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final version paper

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tex/bare_conf.tex
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@@ -130,7 +130,7 @@
\input{misc/functions}
\IEEEoverridecommandlockouts
\IEEEpubid{\makebox[\columnwidth]{\hfill 978-1-5090-2425-4/16/\$31.00~\copyright~2016 IEEE}
\IEEEpubid{\makebox[\columnwidth]{\hfill XXX-X-XXXX-XXXX-X/XX/\$XX.XX~\copyright~2017 IEEE}
\hspace{\columnsep}\makebox[\columnwidth]{ }}
\begin{document}

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tex/chapters/conclusion.tex
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@@ -11,3 +11,6 @@ By incorporating completely different modes, not only transitions, the robustnes
This would additionally allow for on-the-fly switching between sensor models, e.g. different signal strength prediction methods.
Such a modular solution could be able to fit any environment and thus form a highly flexible and adjustable localisation system.
However, adjusting the Markov switching process to any number of modes is no easy task and therefore requires intensive future work.
%only the position estimation of the dominant filter. However, would also be possible to combine estimations provided by different modes.

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tex/chapters/experiments.tex
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@@ -7,8 +7,8 @@ All upcoming experiments were carried out on four floors (0 to 3) of a \SI{77}{m
It includes several staircases and elevators and has a ceiling height of about \SI{3}{m}.
The gridded graph was generated for the complete campus and thus outdoor areas like the courtyard are also walkable.
As \docWIFI{} is attenuated by obstacles and walls, it does not provide a consistent quality over the complete building.
To get an idea about the \docWIFI{} quality, we interpolated the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$, with $l_{\text{max}} = \SI{-75}{\dBm}$ and $l_{\text{min}} = \SI{-90}{\dBm}$, between some measurements using a nearest-neighbour procedure.
In fig. \ref{fig:paths} the resulting colourized floorplan is illustrated.
To get an idea about the quality, we interpolated the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$, with $l_{\text{max}} = \SI{-75}{\dBm}$ and $l_{\text{min}} = \SI{-90}{\dBm}$, between some measurements using a nearest-neighbour procedure.
In fig. \ref{fig:paths} the resulting colourized floorplan is shown.
Here, the intensity of red indicates a low signal strength and thus a bad quality for localising a pedestrian within this area using \docWIFI{}.
% bild: mit pfaden drauf und eventl. wifi qualität in jeweiligen bereichen? (kann frank das)
@@ -36,9 +36,8 @@ Due to legal terms, we are not allowed to depict their positions and therefore o
To model the uncertainty of the \docWIFI{}, a white Gaussian noise with $\sigma_\text{wifi} = \SI{8}{\dBm}$, growing with each measurement's age, was chosen.
The pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically as described in \cite{Fetzer2016OMC}.
As expected before, the kernel density estimation in \eqref{eq:KDE} and the much simpler multivariate normal distribution estimation are both producing similar results in context of the divergence measure given in \eqref{equ:KLD}.
For this reason and because of the faster processing time, especially in context of calculating on a smartphone, we estimated the posteriors of the modes by approximating a multivariate normal distribution (cf. section \ref{sec:divergence}).
For this reason and because of the faster processing time, especially in context of smartphones, we estimated the posteriors of the modes by approximating a multivariate normal distribution (cf. section \ref{sec:divergence}).
For calculating \eqref{equ:KLD} we set $\lambda = 0.03$ based on best practices.
Finally, the pedestrian's most likely position (state) was then estimated using the weighted arithmetic mean of the particle set.
@@ -76,13 +75,15 @@ As mentioned above, every run of a walk starts with a uniform distribution as pr
Due to a low \docWIFI{} coverage at the starting point in seg. 1, the pedestrian's position is falsely estimated into a room instead of the corridor.
All three filters are able to overcome this false detection.
However, the graph-based filter (red) gets then indissoluble captured within a room, because of its restrictive behaviour and the aftereffects of the initial \docWIFI{} readings (cf. fig. \ref{fig:path3} seg. 2).
It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{75} = \SI{3884}{\centimeter}$ and got stuck in \SI{100}{\percent} of all runs.
It provides a \SI{75}{\percent}-quantil of $\tilde{x}_{75} = \SI{3884}{\centimeter}$ and got stuck in \SI{100}{\percent} of all runs.
As expected and discussed earlier, the simple filter (blue) is less prone to bad observations and provides not accurate, but very robust results of $\tilde{x}_{75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$.
Looking at $D_{\text{KL}}$ over time confirms our assumption made in section \ref{sec:divergence}.
The graph-based filter (red) gets stuck and is not able to recover.
Starting on from this point, the Kullback-Leibler divergence $D_{\text{KL}}$ (purple) further increases due to the growing distance between both filters (blue and red) starting at seg. 2 until the end of seg. 4.
It is clearly visible, that this divergence between both filters is a very good indicator to observe, if a filter gets stuck or loses track.
Following, the IMMPF (green) results in a very natural and straight path estimation and a low $D_{\text{KL}}$ between modes.
Of course, the low $D_{\text{KL}}$ of the IMMPF results from the mixing between the modes caused by $\Pi_t$.
Therefore, the matrix $\Pi_t$ can also be seen as some kind of limiter, paying attention that the modes do not diverge to much from each other.
The benefits of mixing both filtering schemes within the scenario of path 3 are thus obvious.
The IMMPF filters with an error of $\tilde{x}_{75} = \SI{667}{\centimeter}$ and $\bar{\sigma} = \SI{558}{\centimeter}$.
@@ -97,17 +98,17 @@ The IMMPF filters with an error of $\tilde{x}_{75} = \SI{667}{\centimeter}$ and
\end{figure}
%
Next, we investigate the performance of our approach by considering the scenario in path 2.
Here, the overall \docWIFI{} quality is rather low, especially in the zig-zag stairwell on the buildings back and the small entrance area at floor 1 (cf. fig. \ref{fig:paths} and fig. \ref{fig:path2} seg. 3).
Path 2 starts in the second floor, walking down the centred stairs into the first floor, then making a right turn and walking the stairs down to zeroth floor, from there we walk back to second floor using the zig-zag stairwell and after finally crossing a room we are back at the start.
Here, the overall \docWIFI{} quality is rather low, especially in the zig-zag stairwell on the building's back and the small entrance area at floor 1 (cf. fig. \ref{fig:paths} and fig. \ref{fig:path2} seg. 3).
Path 2 starts in the second floor, walking down the centred stairs into the first floor, then making a right turn and walking the stairs down to zeroth floor. From there we walk back to the second floor using the zig-zag stairwell and after finally crossing a room we are back at the start.
This is a very challenging scenario, at first the estimation got stuck on the first floor in a room's corner for \SI{20}{\second} (see fig. \ref{fig:path2} seg. 2) and after that the \docWIFI{} is highly attenuated at the beginning and end of seg. 3.
Looking at fig. \ref{fig:path2}, one can observe the impact of the \docWIFI{} quality factor within the Markov transition matrix.
Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between \SIrange{80}{130}{\second} in seg. 3.
Without it, the position estimation (red) is drifting into the courtyard, missing the stairwell and producing high errors between \SIrange{80}{130}{\second} in seg. 3.
As described earlier, the bad \docWIFI{} readings are causing $D_{\text{KL}}$ to grow.
It follows that the accurate dominant filter draws new particles from the uncertain support and therefore worsen the position estimation.
It follows that the accurate dominant filter draws new particles from the uncertain support and therefore worsens the position estimation.
Given this outcome, it is not very satisfying that the system is able to recover thanks to its high diversity during situations with uncertain measurements.
By adding the \docWIFI{} quality factor, the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{75} = \SI{953}{\centimeter}$ with $\bar{\sigma} = \SI{543}{\centimeter}$.
However, this is far from perfect and in some cases ($\sim \SI{9}{\percent}$) the quality factor was not able to prevent the estimation to drift in the courtyard.
This solely happened when particles were sampled directly onto the courtyard while changing from first to zeroth floor (cf. fig. \ref{fig:path2} seg. 3).
However, this is far from perfect and in some cases ($\sim \SI{9}{\percent}$) the quality factor was not able to prevent the estimation from drifting into the courtyard.
This solely happened when particles were sampled directly onto the courtyard while changing from first to zeroth floor (cf. fig. \ref{fig:path2} seg. 3), instead of within the building first.
Those particles then received a high weight due to the attenuated measurements, causing a weight degeneracy.
Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor or optimizing the access-point's parameters can resolve this problem \cite{Ebner-17}.
@@ -125,17 +126,17 @@ An exemplary result for path 1 is illustrated in fig. \ref{fig:path1}.
The path starts on the first floor and finishes on the third after walking two straight stairs.
Using the graph-based filter for localisation, we were able to obtain a very accurate path (blue) in \SI{80}{\percent} of the runs providing $\tilde{x}_{75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$.
Due to a lack of particles near the stairs, the other \SI{20}{\percent} of the estimations given by the graph-based filter failed to detect the first floor change (red).
Using our approach (green), we were able detect all floor changes and thus never lost track.
Using our approach (green), we were able to detect all floor changes and thus never lost track.
Fig. \ref{fig:path1} shows an example, where the dominant filter also failed to change floors within seg. 2.
By looking at seg. 2 of the error plot, we can observe a more or less constant error of \SIrange{5}{6}{\meter}, which then drops rapidly at the beginning of seg. 3.
This reduction of the error is caused by the growing importance of the mixing stage, where more and more particles from the support filter are incorporated into the dominant filter.
By looking at this segment of the error plot, we can observe a more or less constant error of \SIrange{5}{6}{\meter}, which then drops rapidly at the beginning of seg. 3.
This is due to the growing importance of the mixing stage, where more and more particles from the support filter are incorporated into the dominant filter.
Going on in seg. 3, the \docWIFI{} measurements suffer from an attenuation directly after leaving the stairs, what leads to a high error using the graph-based filter (blue and red).
In contrast, the IMMPF is able to compensate the false detection due to an decreasing \docWIFI{} quality and thus a highly focused posterior provided by the dominant filter.
The IMMPF then performs with $\tilde{x}_{75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$.
Those very similar estimation results between IMMPF (green) and the graph-based filter (blue) confirm the efficiency of the mixing and how it is able to keep the accuracy while providing a higher robustness against failures.
%allgemeines abschließendes blabla?
To summarize, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area.
To summarize, the here presented approach was able to recover in all situations and thus never got stuck within a demarcated area.
The above deployed experiments have shown, that the Markov switching process, as presented in sec. \ref{sec:immpf}, enables a reasonable mixing between two particle filters with different transition schemes.
Therefore, the quality and success of the results depend highly on the parameters used within the Markov matrix $\Pi_t$.
Those values are very sensitive and should be chosen carefully in regard to the specific system and use case.

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tex/chapters/method.tex
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@@ -82,7 +82,7 @@ Further, the number of particles in each mode can be selected independently of t
Algorithm \ref{alg:immpf} shows the complete IMMPF procedure in detail.
As prior knowledge, $M$ initial probabilities $P(m_1 \mid \mObsVec_{1})$ and initial distributions $p(\mStateVec_{1} \mid m_1, \mObsVec_{1})$ providing a particle set $\{W^i_{1}, \vec{X}^i_{1} \}_{i=1}^N$ are available.
The mixing step requires that the independently running filtering processes are all finished.
A new iteration $t$ is initiated by the mixing step (line 1 to 7) and requires that the independently running filters (line 8 to 15) have all finished processing within the previous iteration $t-1$.
\begin{algorithm}[t]
\caption{IMMPF Algorithm}
@@ -118,9 +118,9 @@ Within the IMMPF we utilize the restrictive graph-based filter as the \textit{do
Due to its robustness and good diversity the simple, more permissive filter, is then used as \textit{support} for possible sample impoverishment.
The names dominant and support are now applied as synonyms for the respective filters used as modes within the IMMPF.
As a reminder, both filters (modes) are running in parallel for the entire estimation life cycle.
If we recognize that the dominant filter diverges from the supporting filter and thus got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter.
As seen before, the Markov transition matrix $\Pi_t$ provides the probability $P(m_{t+1} \mid m_t)$ for transitioning between modes.
As a reminder, both filters (modes) are running in parallel for the entire IMMPF life cycle.
If we recognize that the dominant filter diverges from the supporting filter and thus probably got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter.
As seen before, the Markov transition matrix $\Pi_t$ provides the probability $P(m_{t+1} \mid m_t)$ for transitioning between both modes.
%In our approach those modes are the dominant graph-based filter and the supporting simple filter.
The dominant filter's probability to draw particles from its own posterior is given by the positive exponential distribution
%
@@ -135,11 +135,11 @@ If the Kullback-Leibler divergence $D_{\text{KL}}$ increases to a certain point,
$\lambda$ depends highly on the respective filter models and is therefore chosen heuristically.
In most cases $\lambda$ tends to be somewhere between $0.01$ and $0.10$.
However, \eqref{equ:KLD} only works reliable if the measurement noise is within reasonable limits, because the support filter using the simple transition depends solely on them.
However, \eqref{equ:KLD} only works reliably if the measurement noise is within reasonable limits, because the support filter using the simple transition depends solely on them.
Especially \docWIFI{} serves as the main source for estimation and thus attenuated or bad \docWIFI{} readings are causing bad estimation results for the supporting filter.
This further leads to a growing $D_{\text{KL}}$, even if the dominant filter provides a good position estimation.
In such scenarios a lower diversity and higher focus of the particle set, as given by the dominant filter, is required.
We achieves this by introducing a \docWIFI{} quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa.
We achieve this by introducing a \docWIFI{} quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa.
The quality factor is defined by
%
\begin{equation}
@@ -182,7 +182,7 @@ Considering the measures \eqref{equ:KLD} and \eqref{eq:wifiQuality} presented ab
This matrix is the centrepiece of our approach.
It is responsible for controlling and satisfying the need of diversity and the need of focus for the whole localisation approach.
How $\Pi_t$ works is straightforward.
If the dominant graph-based filter suffers from sample impoverishment (get stuck or lose track), the probability in $[\Pi_t]_{12} = (1 - f(D_{\text{KL}}))$ increases with diverging support filter.
If the dominant graph-based filter suffers from sample impoverishment (get stuck or lost track), the probability in $[\Pi_t]_{12} = (1 - f(D_{\text{KL}}))$ increases with diverging support filter.
Consequently, the number of particles, the dominant filter draws from the supporting filter, also increases by $[\Pi_t]_{12} \cdot 100\%$.
Similar behaviour applies to the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$.
If the quality is low, the supporting filter regains focus by obtaining particles from the dominant's posterior.

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tex/chapters/relatedwork.tex
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@@ -20,7 +20,7 @@ However, in practice, sample impoverishment is also a problem of environmental r
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.
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 measurements into the importance distribution, dealing with the sample impoverishment.
Other PDO methods are presented in \cite{Li2014}.
@@ -39,11 +39,11 @@ Thereby, they are able to provide a robust and stable position estimation with h
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 sample additional particles from all available particle sets and not just from its own.
This allows merging between different particle filters by providing a possibility for each filter to sample additional 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's 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.
Warum? Weil die meinsten loca systeme auf particle filtern basieren und deswegen bietet es sich an. es erlaubt bereits vorhandene methoden die auf die jeweils einzeln auf die probleme eingehen zu kombinieren und so ein hybrid zu schaffen.
%Warum? Weil die meinsten loca systeme auf particle filtern basieren und deswegen bietet es sich an. es erlaubt bereits vorhandene methoden die auf die jeweils einzeln auf die probleme eingehen zu kombinieren und so ein hybrid zu schaffen.
%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.

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tex/chapters/system.tex
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@@ -35,7 +35,7 @@ All relevant sensor measurements are incorporated into the observation $\mObsVec
\mObsVec = (\mObsHeading, \mObsSteps, \mRssiVec_\text{wifi}, \mObsPressure) \enspace,
\end{equation}
%
Here, $\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number of steps detected for the pedestrian.
Here, $\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number of steps detected for the pedestrian between two consecutive timesteps.
Further, $\mRssiVec_\text{wifi}$ contains the measurements of all nearby \docAP{}s (\docAPshort{}).
Finally, $\mObsPressure$ is the relative barometric pressure with respect to a fixed reference.
@@ -57,13 +57,13 @@ We assume a statistical independence of all sensors. The probability density of
The smartphone's barometer is used to infer the likeliness of the current $z$-location in $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$ and thus enables to walk stairs or to drive elevators.
Here, every predicted relative pressure $\mState_t^{\mStatePressure}$ is compared with the observed one $\mObs_t^{\mObsPressure}$ using a normal distribution.
The state's relative pressure prediction $\mStatePressure$ is estimated within each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ by tracking the pressure between every height-change on the $z$-axis.
The state's relative pressure prediction $\mStatePressure$ is estimated within each transition from $\mStateVec_{t-1}$ to $\mStateVec_t$ by tracking the pressure between every height-change on the $z$-axis \cite{Fetzer2016OMC}.
Absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}.
We are using the wall attenuation factor model based on Friis transmission equation to predict an \docAP{}'s (\docAPshort{}) signal strength at an arbitrary position $\fPos{\mStateVec_t} = (x, y,z)^T$.
This predicted signal strength is then matched against the current observation $\mObs_t^{\mRssiVec_\text{wifi}}$ received from this particular \docAPshort{}, providing a likelihood of the pedestrian being at $\fPos{\mStateVec_t}$.
The positions of detected \docAPshort{}'s are known beforehand.
The main advantage of this approach is that no time-consuming initial calibration phase and updates in case of infrastructural changes are needed.
The main advantage of this approach is that no time-consuming initial calibration phase and updates in case of infrastructural changes are needed \cite{Ebner-17}.
%Barometer
%Due to noisy sensors, we calculate the average $\overline{\mObsPressure}$ of several sensor readings and the sensor's uncertainty $\sigma_\text{baro}$.

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tex/egbib.bib
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@@ -2873,4 +2873,10 @@ year = {2003}
issn = {}
}
@article{Ebner-17,
author={F. Ebner and T. Fetzer and F. Deinzer and M. Grzegorzek},
journal={{IMWUT}},
title={{On Wi-Fi Optimizations for Smartphone-based Indoor Localization}},
year={2017, submitted},
}