FHWS/IPIN2017
Archived
3
0
Fork 0
Code Issues 4 Pull Requests Releases Wiki Activity

tex v2 - without experiments

Browse Source
This commit is contained in:
toni
2017-05-10 23:33:01 +02:00
parent 5b2e1b0c65
commit 210fae56b7
11 changed files with 4856 additions and 10840 deletions
Download Patch File Download Diff File Expand all files Collapse all files

45
tex/chapters/introduction.tex
View File

@@ -1,30 +1,30 @@
\section{Introduction}
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 filters, which update the state estimation recursively with every new incoming measurement.
A powerful method to obtain numerical results for this approach are particle filters.
%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}.
Especially in indoor localisation, particle filters 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 (particles), 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:
At first, new particles are drawn according to some importance distribution, those particles are then weighted by an incremental importance weight distribution and finally a resampling step is deployed to prevent that only a small number of particles have a signifcant weight and all the other will have negligible small weights instead \cite{orhan2012particle}.
In its most basic form, the particle filter is based on three main steps:
At first, new particles are drawn according to some importance distribution, those particles are then weighted by an incremental importance weight distribution and finally a resampling step is deployed to prevent that only a small number of particles have a signifcant weight and all the other will have negligible small weights instead \cite{chen2003bayesian}.
%transition und evaluation einführen
In practice the importance distribution is often represented by the state transition, modelling the dynamics of the system.
In practice, the importance distribution is often represented by the state transition, modelling the dynamics of the system.
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, Ebner2016OPN, 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.
Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Nurminen13-PSI, Ebner-16, Hilsenbeck2014}.
However, as \cite{Li2014} already mentioned, particle filters (and nearly all of its modifications) continue to suffer from two notorious problems: sample degeneracy and impoverishment.
As one can imagine, after a few iterations with continuously reweighting particles, the weight will concentrate on a few particles only.
This is why the resampling step was presented in the first place.
Here, a new set of equally weighted particles is drawn by multiplying high weighted particles while abandoning low weighted ones.
However, this leads to an decreasing diversity of particles after a resampling step, also known as sample impoverishment.
Here, a new set of equally weighted particles is drawn by duplicating highly weighted particles while abandoning low weighted ones.
However, this leads to a decreasing diversity of particles after a resampling step, also known as sample impoverishment.
This high concentration of particles follows a bad approximation of the underlying probability distribution and therefore worse estimation results.
The effect of impoverishment is not solely caused by resampling only.
The effect of impoverishment is not solely caused by resampling.
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.
An example is illustrated in fig. \ref{fig:multimodalPath}, where the state dynamics prohibit walking through walls and consider the human movement speed.
%
\begin{figure}[t]
\centering
@@ -35,23 +35,24 @@ An example is illustrated in fig. \ref{fig:multimodalPath}, where a graph-based
\label{fig:multimodalPath}
\end{figure}
%
Due to uncertain measurements the posterior distribution of the particle filter is captured within a room.
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 particles on the corridor and drawing new particles 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 particles 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.
However, it is obvious that this leads to a higher uncertainty and possibly a 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 not be possible.
Especially, methods using relative measurements like pedestrian dead reckoning 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.
We combine two similar particle filters using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between the modes and a Wi-Fi quality factor.
One with a very restrictive transition scheme, providing very accurate results.
The other with more flexible and simple dynamics, resulting in a higher sample diversity.
Both are then successfully combined, to satisfy the need of diversity and the need of focus.
The main benefit of this approach is that it can be easily adapted to other existing localization approaches based on particle filters.
We tackle this problem in the context of indoor localisation by deploying an interacting multiple model particle filter (IMMPF) for jump Markov non-linear systems \cite{Driessen2005}.
This enables merging of posterior probability distributions, approximated by particle filters.
Within this context a particle filter is also refereed to as a mode of the IMMPF.
We combine two modes using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between them and a Wi-Fi quality factor.
One mode with a very restrictive transition scheme, providing very accurate localisation results.
The other with more flexible, robust and simple transition, resulting in a higher sample diversity.
The modes are then successfully combined, to satisfy \textit{both}, the need of diversity and the need of focus.
This approaches main benefit is, that it can be easily adapted to other existing methods based on particle filters.