/03_multi-sensor-estimation/00_linearization.tex @@ -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) diff --git a/electives/others/amr/parts/03_multi-sensor-estimation/01_least-squares.tex b/electives/others/amr/parts/03_multi-sensor-estimation/01_least-squares.tex new file mode 100644 index 0000000..30838a9 --- /dev/null +++ b/electives/others/amr/parts/03_multi-sensor-estimation/01_least-squares.tex @@ -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 $Mx = b'$ diff --git a/electives/others/amr/parts/03_multi-sensor-estimation/02_nonlinear-least-squares.tex b/electives/others/amr/parts/03_multi-sensor-estimation/02_nonlinear-least-squares.tex new file mode 100644 index 0000000..e69de29