related work angefangen.. aufbau aber noch doof

tex/chapters/introduction.tex

@@ -16,9 +16,9 @@ In most cases, probabilistic methods are used to incorporate those highly differ
 Here, a probability distribution describes the pedestrian's possible whereabouts and therefore the uncertainty of the system. 
 Drawing from a probability distribution and finding an analytical solution for densities is in most cases a difficult task, especially in case of time sequential, non-linear and non-Gaussian models. 
 Due to the high complexity of the human movement, we consider indoor localisation as such.
-A broad class to obtain numerical results instead are the Monte Carlo methods. 
+A broad class to obtain numerical results instead are the Monte Carlo (MC) methods. 
 Here, a set of weighted random samples is used to solve any problem having a probabilistic interpretation. 
-By applying the time sequential hidden Markov process of Bayes filtering, one of the most important Monte Carlo techniques results: particle filtering. 
+By applying the time sequential hidden Markov process of Bayes filtering, one of the most important MC techniques results: particle filtering. 
 A particle filter updates the state estimation recursively in time with every new incoming measurement using the state transition and state evaluation step. 
 
 Based on this general methodology, many different approaches for estimating a position in indoor environments have been developed. 
@@ -64,7 +64,7 @@ However, standard filtering methods are not able to use any future information a
 One very promising way to deal with these problems is smoothing. 
 Smoothing methods are able to make use of future measurements for computing its estimation. 
 By running backwards in time, they are also able to remove multimodalities and improve the overall localization result.
-Since the problem of navigation, especially the representation of complex movement patterns, results in a non-linear and non-Gaussian state space, this work focuses mainly on smoothing techniques based on the broad class of Monte Carlo methods. 
+Since the problem of navigation, especially the representation of complex movement patterns, results in a non-linear and non-Gaussian state space, this work focuses mainly on smoothing techniques based on the broad class of MC methods. 
 %Of course, this excludes linear procedures like Kalman filtering.
 Namely, forward-backward smoothing \cite{doucet2000} and backward simulation \cite{Godsill04:MCS}.
 

tex/chapters/relatedwork.tex

@@ -1,4 +1,36 @@
 \section{Related Work}
+\label{sec:relatedWork}
+% 3/4 Seite ca.
+
+%kurze einleitung zum smoothing
+Filtering algorithm, like the before mentioned particle filter, use all observations $\mObsVec_{1:t}$ until the current time $t$ for computing an estimation of the state $\mStateVec_t$. 
+In a Bayesian setting, this can be formalized as the computation of the posterior distribution $p(\mStateVec_t \mid \mObsVec_{1:t})$.
+By considering a situation given all observations $\vec{o}_{1:T}$ until a time step $T$, where $t \ll T$, standard filtering methods are not able to make use of this additional data for computing $p(\mStateVec_t \mid \mObsVec_{1:T})$.
+This problem can be solved with a smoothing algorithm.
+
+Within this work we utilise two types of smoothing: fixed-lag and fixed-interval smoothing. 
+In fixed-lag smoothing, one tries to estimate the current state, give measurements up to a time $t + \tau$, where $\tau$ is a predefined lag. 
+This makes the fixed-lag smoother able to run online. 
+On the other hand, fixed-interval smoothing requires all observations until time $T$ and therefore only runs offline, after the filtering procedure is finished \cite{chen2003bayesian}. 
+
+
+%historie des smoothings und entwicklung der methoden.
+The origin of MC smoothing can be traced back to Genshiro Kitagawa. 
+In his work \cite{kitagawa1996monte} he presented the simplest form of smoothing as an extension to the particle filter. 
+This algorithm is often called the filter-smoother since it runs online and a smoothing is provided while filtering. 
+This approach can produce an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with computational complexity of only $\mathcal{O}(N)$.
+However, it gives a poor representation of previous states \cite{Doucet11:ATO}.
+Based on this, more advanced methods like the forward-backward smoother \cite{doucet2000} and backward simulation \cite{Godsill04:MCS} were developed.
+Both methods are running backwards in time to reweight a set of particles recursively by using future observations. 
+Algorithmic details will be shown in section \ref{sec:smoothing}.
+
+%wo werden diese eingesetzt, paar beispiele. offline, online 
+In recent years, smoothing gets attention mainly in the field of computer vision and ... Here, ...
+
+Nevertheless, their are some promising approach for indoor localisation systems as well. For example ...
+
+%smoothing im bezug auf indoor
+Smoothing solutions in indoor localisation werden bisher nicht wirklich behandelt.  das liegt hauptsächlich daran das es sehr langsam ist \cite{}. es gibt ansätze von ... und ... diese benutzen blah und blah. wir machen das genauso/besser.
 
 
 

tex/chapters/smoothing.tex

@@ -1,3 +1,4 @@
 \section{Smoothing}
+\label{sec:smoothing}
 
 Consider a situation given all observations until a time step T...