diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf index af77608..63961d0 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 f43787e..2e9a19b 100644 --- a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex +++ b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex @@ -64,7 +64,7 @@ \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/02_nonlinear-least-squares.tex} % \input{parts/03_multi-sensor-estimation/} \end{document} 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 index 30838a9..b51d0da 100644 --- 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 @@ -1,4 +1,10 @@ \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 $Mx = b'$ +\bi{Man. sol.}: comp. $M = A^\top A$, $b' = A^\top b$, then $Mx = b'$. + +\bi{Prob. sol.}: $\text{argmax} p(\vec{x} \divider \vec{z})$ with +\begin{itemize} + \item \bi{Max. Like} $p(\vec{x} | \vec{z}) \propto p(\vec{z} | \vec{x}) = \prod_{i = 1}^N p(\vec{z}_i | \vec{x})$ + \item \bi{M a Post} $p(\vec{x} | \vec{z}) \propto p(\vec{z} | \vec{x}) p(\vec{x}) = p(\vec{x}) \prod_{i = 1}^N p(\vec{z}_i | \vec{x})$ +\end{itemize} 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 index e69de29..9ea0740 100644 --- 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 @@ -0,0 +1,6 @@ +\subsection{Non-Linear Least Squares} +Find $\vec{x}^* = \text{argmax} p(\vec{x} | \vec{z}) = \argmin{}(-\log(p(\vec{x}|\vec{z})))$ + +\bi{Gauss-Newton} + +\bi{Levenberg-Marquardt}