sample impoverishment weiter gemacht

tex/chapters/introduction.tex

@@ -7,7 +7,7 @@ In terms of European architecture, the problems emanating from these buildings w
 In the scope of this work, we deployed an indoor localization system to a 13th century building.
 The first 300 years the building was used as a convent, after that it had different functions ranging from a granary to an office for Bavarian officials. 
 Over this period, the building had major construction measures and was extended several times.
-Since 1936, the \SI{2500}{m$^2$} building acts as a museum of the medieval town Rothenburg ob der Tauber \cite{Rothenburg}. 
+Since 1936, the \SI{2500}{m$^2$} building acts as a museum of the medieval town Rothenburg ob der Tauber \cite{Rothenburg}, Germany. 
 
 Such buildings are often full of nooks and crannies, what makes it hard for dynamical models using any kind of pedestrian dead reckoning (PDR). Here, the error accumulates not only over time, but also with the number of turns and steps made \cite{Ebner-15}. 
 There is also a higher chance of detecting false or misplaced turns, what can cause the position estimation to lose track or get stuck within a demarcated area. 
@@ -39,5 +39,5 @@ A barometer based activity recognition enables to go into the third dimension an
 
 The goal of this work is to propose a fast to deploy and low-cost localization solution, that provides reasonable results in a high variety of situations.
 Consequently, we believe that by utilizing our localization approach to such a challenging scenario, it is possible to prove those characteristics. 
-It should finally be mentioned, that the here presented work is an updated and highly re-factored version of the winner of the smartphone-based competition at IPIN 2016 \cite{Ebner-15}. 
+Finally, it should be mentioned that the here presented work is an updated and highly updated version of the winner of the smartphone-based competition at IPIN 2016 \cite{Ebner-15}. 
 

tex/chapters/relatedwork.tex

@@ -11,7 +11,7 @@ Here, new particles are drawn according to some importance distribution, often r
 Those particles are then weighted by the state evaluation given different sensor measurements.
 A resampling step is deployed to prevent that only a small number of particles have a signifcant weight \cite{chen2003bayesian}.
 Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Fetzer-16, Ebner-16, Hilsenbeck2014}.
-Additionally, within this paper we present a method, which is designed to run solely on a smartphone.
+Additionally, within this paper we present a method, which is designed to run solely on a commercial smartphone.
 
 In its most basic form, the state transition is given by.. einfach distanz und heading.. intersection with walls usw.
 
@@ -48,13 +48,25 @@ Thus \cite{Ebner-17} suggests to only consider floors/ceilings, what can be calc
 To further reduce the setup-time, \cite{WithoutThePain} introduces an approach that works without any prior knowledge.
 They use a genetic optimization algorithm to estimate the parameters for a signal strength prediction, including the access points (AP) position, and the pedestrian's locations during the walk.
 The estimated parameters can be refined using additional walks.
-Within this work we present a similar optimization approach for estimating the AP's location. 
+Within this work we present a similar optimization approach for estimating the AP's location in 3D. 
 However, instead of taking multiple measuring walks, the locations are optimized based only on some reference measurements, what further decreases the setup-time.
-Additionally, our approach extends to the third dimension.
+Additionally, we will show that such an optimization scheme can partly compensate for the above abolished intersection-tests.
 
+%immpf
+Besides well chosen probabilistic models, the system's performance is also highly affected by handling problems which are based on the nature of particle filter.
+They are often caused by restrictive assumptions about the dynamic system, like the aforementioned sample impoverishment. 
+The authors of \cite{Sun2013} handled the problem by using an adaptive number of particles instead of a fixed one. 
+The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
+The problem of sample impoverishment is then encountered by adapting the number of particles depend upon the systems current uncertainty \cite{Fetzer-17}.
 
-Besides well chosen probabilistic models, the system's performance is also highly affected by handling problems which are .. based on the nature of particle filters. One very affecting problem is the before mentioned sample impoverishment. In blabal \cite{} this problems was tackled by and. In \cite{} we deployed a ... . However, deploying a IMMPF is in most cased not a necassary step, thus we present i much simple, but also very heuristic model within this paper. 
+However, in practice sample impoverishment is often a problem of environmental restrictions and system dynamics.
+Therefore, such a method fails, since it is not able to propagate new particles into the state space due to environmental restrictions e.g. walls or ceilings.
+In \cite{Fetzer-17} we deployed an interacting multiple model particle filter (IMMPF) to solve the sample impoverishment. 
+We combine two particle filter using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between both.
 
+However, deploying a IMMPF is in most cased not a necessary step, thus we present i much simple, but also very heuristic model within this paper. 
+
+%estimation
 Finally, as the name recursive state estimation states, it requires to find the most probable state within the state space, to provide the “best estimate” of the underlying problem.
 In the discrete manner of a sample representation this is often done by providing a single value, also known as sample statistic, to serve as a “best guess”. 
 This value is then calculated by means of simple parametric point estimators, e.g. the weighted-average over all samples, the sample with the highest weight or by assuming other parametric statistics like normal distributions