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tex/chapters/work.tex
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@@ -3,7 +3,7 @@
The \docWIFI{} sensor infers the pedestrian's current location based on a comparison between live observations
(the smartphone continuously scans for nearby \docAP{}s) and fingerprints or
signal strength predictions for well known locations. The location that fits the observations best,
signal strength predictions for well-known locations. The location that fits the observations best,
is the pedestrian's current location. Assuming statistical independence of all transmitters
installed within a building, this matching probability can be written as
@@ -63,11 +63,11 @@
like one floor, solely divided by drywalls of the same thickness and material.
%
The log normal shadowing-, or wall-attenuation-factor model \cite{PathLossPredictionModelsForIndoor}
is a slight modification, to adapt the log distance model to indoor use cases.
is a slight modification, to adapt the log distance model to indoor use-cases.
It introduces an additional parameter, that considers obstacles between (line-of-sight) the \docAPshort{} and the
location in question by attenuating the signal with a constant value.
%
Depending on the use case, this value describes the number and type of walls, ceilings, floors etc. between both positions.
Depending on the use-case, this value describes the number and type of walls, ceilings, floors etc. between both positions.
For obstacles, this requires an intersection-test of each obstacle with the line-of-sight, which is costly
for larger buildings. For real-time use on a smartphone, a (discretized) model pre-computation might thus be necessary
\cite{competition2016}.
@@ -76,7 +76,7 @@
Throughout this work, we thus use a tradeoff between both models, where walls are ignored and only floors/ceilings are considered.
Assuming buildings with even floor levels, the number of floors/ceilings between two position can be determined
without costly intersection checks and thus allows for real-time use cases running on smartphones.
without costly intersection checks and thus allows for real-time use-cases running on smartphones.
\begin{equation}
\mRssi = \mTXP{} + 10 \mPLE{} + \log_{10} \frac{d}{d_0} + \numFloors{} \mWAF{} + \mGaussNoise{}
@@ -92,14 +92,14 @@
\subsection {Model Parameters}
As previously mentioned, for the prediction model to work, one needs to know the location $\mPosAPVec_i$ for every
As previously mentioned, for the prediction model to work, it is necessary to know the location $\mPosAPVec_i$ for every
permanently installed \docAP{} $i$ within the building to derive the distance $d$, plus its environmental parameters
\mTXP{}, \mPLE{} and \mWAF{}.
While it is possible to use empiric values for those environmental parameters \cite{Ebner-15}, the positions are mandatory.
For many buildings, there should be floorplans that include the locations of all installed transmitters.
If so, a model setup takes only several minutes to (vaguely) position the \docAPshort{}s within a virtual
map and assigning them some fixed, empirically chosen parameters for \mTXP{}, \mPLE{} and \mWAF{}.
map and assign some fixed, empirically chosen parameters for \mTXP{}, \mPLE{} and \mWAF{}.
Depending on the building's architecture this might already provide enough accuracy for some use-cases,
where a vague location information is sufficient.
@@ -119,7 +119,7 @@
For systems that demand a higher accuracy, one can choose a compromise between fingerprinting and
aforementioned pure empiric model parameters by optimizing those parameters
based on a few reference measurements throughout the building.
Obviously, the more parameters are staged for optimization ($\mPosAPVec{}, \mTXP{}, \mPLE{}, \mWAF{}$) the more
The more parameters are staged for optimization ($\mPosAPVec{}, \mTXP{}, \mPLE{}, \mWAF{}$) the more
reference measurements are necessary to provide a stable result.
Depending on the desired accuracy, setup time and whether the transmitter positions are known or unknown,
several optimization strategies arise, where not all 6 parameters are optimized, but only some of them.
@@ -142,10 +142,10 @@
Just optimizing \mTXP{} and \mPLE{} with constant \mWAF{} and known transmitter position
usually means optimizing a convex function, as can be seen in \reffig{fig:wifiOptFuncTXPEXP}.
For such error functions, algorithms like gradient descent and simplex \cite{gradientDescent, downhillSimplex1, downhillSimplex2}
are well suited and will provide the global minima.
are well suited and will provide the global minimum.
However, optimizing an unknown transmitter position usually means optimizing a non-convex, discontinuous
function, especially when the $z$-coordinate, that influences the number of attenuating floors / ceilings,
function, especially when the $z$-coordinate, that influences the number of attenuating floors/ceilings,
is involved.
While the latter can be mitigated by introducing a continuous function for the
number $n$, e.g. a sigmoid, the function is not necessarily convex.
@@ -188,18 +188,19 @@
% \label{fig:wifiOptFuncPosYZ}
%\end{figure}
Such functions demand for optimization algorithms, that are able to deal with non-convex functions,
like genetic approaches. However, initial tests indicated that while being superior to simplex
and similar algorithms, the results were not satisfactorily and the optimization often did not converge.
Such functions demand for optimization algorithms, that are able to deal with non-convex functions.
We thus used a genetic algorithm to perform this task.
However, initial tests indicated that while being superior to simplex
and similar algorithms, the results were not yet satisfying as the optimization often did not converge.
As the Range of the six to-be-optimized parameters is known ($\mPosAPVec{}$ within the building,
\mTXP{}, \mPLE{}, \mWAF{} within a sane interval around empiric values), we used some modifications.
The algorithms initial population is uniformly sampled from the known range. During each iteration
As the range of the six to-be-optimized parameters is known ($\mPosAPVec{}$ within the building,
\mTXP{}, \mPLE{}, \mWAF{} within a sane interval around empiric values), we slightly modified the
genetic algorithm: The initial population is now uniformly sampled from the known range. During each iteration,
the best \SI{25}{\percent} of the population are kept and the remaining entries are
re-created by modifying the best entries with uniform random values within
$\pm$\SI{10}{\percent} of the known range. To stabilize the result, the allowed modification range
$\pm$\SI{10}{\percent} of the known range. The result is stabilized by narrowing the allowed modification range
%(starting at \SI{10}{\percent})
is reduced over time, often referred to as {\em cooling} \cite{Kirkpatrick83optimizationby}.
over time, often referred to as {\em cooling} \cite{Kirkpatrick83optimizationby}.
\subsection{Modified Signal Strength Model}
@@ -215,30 +216,39 @@
%the inferred location was more erroneous than before.
As the used model tradeoff does not consider walls, it is expected to provide erroneous values
for regions that are heavily shrouded, e.g. by steel-enforced concrete or metallised glass.
for regions that are heavily shrouded, e.g. by steel-enforced concrete or metallized glass.
Instead of using only one optimized model per \docAP{}, we use several instances with different
parameters that are limited to some region within the building. By reducing the area
that the model has to describe, we expect the limited number of model parameters to
provide better (local) results.
{\em \optPerFloor{}} will use one model for each story, that is optimized using
only the fingerprints that belong to the corresponding floor. During evaluation,
the $z$-value from $\mPosVec{}$ in \refeq{eq:wifiProb} is used to select the correct model
for this location's signal strength estimation.
\begin{itemize}
\item{
{\em \optPerFloor{}} will use one model for each story, that is optimized using
only the fingerprints that belong to the corresponding floor. During evaluation,
the $z$-value from $\mPosVec{}$ in \refeq{eq:wifiProb} is used to select the correct model
for this location's signal strength estimation.
}
\item{
{\em \optPerRegion{}} works similar, except that each model is limited to a predefined,
axis-aligned bounding box. This approach allows for an even more refined distinction between
several areas like in- and outdoor regions or locations that are expected to highly differ
from their surroundings.
}
{\em \optPerRegion{}} works similar, except that each model is limited to a predefined,
axis-aligned bounding box. This approach allows for an even more refined distinction between
several areas like in- and outdoor-regions or locations that are expected to highly differ
from their surroundings.
\end{itemize}
Especially the second model imposes a potential issue we need to address:
If an \docAPshort{} is seen only once or twice within such a bounding box, it is impossible
to optimize its parameters, just like a line can not be defined using one single point.
to optimize its parameters, just like a line cannot be defined using one single point.
However, due to \refeq{eq:wifiProb}, we need each model to provide the same number of
\docAP{}s. Otherwise regions with less known transmitters would automatically be more
likely than others. We therefore use fixed model parameters,
\mTXP = \SI{-100}{\decibel{}m}, \mPLE = 0 and \mWAF = \SI{0}{\decibel}. This yields
$\mTXP = \SI{-100}{\decibel{}m}$, $\mPLE = 0$ and $\mWAF = \SI{0}{\decibel}$ for every
transmitter with less than three reference measurements per region. This yields
a model that always returns \SI{-100}{\decibel{}m}, independent of the distance from the transmitter.
While this most probably is not the correct reading for all locations, it works
for most cases, as usual smartphones are unable to measure signals below this threshold.
@@ -250,10 +260,10 @@
\label{sec:wifiQuality}
Evaluations within previous works showed, that there are many situations where the overall \docWIFI{} location estimation
is highly erroneous. Either when the signal strength prediction model does not match real world
is highly erroneous. Either when the signal strength prediction model does not match real-world
conditions or the received measurements are ambiguous and there is more than one location
within the building that matches those readings. Both cases can occur e.g. in areas surrounded by
concrete walls, where the model does not match the real world conditions as those walls are not considered,
concrete walls, where the model does not match the real-world conditions as those walls are not considered,
and the smartphone barely receives \docAPshort{}s due to the high attenuation.
If such a sensor error occurs only for a short time period, the recursive density estimation from
@@ -267,32 +277,34 @@
temporarily disabling \docWIFI{}'s contribution within the evaluation \refeq{eq:evalDensity}
if the quality is insufficient.
In \refeq{eq:wifiQuality} we use the average signal strength of all \docAP{}s seen within one measurement
and scale this value to match a region of $[0, 1]$ depending on an upper- and lower bound.
In \refeq{eq:wifiQuality} we use the average signal strength $\bar\mRssi$ among all \docAP{}s seen within one measurement
$\mRssiVec$ and scale this value to match a region of $[0, 1]$ depending on an upper and lower bound.
If the returned quality is below a certain threshold, \docWIFI{} is ignored within the evaluation.
\begin{equation}
\newcommand{\leMin}{l_\text{min}}
\newcommand{\leMax}{l_\text{max}}
\text{quality}(\mRssiVec) =
\max(0,
\min(
\max \left(0,
\min \left(
\frac{
\bar\mRssi - \leMin
}{
\leMax - \leMin
},
1
)
)
\right)
\right)
,\enskip
\bar\mRssi = \frac{1}{n} \sum_{i = 1}^{n} \mRssi_i
\label{eq:wifiQuality}
\end{equation}
\subsection {VAP grouping}
\subsection {Virtual \docAP{}s}
\label{sec:vap}
Assuming normal conditions, the received signal strength at one location will also (strongly) vary over time
due to environmental conditions like temperature, humidity, open / closed doors and RF interference.
due to environmental conditions like temperature, humidity, open/closed doors and RF interference.
Fast variations can be addressed by averaging several consecutive measurements at the expense
of a delay in time.
To prevent this delay we use the fact, that many buildings use so called virtual access points