%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Presentation for: % % Workshop on Adaptive Filters in Bucure\c{s}ti / Romania % (March 2003) % % (c) Matthias M\"{u}hlich, 03/2003 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % this file must be processed with pdflatex! \documentclass[english,pdftex]{article} \usepackage{babel} %% hyphenation patterns - takes global option english \usepackage{palatino} %% Palatino fonts \usepackage{mathptm} %% PostScript Type 1 math fonts \usepackage{textcomp} %% symbols \usepackage[paneltoc,sectionbreak]{pdfwin} %% my presentation style file %% takes global options english + pdftex % character protruding; disabled for higher compatibility %\input{normprot.tex} % abbreviation for vectors \input{shortvec.tex} % SETUP OF PDFWIN PACKAGE % % define windows and margins \SetScreen{width=12cm, height=9cm} \SetWindow{text}{basex=0.2cm, basey=0.2cm, width=9.4cm,height=8.6cm, borderthickness=0.4mm} \SetWindow{panel}{basex=9.8cm, basey=0.2cm, width=2cm, height=8.6cm, borderthickness=0.4mm} \SetButtons{width=1.6cm, shadowdepth=0.3mm} \SetMargins{.5cm}{.5cm}{.5cm}{.5cm} % % define panel \SetLogo{filename=JWGU-Logo.png,width=1.3cm, shadowdepth=.7mm} \SetScreen{type=wallpaper, filename=marble.png} \SetPaneltext{\scriptsize\sffamily Filter-Workshop\\Bucure\c{s}ti 2003} \renewcommand{\DrawNavigationPanel}{ \ShowPageInfo\par\vfill \FirstLastButton\par\vfill \PrevNextButton\par\vfill \BackForwardButton\par\vfill \FullScreenButton\par\vfill \SearchButton\par\vfill \CloseButton\par\vfill } % COLORS % % windows \definecolor{titlecolor}{rgb}{.7,.15,.1} \definecolor{TextBackgroundColor}{rgb}{.7,.8,1.0} \definecolor{TextBorderColor}{rgb}{0,0,.5} % % colors for presentation \definecolor{StateColor}{rgb}{0,0,.6} \definecolor{StateFuncColor}{rgb}{.4,0,.3} \definecolor{StateNoiseColor}{rgb}{.3,.3,.7} \definecolor{MeasColor}{rgb}{0,.5,0} \definecolor{MeasFuncColor}{rgb}{.4,.3,0} \definecolor{MeasNoiseColor}{rgb}{.3,.7,.3} \definecolor{InputColor}{rgb}{.7,0,0} % % colors for environments \definecolor{CodeTextColor}{rgb}{0,0.3,0} \definecolor{CodeMathColor}{rgb}{0.1,0.3,0.6} \definecolor{MyBoxColor1}{rgb}{.8,.5,.1} \definecolor{MyBoxColor2}{rgb}{.9,.8,.3} \definecolor{MyBoxiiColor1}{rgb}{.8,.6,.4} \definecolor{MyBoxiiColor2}{rgb}{.9,.8,.7} \definecolor{MyCodeBoxColor1}{rgb}{.3,.6,.2} \definecolor{MyCodeBoxColor2}{rgb}{.8,.9,.7} % % misc \definecolor{dgreen}{rgb}{0,.6,0} % LAYOUT % % general layout \tolerance=2000 \emergencystretch=5em \fboxsep=3mm \setlength{\parskip}{4pt plus 2pt minus 1pt} \setlength{\parindent}{0pt} \frenchspacing % % define page transition style \pdfpageattr{/Trans << /S /Dissolve /D 0.3 >>} % % replace default font (roman default) by computer modern sans serif; % Palatino only for panel % NOTE: brute force, no good style here... \renewcommand{\rmdefault}{cmss} % % redefine vector style (boldface instead of arrow on top) \renewcommand{\vec}[1]{\mathbf{#1}} % % redefine section numbering: only section (and no subsection or lower) % gets a number \setcounter{secnumdepth}{1} % NEW COMMANDS % \newcommand{\Realnumbers}{\mathrm{I\!R}} \newcommand{\Expect}[1]{\mbox{{\sf E}}\left[ #1 \right]} \newcommand{\Cov}[1]{\mbox{\sf Cov}\left[ #1 \right]} % \newcommand{\mybox}[1]{\begin{center}% \fboxrule=.5mm% \fcolorbox{MyBoxColor1}{MyBoxColor2}{% \parbox[c]{.9\textwidth}{#1}}% \end{center}} % \newcommand{\myboxii}[1]{\begin{center}% \fboxrule=.5mm% \fcolorbox{MyBoxiiColor1}{MyBoxiiColor2}{% \parbox[c]{.9\textwidth}{#1}}% \end{center}} % \newcommand{\mycodebox}[1]{\begin{center}% \fboxrule=.5mm% \ttfamily\bfseries% \color{CodeTextColor}% \fcolorbox{MyCodeBoxColor1}{MyCodeBoxColor2}{% \parbox[c]{.9\textwidth}{#1}}% \end{center}} % \newcommand{\codemath}[1]{\textcolor{CodeMathColor}{$#1$}} \newcommand{\codetext}[1]{\textsf{\mdseries\small #1}} %==================================================================== \begin{document} % produce panel TOC entry for title page \AddPanelTocEntry{Title Page}% {\centering {\Huge\bfseries\color{titlecolor} Particle Filters\rule[-.6ex]{0pt}{5ex}\\ \LARGE an overview\rule[-.6ex]{0pt}{3ex}\\ } \vspace*{8mm} {\Large Matthias M\"{u}hlich}\\[3ex] \large Institut f{\"u}r Angewandte Physik\\ J.W.Goethe-Universit{\"a}t Frankfurt\\ \href{mailto:muehlich@iap.uni-frankfurt.de}{\color{black}muehlich@iap.uni-frankfurt.de}\\ } \newpage % replacement title page {\centering {\Huge\bfseries\color{titlecolor} Particle Filters\rule[-.6ex]{0pt}{5ex}\\ \LARGE a tutorial\rule[-.6ex]{0pt}{3ex}\\ } \vspace*{8mm} {\Large Matthias M\"{u}hlich}\\[3ex] \large Institut f{\"u}r Angewandte Physik\\ J.W.Goethe-Universit{\"a}t Frankfurt\\ \href{mailto:muehlich@iap.uni-frankfurt.de}{\color{black}muehlich@iap.uni-frankfurt.de}\\ } \section{Introduction} \label{Intro} % change text window style from normal (-> title page) to transparent % (-> rest of talk); must appear after page break, i.e. section command % ("sectionbreak" option for pdfwin produces page break at each \section % command) \SetWindow{text}{type=transparent, borderthickness=0.5mm} An increasing number of researchers is using a family of techniques and algorithms called \begin{itemize} \itemsep=-1mm \item \textit{condensation algorithms} \item \textit{bootstrap filtering} \item \textit{particle filters} \item \textit{interacting particle approximations} \item \textit{sequential Monte Carlo methods} \item \textit{SIS, SIR, ASIR, RPF, \dots} \end{itemize} Time scale: last 10 years [e.g. Isard \& Blake 1996; Kitagawa 1996; Gordon, Salmond \& Smith 1993] % \mybox{The question of this talk is: What is behind all that?} \newpage \subsection{General Classification of %On-line Filter Strategies} Gaussian models: \begin{itemize} \item Kalman filter \item extended Kalman filter \item linear-update filter / linear regression filter /\\ statistical linearization filter \begin{itemize} \item unscented filter \item central difference filter \item divided difference filter \end{itemize} \item assumed density filter / moment matching \end{itemize} \newpage Mixture of Gaussian models: \begin{itemize} \item assumed density filter / pseudo-Bayes \item Gaussian-sum filter \end{itemize} \bigskip Nonparametric models: \begin{itemize} \item \textcolor{red}{\bfseries particle filter class} \item histogram filter \end{itemize} \newpage \subsection{Some Basic Remarks} \begin{itemize} \item various applications: computer vision (i.e. tracking), control theory, econometrics (stock markets, monetary flow, interest rates), \dots \item we deal with discrete time systems only \item no out-of-sequence measurements \item we are mainly interested in estimating the state at time $k$ from measurements up to time $k'=k$ (opposite: smoothing ($k'>k$) and prediction ($k'