\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. 
A powerful method to obtain numerical results for this approach are particle filter. 

Especially in indoor localisation, particle filter can lately be considered as the standard method for solving complex non-linear problems \cite{}.
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:
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 

most localisation distribution differ how the transition and evaluation are blub \cite{}.

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

Besides the normal bootstrap or condensation particle filter, their are many different abformen, welche aber grundsätzlich  aus den oben gennanten schritten bestehen.


 

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. 
