added tex

tex/chapters/abstract.tex

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+\begin{abstract}
+Noch nichts. Hier kommt aber bald was.
+\end{abstract}
+%\begin{IEEEkeywords} indoor positioning, Monte Carlo smoothing, particle smoothing, sequential Monte Carlo\end{IEEEkeywords}

tex/chapters/conclusion.tex

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+\section{Conclusion}
+Kommt schon noch.

tex/chapters/experiments.tex

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+\section{Experiments}
+
+
+
+

tex/chapters/introduction.tex

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+\section{Introduction}
+
+Localising pedestrians inside buildings can be considered as a time-sequential, non-linear and non-Gaussian state estimation problem. 
+Such problems are often solved by using Bayesian filter, which update the state estimation recursively with every new incoming measurement. 
+A powerful method to obtain numerical results for this approach are particle filter. 
+
+Especially in indoor localisation, particle filter can lately be considered as the standard method for solving complex non-linear problems \cite{}.
+By using a set of weighted random samples, they approximate a probability distribution describing the pedestrian's possible whereabouts and therefore the uncertainty of the system. 
+In its most basic form, the particle filter operates three main steps:
+At first, new samples are drawn according to some importance distribution, those samples are then weighted by an incremental importance weight distribution and finally a resampling step is deployed to prevent that only a small number of samples have a signifcant weight and all the other will have negligible small weights instead \cite{orhan2012particle}.
+
+In practice imprtance dis and weight dist are .... blabal 
+
+most localisation distribution differ how the transition and evaluation are blub \cite{}.
+
+However, as \cite{Li2014} already mentioned, particle filter (and nearly all of its modifications) continue to suffer from two notorious problems: sample degeneracy and impoverishment. 
+
+sample degenerecy due to resampling, this again causes impoverishment ... teufelkreis
+
+Besides the normal bootstrap or condensation particle filter, their are many different abformen, welche aber grundsätzlich  aus den oben gennanten schritten bestehen.
+
+
+ 
+
+Consider a standard filtering problem.. kurz nochmal particle filter einführen. und beispiel indoor
+
+sample impoverishment or particle depletion is.. allgemein etwas darüber  .. is often explained as problem solely caused by the resampling step. Especially by using restrictive transition models, this is not true. 
+
+in the context of indoor localization particle deplation is a allgegenwärtiges problem due to restricting maps. within the transition step they are used to prevent walking through walls and provide a natural and realistic movement. however, this often causes particles to get stuck within a room and standard filtering methods are not able to recover.
+
+we solve this problems in context of indoor localization by using a multiple model particle filter. ... the transition matrix is set updated every timestep depending upon the kullback leibler divergence between the modes.. 
+
+this not only solves the problem of stucking, but also open a lot possibilietes for future work. 
+
+
+
+
+
+
+paar notizen:
+
+jennsen shannon divergence ist zwar symmetrisch und die wurzel davon zählt als metrik, ist aber in unserem kontext eher inpraktikabel da der upperbound bei ln(2) liegt.. das sorgt für ... deshalb nehmen wir die einfach kld! diese ist nach oben hin offen und somit erlaubt diese eine bessere aussage nicht nur darüber wie unterschiedlich die beiden verteilungen sind, sondern auch wie weit sie sich im wahrscheinlichkeitsraum voneinander entfernt befinden. "direct divergence measure"
+
+aus gründen der simplicity haben wir alle modelle so einfach wie möglich gehalten um nur den vorzug der neuen methode zu erhalten. für weitere informationen, optimale parameter ... siehe paper, paper paper von uns. 

tex/chapters/method.tex

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+
+\section{Similarity Resampling}
+\label{sec:res}
+
+Hier kommt die tolle neue Methode.
+
+

tex/chapters/relatedwork.tex

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+\section{Related Work}
+\label{sec:relatedWork}
+% 3/4 Seite ca.
+
+andere arbeiten die particle depletion verhindern wollte -> was haben die so gemacht?
+
+basic idea of this work is to combine two different filters. on depending upon realistic movement and the other observing absolut positions to prefent particle depletion due to relative measurements. 
+
+combining different filters.
+
+jump markov non linear system.
+
+interacting multiple model
+
+particle filter
+
+
+
+

tex/chapters/system.tex

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+\section{Recursive State Estimation}
+\label{sec:rse}
+
+Wie immer. bisschen umschreiben halt.
+
+
+As mentioned before, most smoothing methods require a preceding filtering. 
+Similar to our previous works, we consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem. 
+Therefore, a Bayes filter that satisfies the Markov property is used to calculate the posterior:
+	%
+	\begin{equation}
+		\arraycolsep=1.2pt
+		\begin{array}{ll}
+			&p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\ 
+				&\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
+				\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
+				\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}}
+		\end{array}
+		\label{equ:bayesInt}
+	\end{equation}
+	%
+Here, the previous observation $\mObsVec_{t-1}$ is included into the state transition \cite{Ebner-15}. 
+For approximating eq. \eqref{equ:bayesInt} by means of MC methods, the transition is used as proposal distribution, also known as CONDENSATION algorithm \cite{isard1998smoothing}. 
+This algorithm also performs a resampling step to handle the phenomenon of weight degeneracy.
+
+In the context of indoor localisation, the hidden state $\mStateVec$ is defined as follows:
+	\begin{equation}
+		\mStateVec = (x, y, z, \mStateHeading, \mStatePressure),\enskip
+		x, y, z, \mStateHeading, \mStatePressure \in \R \enspace,
+	\end{equation}
+	%
+where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the relative atmospheric pressure prediction in hectopascal (hPa). Further, the observation is given by
+	%
+	\begin{equation}
+		\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{ib}, \mObsHeading, \mObsSteps, \mObsPressure, \mObsActivity) \enspace,
+	\end{equation}
+	%
+covering all relevant sensor measurements. 
+Here, $\mRssiVec_\text{wifi}$ and $\mRssiVec_\text{ib}$ contain the measurements of all nearby \docAP{}s (\docAPshort{}) and \docIBeacon{}s, respectively. 
+$\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number of steps detected for the pedestrian. 
+$\mObsPressure$ is the relative barometric pressure with respect to a fixed reference. 
+Finally, $\mObsActivity$ contains the activity currently estimated for the pedestrian, which is one of:
+unknown, standing, walking, walking up the stairs or walking down the stairs.
+
+The probability density of the state evaluation is given by 
+	%
+	\begin{equation}
+		%\begin{split}
+			p(\vec{o}_t \mid \vec{q}_t) = 
+			p(\vec{o}_t \mid \vec{q}_t)_\text{baro} 
+			\,p(\vec{o}_t \mid \vec{q}_t)_\text{ib}
+			\,p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}
+			\enspace
+		%\end{split}
+		\label{eq:evalBayes}
+	\end{equation}
+	%
+and therefore similar to \cite{Ebner-16}.
+Here, we assume a statistical independence of all sensors and every single component refers to a probabilistic sensor model. 
+The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$, whereby absolute position information
+is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for \docIBeacon{}s and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. 
+
+