fixed minor typos

added some comments

tex/chapters/introduction.tex

@@ -30,15 +30,21 @@ For example, a barometer can be used to determine the probability of being on a
 
 Despite the many advances made in the last years, nearly all systems suffer from more or less the same problems. 
 Of course, every sensor model brings its very own weaknesses. 
-Like mentioned before, PDR suffers from an accumulating bias, the signal of Wi-Fi gets attenuated by walls and the barometric pressure is highly affected by weather patterns and humidity \cite{Binghao13-UBI}. 
+Like mentioned before, PDR suffers from an accumulating bias,
+the signal of Wi-Fi gets attenuated by walls
+\commentByFrank{falls noch platz ist: noch mehr nachteile :P \docWIFI{} location estimation strongly depends on the quality of the signal-strength estimation model (oder fingerprinting) and the way the smartphone is held}
+and the barometric pressure is highly affected by weather patterns and humidity
+\commentByFrank{spontane fenster/tuer oeffnung}
+\cite{Binghao13-UBI}. 
 That is the reason for the use of statistical methods in the first place. Nevertheless, there are even more profound problems regarding the whole position estimation procedure. 
 
 Current transition models, which aim to approximate the movement, are still very restrictive and unable to handle unforeseen events. 
 Faulty sensor measurements, like a falsely detected turn, can cause the estimation to lose track.
-For example by taking a turn too soon and walking into a room instead of another big hallway. 
+For example by taking \commentByFrank{by taking -> by recognising?} a turn too soon and walking into a room instead of another big hallway. 
 Due to this, the filter needs some time to recover, which again takes a while because of the restrictive model (e.g. no walking through walls and only realistic walking speed). 
 This temporal delay worsens the estimate immensely. 
-A solution to recover from such filter divergences faster, is using methods for re-initializing the filtering procedure \cite{Nurminen2014}. 
+A solution to recover from such filter divergences faster, is using 
+\commentByFrank{is using -> involves?} methods to re-initialize the filtering procedure \cite{Nurminen2014}. 
 However, even this can not completely prevent delays. 
 Another reason for possible time delays are slow sensor updates. 
 For example, most mobile devices restrict the Wi-Fi module to update only every few seconds, to save on battery. 
@@ -47,7 +53,12 @@ For example, most mobile devices restrict the Wi-Fi module to update only every
 	\centering
 	\def\svgwidth{0.9\columnwidth}
   \input{gfx/multimodalpath.eps_tex}
-	\caption[An example of the occurrence of a multimodal distribution.]{An example of the occurrence of a multimodal distribution. At time $t-1$ the floor gets separated by a wall and the mode of the distribution (colored circle), representing the current position, splits apart. The most likely position (green line) is estimated somewhere in-between. After a right turn, the distribution slowly starts to recover its unimodality.}
+	\caption[An example of the occurrence of a multimodal distribution.]{
+	An example of the occurrence of a multimodal distribution.
+	At time $t-1$ the floor is separated by a wall and the mode of the distribution (coloured circle),
+	\commentByFrank{mode of the weglassen? einfach: distribution ... splits}
+	 representing the current position, splits apart.
+	The most likely position (green line) is estimated somewhere in-between. After a right turn, the distribution slowly starts to recover its unimodality.}
 	\label{fig:multimodalPath}
 \end{figure}
 
@@ -55,14 +66,14 @@ Further critical problems arise from multimodal distributions.
 Those are caused by multiple possible position estimates. 
 Fig. \ref{fig:multimodalPath} illustrates an example where a floor gets separated by a wall.
 Due to inaccurate measurements and a PDR approach for evaluating the movement, the distribution splits apart. 
-Therefore, the most likely position is somewhere in-between. 
-Only after the pedestrian turns right, the distribution is again unimodal, since moving through walls is prohibited. 
+Therefore, the most likely position \commentByFrank{wenn avg ueber alle particles, was ja default ist} is somewhere in-between. 
+Only after the pedestrian turns right, the distribution is again unimodal, since moving through walls is impossible. 
 As one can imagine, this can lead to serious problems in big indoor environments. 
 Such a situation can be improved by incorporating future measurements (e.g. the right turn) or predictive information (e.g. the most likely path) to the filtering procedure \cite{Ebner-16}. 
 However, standard filtering methods are not able to use any future information and the possibilities to make a distant forecast are also limited \cite{robotics, Doucet11:ATO, chen2003bayesian}.
 
 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. 
+Smoothing methods are able to make use of future measurements for computing their 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 MC methods. 
 %Of course, this excludes linear procedures like Kalman filtering.
@@ -70,7 +81,7 @@ Namely, forward-backward smoothing \cite{doucet2000} and backward simulation \ci
 
 Within this work, we investigate the benefits and drawbacks of those techniques using our indoor localisation system presented in \cite{Ebner-16}. 
 We provide both, fixed-lag and fixed-interval smoothing as well as two novel approaches for incorporating them easily within the localisation procedure. 
-The main goal is to solve the above mentioned problems and to investigate new possibilities for even more advanced systems.
+The main goal is to solve above mentioned problems and to investigate new possibilities for even more advanced systems.
 
 
 

tex/chapters/relatedwork.tex

@@ -3,13 +3,13 @@
 % 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 $\mStateVec_t$. 
+Filtering algorithm, like aforementioned 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. 
+In fixed-lag smoothing, one tries to estimate the current state, given 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}. 
 
@@ -19,7 +19,9 @@ 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 $\mathcal{O}(N)$.
+\commentByFrank{kleines n?}
 However, it gives a poor representation of previous states \cite{Doucet11:ATO}.
+\commentByFrank{wenn noch platz, einen satz mehr dazu warum es schlecht ist?}
 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}.