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

added related work

Browse Source
This commit is contained in:
toni
2017-04-22 01:29:12 +02:00
parent a9b057c284
commit b45b9bd291
4 changed files with 151 additions and 36 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
tex/bare_conf.tex
View File

@@ -141,7 +141,7 @@
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Recovering from Particle Depletion in Context of Indoor Localisation}
\title{Recovering from Sample Impoverishment in Context of Indoor Localisation}
% author names and affiliations

28
tex/chapters/introduction.tex
View File

@@ -6,9 +6,9 @@ A powerful method to obtain numerical results for this approach are particle fil
%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 (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 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 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}.
%transition und evaluation einführen
In practice the importance distribution is often represented by the state transition, modelling the dynamics of the system.
@@ -16,11 +16,11 @@ A new weight is then obtained by the state evaluation given different sensor mea
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.
As one can imagine, after a few iterations with continuously reweighting samples, the weight will concentrate on a few samples only.
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 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.
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.
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.
Restrictive transition models, as they are used in indoor localisation applications, also enhance this effect significantly.
@@ -36,10 +36,10 @@ An example is illustrated in fig. \ref{fig:multimodalPath}, where a graph-based
\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.
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 samples randomly in the building.
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.
@@ -47,13 +47,11 @@ Especially, methods using relative measurements like pedestrian dead reckoning a
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.
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.

59
tex/chapters/relatedwork.tex
View File

@@ -1,28 +1,51 @@
\section{Related Work}
\label{sec:relatedWork}
% 3/4 Seite ca.
% 1/2 - 3/4 Seite ca.
%klassisch resampling
A common way to handle degeneracy and impoverishment is to apply suitable resampling methods.
The four most popular and well established approaches found in literature are multinomial, stratified, systematic and residual resampling.
They are also referred to as traditional methods, since a single distribution is used for resampling and the number of times a particle is re-drawn is always proportional to is weight \cite{Li2015b}.
%advanced resampling
A more advanced method, with an adaptive particle size instead of a fixed one, is KLD-resampling.
It determines the number of particles to resample so that the Kullback-Leibler divergence between the distribution before resampling and after resampling does not exceed a pre-specified error bound \cite{Sun2013}.
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.
In \cite{Li2015b} an overview of different resampling approaches are given.
%allgemien auf andere methoden überleiten
As seen, resampling methods are able to reduce impoverishment to a certain degree by themselves.
However, in practice sample impoverishment is also a problem of environmental restrictions and system dynamics.
Here, classical resampling schemes fail, since they are not able to propagate new particles into the state space.
More promising and intelligent solutions are given by techniques of Particle Distribution Optimization (PDO).
These variations of techniques are acting in different ways to optimize the spatial distribution of particles and are particularly effective in alleviating sample degeneracy and impoverishment \cite{Li2014}.
For example in \cite{Xiaoqin2008} a Particle Swarm Optimization is used as importance distribution for visual tracking.
Particles are iteratively updated according to their own experience and the experience of the swarm (or neighboring particles).
This allows for a multi-layer importance sampling and incorporation of the current measurement into the importance distribution, dealing with the sample impoverishment.
Other PDO methods are presented in \cite{Li2014}.
%hinführen zu IMM
In context of this work, our aim is to present a general solution that can be easily adapted to common localisation systems.
A promising approach for an easy to deploy PDO are Interacting Multiple Models (IMM) \cite{Bar-Shalom1988}.
IMM are able to mix appropriate dynamical systems based on a Bayesian probability metric and Gaussian noise.
Therefore, a set of modes like Kalman Filters are running in parallel.
The mixing between modes is done by using a Markov Chain process, providing a probability for every mode and a transition matrix for switching between them.
The most proper mode is then chosen for the current state estimation, what allows
the right choice to the right time.
For example \cite{Zhang2013} uses IMM to switch between a line-of-sight and a non-line-of-sight filtering procedure for indoor localisation.
Thereby, they are able to provide a robust and stable position estimation in both environments.
An extension to particle filters and therefore to non-linear and non-Gaussian system was presented by \cite{Boers2003}.
The so called Interacting Multiple Model Particle Filter (IMMPF) was then further developed by \cite{Driessen2005}, adding a direct sampling approach.
This allows a merging between different particle filters by providing a possibility for each filter to additional sample particles from all available particle sets and not just from its own.
It is obvious that the possibility to draw from other particle sets is based on the mode probability and the transition matrix provided by the Markov Chain process and therefore does not violate the Markov property.
Now, the key idea of this work is to satisfy the trade-off between diversity and focus by using appropriate modes within the IMMPF.
resampling approaches presented in and ... not able to solve impovershement, especially the one caused by a restrictive transition model.
trade of effective sample size
%Therefore, two different dynamical models are utilized and a novel approach for a non-trivial Markov switching Process based on Kullback-Leibler divergence and a Wi-Fi quality factor are presented.
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.
combining different filters.
jump markov non linear system.
interacting multiple model
particle filter

98
tex/egbib.bib
View File

@@ -2747,7 +2747,6 @@ mendeley-groups = {IPIN 2017},
number = {8},
pages = {3944--3954},
title = {{Fight sample degeneracy and impoverishment in particle filters: A review of intelligent approaches}},
url = {https://arxiv.org/pdf/1308.2443.pdf},
volume = {41},
year = {2014}
}
@@ -2763,9 +2762,104 @@ 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}
}
@article{Li2015b,
abstract = {Two decades ago, with the publication of [1], we witnessed the rebirth of particle filtering (PF) as a methodology for sequential signal processing. Since then, PF has become very popular because of its ability to process observations represented by nonlinear state-space models where the noises of the model can be non-Gaussian. This methodology has been adopted in various fields, including finance, geophysical systems, wireless communications, control, navigation and tracking, and robotics [2]. The popularity of PF has also spurred the publication of several review articles [2]-[6].},
author = {Li, Tiancheng and Boli{\'{c}}, Miodrag and Djuri{\'{c}}, Petar M.},
doi = {10.1109/MSP.2014.2330626},
issn = {10535888},
journal = {IEEE Signal Processing Magazine},
month = {may},
number = {3},
pages = {70--86},
title = {{Resampling Methods for Particle Filtering: Classification, implementation, and strategies}},
volume = {32},
year = {2015}
}
@article{Sun2013,
author = {Sun, S. and Li, T. and Sattar, T.P.},
doi = {10.1049/el.2013.0233},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Sun, Li, Sattar - 2013 - Adapting sample size in particle filters through KLD-resampling.pdf:pdf},
isbn = {1350-911X},
issn = {0013-5194},
journal = {Electronics Letters},
mendeley-groups = {IPIN 2017},
month = {jun},
number = {12},
pages = {740--742},
title = {{Adapting sample size in particle filters through KLD-resampling}},
volume = {49},
year = {2013}
}
@inproceedings{Xiaoqin2008,
abstract = {Visual tracking usually involves an optimization process for estimating the motion of an object from measured images in a video sequence. In this paper, a new evolutionary approach, PSO (particle swarm optimization), is adopted for visual tracking. Since the tracking process is a dynamic optimization problem which is simultaneously influenced by the object state and the time, we propose a sequential particle swarm optimization framework by incorporating the temporal continuity information into the traditional PSO algorithm. In addition, the parameters in PSO are changed adaptively according to the fitness values of particles and the predicted motion of the tracked object, leading to a favourable performance in tracking applications. Furthermore, we show theoretically that, in a Bayesian inference view, the sequential PSO framework is in essence a multilayer importance sampling based particle filter. Experimental results demonstrate that, compared with the state-of-the-art particle filter and its variation - the unscented particle filter, the proposed tracking algorithm is more robust and effective, especially when the object has an arbitrary motion or undergoes large appearance changes.},
author = {Xiaoqin, Zhang and Weiming, Hu and Maybank, S and Xi, Li and Mingliang, Zhu},
booktitle = {Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on},
doi = {10.1109/CVPR.2008.4587512},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Xiaoqin Zhang et al. - 2008 - Sequential particle swarm optimization for visual tracking.pdf:pdf},
isbn = {1063-6919},
issn = {1063-6919},
keywords = {Bayes methods,Bayesian inference view,Bayesian methods,Inference algorithms,Monte Carlo methods,Motion measurement,Nonhomogeneous media,Particle filters,Particle swarm optimization,Particle tracking,Video sequences,image sampling,image sequences,importance sampling,motion estimation,multilayer importance sampling,particle filtering (numerical methods),particle swarm optimisation,sequential particle swarm optimization,temporal continuity information,unscented particle filter,video sequence,video signal processing,visual tracking},
mendeley-groups = {IPIN 2017},
month = {jun},
pages = {1--8},
publisher = {IEEE},
title = {{Sequential particle swarm optimization for visual tracking}},
year = {2008}
}
@inproceedings{Zhang2013,
abstract = {This paper presents a wireless network infrastructure based localization system using ultrasonic transmitter and receiver for obtaining accurate TDOA measurements and Interacting Multiple Model (IMM) estimator for calculating the actual position of the target by running two filters, i.e. extended Kalman filter (EKF) and robust extended Kalman filter (REKF), which offers the protection against the noise in both line-of-sight (LOS) and non-line-of-sight (NLOS) environments. The experiment results showed that the system utilized the advantages of EKF and REKF for different environments and thus was able to provide a localization solution with high accuracy.},
author = {Zhang, Rui and H{\"{o}}flinger, Fabian and Reindl, Leonhard},
booktitle = {IEEE Transactions on Instrumentation and Measurement},
doi = {10.1109/TIM.2013.2256713},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Hoflinger, Reindl - 2013 - TDOA-Based Localization Using Interacting Multiple Model Estimator and Ultrasonic TransmitterReceiver.pdf:pdf},
isbn = {9781467315906},
issn = {00189456},
keywords = {Indoor localization,Kalman filter,M-estimator,interacting multiple model (IMM),time difference of arrival (TDOA),ultrasound},
mendeley-groups = {IPIN 2017},
month = {aug},
number = {8},
pages = {2205--2214},
title = {{TDOA-Based localization using interacting multiple model estimator and ultrasonic transmitter/receiver}},
volume = {62},
year = {2013}
}
@article{Bar-Shalom1988,
abstract = {An important problem is the estimation of the state of a linear system with Markovian switching coefficients. In this problem, the dynamics of the system is represented by multiple models which are hypothesized to be correct. The Interacting Multiple Model (IMM) algorithm is a novel approach to merging the different model hypotheses. In the IMM algorithm, the state estimate is computed under each possible model hypothesis over the most recent sampling period with each model using a different combination of previous model-conditioned estimates. In this paper, the second order Interacting Multiple Model (IMM2) algorithm is developed for estimating the state of a linear system with Markovian switching coefficients. In the IMM2 algorithm, the state estimate is computed under each possible model hypothesis over the two most recent sampling periods with each model hypothesis using a different combination of the previous model-conditioned estimates. Simulation results are given for a target tracking example to demonstrate the performance of the IMM2 algorithm relative to that of the IMM and second order Generalized Pseudo-Bayesian algorithms.},
author = {Bar-Shalom, Yaakov},
doi = {10.1109/9.1299},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Blom, Bar-Shalom - 1988 - The interacting multiple model algorithm for systems with Markovian switching coefficients.pdf:pdf},
isbn = {0-7803-0860-3},
issn = {00189286},
journal = {IEEE Transactions on Automatic Control},
mendeley-groups = {IPIN 2017},
number = {8},
pages = {780--783},
title = {{Interacting multiple model algorithm for systems with Markovian switching coefficients.}},
volume = {33},
year = {1988}
}
@article{Boers2003,
abstract = {A new method for multiple model particle (nonlinear) filtering for Markovian switching systems is presented. This new method is a combination of the interacting multiple model (IMM) filter and a (regularised) particle filter. The mixing and interaction is similar to that in a conventional IMM filter. However, in every mode a regularised particle filter is running. The regularised particle filter probability density is a mixture of Gaussian probability densities. The proposed method is able to deal with nonlinearities and non-Gaussian noise. Furthermore, the new method keeps a fixed number of particles in each mode, and therefore it does not suffer from the potential drawbacks of existing multiple model particle filters for Markovian switching systems.},
author = {Boers, Y and Driessen, J N},
doi = {10.1049/ip-rsn},
file = {:home/toni/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Boers, Driessen - 2003 - Interacting multiple model particle filter.pdf:pdf},
issn = {13502395},
journal = {October},
mendeley-groups = {IPIN 2017},
number = {5},
pages = {344--349},
title = {{Interacting multiple model particle filter}},
volume = {150},
year = {2003}
}