52 lines
4.2 KiB
TeX
52 lines
4.2 KiB
TeX
\section{Related Work}
|
|
\label{sec:relatedWork}
|
|
% 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.
|
|
|
|
|
|
%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.
|
|
|
|
|
|
|
|
|
|
|
|
|