near to final draft

tex/chapters/conclusion.tex

@@ -1,5 +1,4 @@
 \section{Conclusion}
-
 Within this work a novel approach for utilizing the forward-backward smoother and backward simulation to problems of indoor localisation was presented.
 Both were implemented as fixed-lag and fixed-interval smoother. 
 It was shown that smoothing methods are able to decrease the estimation error and improving the overall localisation.

tex/chapters/experiments.tex

@@ -10,8 +10,8 @@
 	\label{fig:paths}
 \end{figure}
 %
-The experiments were carried out on all floors (0 to 3) of the faculty building. 
-Each floor is about \SI{77}{\meter} x \SI{55}{\meter} in size, with a ceiling height of \SI{3}{\meter}.
+The experiments were carried out on all four floors of the faculty building. 
+Each floor is about \SI{77}{\meter} x \SI{55}{\meter} in size, with a ceiling height of about \SI{3.0}{\meter}.
 To resemble real-world conditions, the evaluation took place during an in-house exhibition. 
 Thus, many places were crowded and Wi-Fi signals attenuated.
 As can be seen in fig. \ref{fig:paths} we arranged 4 distinct walks, covering different distances, critical sections and uncertain decisions leading to multimodalities. 
@@ -29,7 +29,7 @@ Even though, the error during the following few seconds is expected to be much h
 
 The measurements were recorded using a Motorola Nexus 6 and a Samsung Galaxy S5.
 As the Galaxy's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only, its scans take much longer than those of the Nexus: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}.
-Additionally, the Galaxy's barometer sensor provides fare more inaccurate and less frequent readings than the Nexus does. 
+Additionally, the Galaxy's barometer sensor provides far more inaccurate and less frequent readings than the Nexus does. 
 This results in a better localisation using the Nexus smartphone.	
 The computation for both filtering and smoothing was done offline using the aforementioned \mbox{CONDENSATION} algorithm and multinomal (cumulative) resampling. 
 For each path we deployed 10 MC runs using \SI{2500}{} particles. BS uses $500$ sample realisations drawn with a cumulative frequency.
@@ -89,8 +89,8 @@ Now, the positional average error along all 4 paths using the Nexus and the Gala
 The BS performs with an average error of \SI{2.21}{\meter} for filtering and  \SI{1.51}{\meter} for smoothing.
 The difference between both filtering steps is of course based upon the randomized behaviour of the respective probabilistic models. 
 It is interesting to note, that the positional error is very similar for both used smartphones, although the approximation error varies greatly. 
-Using the FBS, the Galaxy donates an average approximation error of \SI{4.03}{\meter} by filtering with \SI{7.74}{\meter}. 
-In contrast the Nexus 6 filters at \SI{5.11}{\meter} and results in \SI{3.87}{\meter} for smoothing.
+Using the FBS, the Galaxy provides an average approximation error of \SI{4.03}{\meter} while filtering resulted in \SI{7.74}{\meter}. 
+In contrast, the Nexus 6 filters with an error of \SI{5.11}{\meter} and \SI{3.87}{\meter} for smoothing.
 The BS has a similar improvement rate.
 
 
@@ -106,7 +106,7 @@ It can be clearly seen, how the smoothing compensates for the faulty detected fl
 Additionally, the initial error is reduced extremely, approximating the pedestrian's starting position down to a few centimetres.
 In the context of reducing the error as far as possible, fig. \ref{fig:int_path2} b) is a very interesting example. 
 Here, the filter offers a lower approximation and positional error in regard to the ground truth. 
-However it is obvious that smoothing causes the estimation to behave more natural instead of walking the supposed path. 
+However it is obvious that smoothing causes the estimation to behave more natural, due to the restrictive smoothing transition, instead of walking the supposed path. 
 This phenomena could be observed for both smoothers respectively.
 
 At next, we discuss the advantages and disadvantages of utilizing FBS and BS as fixed-lag smoother. 
@@ -128,8 +128,8 @@ For better distinction, the path was divided into $10$ individual segments.
 	\label{fig:lag_error_path4}
 \end{figure}
 %
-Again it can be observed, that both smoother enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 7). 
-Immediately after the first floor change, a long and straight walk down the hallway follows. 
+Again it can be observed, that both smoothers enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 7). 
+Immediately after the \newline first floor change, a long and straight walk down the hallway follows. 
 While the Wi-Fi component pulls the pedestrian into the rooms on the right side, the actual walking route was located on the left side of the floor (see ground truth in fig. \ref{fig:lag_comp_path4} seg. 6). 
 Here, the BS is able to slightly improve the path, whereas the FBS follows the filtering until the upcoming staircase provides the necessary information for adjustments.
 %It follows a critical area with high errors and multimodalities.
@@ -141,7 +141,7 @@ Especially in seg. 8 and 9 a big crowd was gathered and highly attenuated the Wi
 For an excessive amount of time, the absolute location estimated by the Wi-Fi component got stuck in the middle of seg. 8 and therefore delayed the estimation.
 The next viable measurements were then provided at the end of seg. 9.
 This suggests that the here presented smoothing transition is able to improve the estimated path visibly, but does not compensate for those jumps in a timely manner.  
-Finally, the BS provides an approximation error alongside all paths of $\SI{6.48}{\meter}$ for the Galaxy and $\SI{4.47}{\meter}$ for the Nexus by filtering with $\SI{7.92}{\meter}$ and $\SI{5.50}{\meter}$ respectively. 
+Finally, the BS provides an approximation error alongside all paths of $\SI{6.48}{\meter}$ for the Galaxy and $\SI{4.47}{\meter}$ for the Nexus, while filtering resulted in $\SI{7.92}{\meter}$ and $\SI{5.50}{\meter}$ respectively. 
 Whereas FBS improves the Galaxy's estimation from $\SI{7.73}{\meter}$ to $\SI{6.68}{\meter}$ and from $\SI{5.66}{\meter}$ to $\SI{4.80}{\meter}$ for the Nexus.
 As stated before, the main advantage of BS over FBS is the better computational time by just using a sub-set of particles for calculations.
 

tex/chapters/filtering.tex

@@ -84,7 +84,7 @@
 		While sampling, to-be-walked edges are not chosen uniformly, but depending on a probability $p(\mEdgeAB)$.
 		The latter depends on several constraints and recent sensor-readings from the smartphone. Using those readings
 		directly within the transition step provides a more robust posterior distribution. Adding them to the evaluation
-		instead, would lead to sample impoverishment due to the used Monte Carlo methods \cite{Isard98:CCD}.
+		instead, would lead to sample impoverishment due to the used MC methods \cite{Isard98:CCD}.
 		
 		%\commentByFrank{ist das verstaendlich oder schon zu kurz?}
 				
@@ -141,7 +141,7 @@
 			
 		%\subsubsection{Activity-Detection}
 			Additionally we perform a simple activity detection for the pedestrian, able to distinguish between several actions 
-			$\mObsActivity \in \{ \text{unknown}, \text{standing}, \text{walking}, \text{stairs\_up}, \text{stairs\_down} \}$.
+			$\mObsActivity \in \{ \tt{unknown}, \tt{standing}, \tt{walking}, \tt{stairs\_up}, \tt{stairs\_down} \}$.
 			%
 			%\commentByFrank{bei mir ueberlappt aktuell nix, muessten mal testen was besser ist. beim ueberlappen ist das delay halt kuerzer. denke das schon ok.}
 			%

tex/chapters/introduction.tex

@@ -69,7 +69,7 @@ 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 weighted average position is somewhere in-between. 
+Depending on the chosen estimator, the approximated position might be located somewhere in-between as seen in fig. \ref{fig:multimodalPath}.
 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)
@@ -77,7 +77,7 @@ Such a situation can be improved by incorporating future measurements (e.g. the
 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. 
+One promising way to deal with these problems is smoothing. 
 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 localisation 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. 
@@ -87,7 +87,7 @@ Namely, forward-backward smoothing \cite{doucet2000} and backward simulation \ci
 Within this work, we investigate the benefits and drawbacks of those techniques using a conventional localisation system \cite{Ebner-16}. 
 We provide both, fixed-lag and fixed-interval smoothing as well as a novel approach for incorporating them easily within the localisation procedure. 
 Additionally, we enrich the state transition model with an activity recognition to distinguish between walking, standing and walking stairs.
-The main goal is to solve above mentioned problems and to investigate new possibilities for even more advanced systems.
+The main goal is to solve the above mentioned problems and to investigate new possibilities for even more advanced systems.
 All of our contributions are supported by an extensive experimental evaluation.
 
 

tex/chapters/relatedwork.tex

@@ -4,7 +4,7 @@
 
 %kurze einleitung zum smoothing
 Sequential MC filters, like the 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 $p(\mStateVec_t \mid \mObsVec_{1:t})$ using a sample of $N$ independent random variables, $\vec{X}^i_{t} \sim p(\mStateVec_t \mid \mObsVec_{1:t})$ for $i = 1,...,N$ for approximation. 
+In a Bayesian setting, this can be formalized as the computation of the posterior distribution $p(\mStateVec_t \mid \mObsVec_{1:t})$ using a sample set of $N$ independent random variables, $\vec{X}^i_{t} \sim p(\mStateVec_t \mid \mObsVec_{1:t})$ for $i = 1,...,N$ for approximation. 
 Due to importance sampling, a weight $W^i_t$ is assigned to each sample $\vec{X}^i_{t}$.
 In the context of particle filtering $\{W^i_{1:t}, \vec{X}^i_{1:t} \}_{i=1}^N$ is a weighted set of samples, also called particles.
 Therefore a particle is a representation of one possible system state $\mStateVec$.

tex/chapters/smoothing.tex

@@ -1,7 +1,7 @@
 \section{Smoothing}
 \label{sec:smoothing}
 
-The main purpose of this work is to provide MC smoothing methods in context of indoor localisation.
+The main purpose of this work is to provide MC smoothing methods in the context of indoor localisation.
 As mentioned before, those algorithms are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$ and are therefore able to make use of future observations between $t$ and $T$, where $t \ll T$.
 %Especially fixed-lag smoothing is very promising in context of pedestrian localisation. 
 In the following we discuss the algorithmic details of the forward-backward smoother and the backward simulation. 
@@ -9,7 +9,7 @@ Further, a novel approach for incorporating them into the localisation system is
 
 \subsection{Forward-backward Smoother}
 
-The forward-backward smoother (FBS) of \cite{Doucet00:OSM} is a well established alternative to the simple filter-smoother. The foundation of this algorithm was again laid by Kitagawa in \cite{kitagawa1987non}. 
+The forward-backward smoother (FBS) of \cite{doucet2000} is a well established alternative to the simple filter-smoother. The foundation of this algorithm was again laid by Kitagawa in \cite{kitagawa1987non}. 
 An approximation is given by
 \begin{equation}
 p(\vec{q}_t \mid \vec{o}_{1:T}) \approx \sum^N_{i=1} W^i_{t \mid T} \delta_{\vec{X}^i_{t}}(\vec{q}_{t}) \enspace, 

tex/chapters/system.tex

@@ -4,7 +4,7 @@
 
 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, which is given by
+Therefore, a Bayes filter that satisfies the Markov property is used to calculate the posterior:
 	%
 	\begin{equation}
 		\arraycolsep=1.2pt
@@ -12,16 +12,16 @@ Therefore, a Bayes filter that satisfies the Markov property is used to calculat
 			&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}} \enspace.
+				\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{Koeping14-PSA}. 
+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 context of indoor localisation, the hidden state $\mStateVec$ is defined as follows:
+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,

tex/egbib.bib

@@ -549,17 +549,6 @@ ISSN={0162-8828},}
     year = {2011},
 }
 
-@ARTICLE{Doucet00:OSM,
-	author = {Arnaud Doucet and Simon Godsill and Christophe Andrieu},
-	title = {{On Sequential Monte Carlo Sampling Methods for Bayesian Filtering}},
-	journal = {Statistics and Computing},
-	year = {2000},
-	IGNOREmonth = {July},
-	volume = {10},
-	number = {3},
-	pages = {197-208},
-}
-
 @article{Gordon93:NAT,
 	author = {N. J. Gordon and D. J. Salmond and A. F. M. Smith},
 	title = {{Novel approach to nonlinear/non-Gaussian Bayesian state estimation}},
@@ -2074,7 +2063,7 @@ year = {2014}
 	isbn={978-3-540-78639-9},
 	booktitle={Bildverarbeitung f\"ur die Medizin 2008},
 	series={Informatik Aktuell},
-	editor={Tolxdorff, Thomas and Braun, J\"urgen and Deserno, Thomas M. and Horsch, Alexander and Handels, Heinz and Meinzer, Hans-Peter},
+	IGNOREeditor={Tolxdorff, Thomas and Braun, J\"urgen and Deserno, Thomas M. and Horsch, Alexander and Handels, Heinz and Meinzer, Hans-Peter},
 	doi={10.1007/978-3-540-78640-5_58},
 	title={{3D Blood Flow Reconstruction from 2D Angiograms}},
 	publisher={Springer Berlin Heidelberg},
@@ -2105,7 +2094,7 @@ journal={Statistics and Computing},
 volume={10},
 number={3},
 doi={10.1023/A:1008935410038},
-title={On sequential Monte Carlo sampling methods for Bayesian filtering},
+title={{On Sequential Monte Carlo Sampling Methods for Bayesian Filtering}},
 publisher={Kluwer Academic Publishers},
 keywords={Bayesian filtering; nonlinear non-Gaussian state space models; sequential Monte Carlo methods; particle filtering; importance sampling; Rao-Blackwellised estimates},
 author={Doucet, Arnaud and Godsill, Simon and Andrieu, Christophe},
@@ -2320,15 +2309,6 @@ IGNOREmonth={Apr},
   publisher={John Wiley \& Sons}
 }
 
-@inproceedings{doucet2000rao,
-  title={Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks},
-  author={Doucet, Arnaud and De Freitas, Nando and Murphy, Kevin and Russell, Stuart},
-  booktitle={Proc. of the Sixteenth Conf. on Uncertainty in Artificial Intelligence},
-  pages={176--183},
-  year={2000},
-  organization={Morgan Kaufmann Publishers Inc.}
-}
-
 @article{briers2010smoothing,
   title={Smoothing Algorithms for State-Space Models},
   author={Briers, Mark and Doucet, Arnaud and Maskell, Simon},