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tex/chapters/introduction.tex
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Localising pedestrians inside buildings can be considered as a time-sequential, non-linear and non-Gaussian state estimation problem. 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. 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. A powerful method to obtain numerical results for this approach are particle filters.
Especially in indoor localisation, particle filter can lately be considered as the standard method for solving complex non-linear problems \cite{}. %einführen von partikel filter ganz allgemein
Especially in indoor localisation, particle filter can lately be considered as the standard method for solving complex non-linear problems \cite{Doucet11:ATO}.
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. 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: 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}. 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 %transition und evaluation einführen
In practice the importance distribution is often represented by the state transition, modelling the dynamics of the system.
most localisation distribution differ how the transition and evaluation are blub \cite{}. A new weight is then obtained by the state evaluation given different sensor measurements.
Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Nurminen13-PSI, Ebner-15, Hilsenbeck2014}.
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. 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 As one can imagine, after a few iterations with continuously reweighting samples, the weight will concentrate on a few samples only.
This is why the resampling step was presented in the first place.
Here, a new set of equally weighted samples is drawn by multiplying high weighted samples while abandoning low weighted ones.
However, this leads to an decreasing diversity of samples after a resampling step, also known as sample impoverishment.
This high concentration of samples follows a bad approximation of the underlying probability distribution and therefore worse estimation results.
Besides the normal bootstrap or condensation particle filter, their are many different abformen, welche aber grundsätzlich aus den oben gennanten schritten bestehen. The effect of impoverishment is not solely caused by resampling only.
Restrictive transition models, as they are used in indoor localisation applications, also enhance this effect significantly.
An example is illustrated in fig. \ref{fig:multimodalPath}, where a graph-based structure prohibits walking through walls and considers the human movement speed.
%
\begin{figure}[t]
\centering
\def\svgwidth{0.9\columnwidth}
\input{gfx/multimodalPath.eps_tex}
\caption[An example of the occurrence of sample impoverishment.]{
An example of the occurrence of sample impoverishment enhanced by a restrictive transition model that prevents sampling through walls. At time $t-1$ the approximated position (green line) drifts apart from the ground truth (black line) due to uncertain measurements. The posterior distribution is then captured within the room and not able to recover by itself. }
\label{fig:multimodalPath}
\end{figure}
%
Due to uncertain measurements the posterior distribution of the particle filter is captured within a room.
Between time $t-1$ and $t$, the resampling step abandons all samples on the corridor and drawing new samples outside the room is not possible due to the restricted transition.
At this point, standard filtering methods are not able to recover.
A simple solution would be drawing a handful new samples randomly in the building.
However, it is obvious that this leads to a higher uncertainty and possible a highly multimodal posterior distribution.
Additionally, very uncertain absolute measurements, like attenuated Wi-Fi signals, can cause unpredictable jumps to such a newly drawn position, which would otherwise be not possible.
Especially, methods using relative measurements like pedestrian dead reckoning approaches are losing their importance.
As mentioned before, sample degeneracy and impoverishment are a pair of contradictions that can be described as a trade-off between the need of diversity and the need of focus \cite{Li2014}.
We tackle this problem in context of indoor localisation by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems \cite{Driessen2005}.
This enables a merging between posterior probability distributions approximated by particle filters, refereed as modes within this context.
combining two particles filters, one with a very restrictive transition scheme sehr genaue ergebnisse, and one with a more flexible but schlechtere ergebnisse scheme werden gewinnrbingen gemixed within the IMMPF,
Therefore a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between the modes and a
The main benefit of this approach is that it be easily adapted to other existing localization approaches based on particle filters.
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.
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.

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tex/chapters/relatedwork.tex
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\label{sec:relatedWork} \label{sec:relatedWork}
% 3/4 Seite ca. % 3/4 Seite ca.
resampling approaches presented in and ... not able to solve impovershement, especially the one caused by a restrictive transition model.
trade of effective sample size
andere arbeiten die particle depletion verhindern wollte -> was haben die so gemacht? 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. 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.

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tex/egbib.bib
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year = {2014} year = {2014}
} }
@article{Driessen2005,
abstract = {An efficient particle filtering algorithm is presented for state estimation of jump Markov nonlinear systems. The standard particle filter can easily suffer from particle degeneracy around mode changes. The new algorithm allows the user to fully control the number of particles in a certain mode, without distorting or violating the Markov property. This property can be exploited to prevent the filter degenerating.},
author = {Driessen, H. and Boers, Y.},
doi = {10.1049/ip-rsn:20045075},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Driessen, Boers - 2005 - Efficient particle filter for jump Markov nonlinear systems.pdf:pdf},
issn = {1350-2395},
journal = {Radar, Sonar and Navigation, IEE Proceedings -},
mendeley-groups = {IPIN 2017},
number = {5},
pages = {323--326},
title = {{Efficient particle filter for jump Markov nonlinear systems}},
url = {http://digital-library.theiet.org/content/journals/10.1049/ip-rsn{\_}20045075 http://ieeexplore.ieee.org/ielx5/2198/32393/01512727.pdf?tp={\&}arnumber=1512727{\&}isnumber=32393{\%}5Cnhttp://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1512727{\&}navigation=1},
volume = {152},
year = {2005}
}

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