850 lines
51 KiB
TeX
Executable File
850 lines
51 KiB
TeX
Executable File
\section{Experiments}
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% intro
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Within our experiments we will first have a look at model optimizations to reduce the error (in \decibel)
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between model predictions and real-world conditions in section \ref{sec:evalModelOpt}.
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%
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Hereafter, in section \ref{sec:evalWifiMeter} we examine the resulting accuracy (in \meter)
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when using the optimized models for localization solely by the \docWIFI{} component without additional sensors, assumptions or filtering.
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%
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Finally, all models are evaluated in the context of our indoor localization system \refeq{eq:recursiveDensity},
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using additional smartphone sensors and the building's floorplan in section \ref{sec:evalFiltered}.
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All optimizations and evaluations took place within two adjacent buildings (4 and 2 floors, respectively)
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and two connected outdoor regions (entrance and inner courtyard),
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\SI{110}{\meter} x \SI{60}{\meter} in size.
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Within all \docWIFI{} observations, we only consider the \docAP{}s that are permanently installed
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and can be identified by their well-known MAC address.
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Temporal and movable transmitters like smart TVs or smartphone hotspots are ignored as they might cause estimation errors.
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The \docWIFI{} quality factor from section \ref{sec:wifiQuality} was configured with
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a lower bound of \SI{-85}{\decibel m}, an upper bound of \SI{-70}{\decibel m} and a threshold of $0.25$.
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%
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Unfortunately, due to legal reasons, our institution does not allow depicting the actual location
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of installed transmitters within the following figures.
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%modell direkt fuer den gelaufenen pfad optimiert (also wirklich jede wifi messung direkt auf den ground-truth)
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%der fehler wird zwar kleiner, ist aber immernoch deutlich spürbar. das spricht dafür, dass das modell einfach nicht
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%gut geeignet ist.
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%optimierungs input: alle 4 walks samt ground-truth
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%dann kommt fuer die 4 typen [fixed, all same par, each par, each par pos]
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%log probability 50 75, meter 50, 75
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% -------------------------------- optimization -------------------------------- %
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\subsection{Model optimization}
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\label{sec:evalModelOpt}
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As the signal strength prediction model is the core of the absolute positioning component
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described in section \ref{sec:system}, we start with the model parameter optimization (see section \ref{sec:optimization}).
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\mTXP{}, \mPLE{} and \mWAF{} will be estimated based on some reference measurements using
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various optimization strategies. The results of those optimization strategies are compared
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with each other and an empiric parameter choice:
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\mTXP{} = \SI{-40}{\decibel{}m} @ \SI{1}{\meter}
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(defined by the usual \docAPshort{} transmit power for Europe), a path loss exponent $\mPLE{} = 2.5$ and
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$\mWAF{} = \SI{-8}{\decibel}$ per floor/ceiling (made of reinforced concrete)
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\cite{PathLossPredictionModelsForIndoor, ElectromagneticPropagation, ANewPathLossPrediction}.
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\reffig{fig:referenceMeasurements} depicts the location of the used 121 reference measurements.
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Each location was scanned 30 times ($\approx$ \SI{25}{\second} scan time),
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non-permanent \docAP{}s were removed, the values were grouped per physical transmitter (see section \ref{sec:vap})
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and aggregated to form the average signal strength per transmitter.
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\begin{figure}
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\begin{subfigure}[t!]{0.48\textwidth}
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\input{gfx2/all_fingerprints.tex}
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\caption{
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The size of each square denotes the number of permanently installed \docAPshort{}s
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that were visible while scanning, and ranges between 2 and 22 with an average of 9.
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}
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\label{fig:referenceMeasurements}
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\end{subfigure}
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\enskip\enskip
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\begin{subfigure}[t!]{0.48\textwidth}
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\input{gfx2/model-bboxes.tex}
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\caption{
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Each distinct floor-color denotes a region (6 indoors, 1 outdoors) for {\em \optPerRegion{}}.
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Often more than one bounding box is needed to describe the region's shape.
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}
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\label{fig:modelBBoxes}
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\end{subfigure}
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\caption{Locations of the 121 reference measurements (left) and bounding-boxes used for {\em \optPerRegion{}} (right).}
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\end{figure}
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% used reference measurements
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%\begin{figure}
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% {
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% \centering
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% \input{gfx/all_fingerprints.tex}
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% }
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% \caption{
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% Locations of the 121 reference measurements.
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% The size of each square denotes the number of permanently installed \docAPshort{}s
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% that are visible at this location,
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% and ranges between 2 and 22 with an average of 9.
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% }
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% \label{fig:referenceMeasurements}
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%\end{figure}
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% visible APs:
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% cnt(121) min(2.000000) max(22.000000) range(20.000000) med(8.000000) avg(9.322314) stdDev(4.386709)
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\begin{figure}
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\centering
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\input{gfx/compare-wifi-in-out.tex}
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\caption{
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Measurable signal strengths of a testing \docAPshort{} (black dot).
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While the signal diminishes slowly along the corridor (wide rectangle)
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the metallized windows (dashed outline) attenuate the signal by over \SI{30}{\decibel} (small rectangle).
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}
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\label{fig:wifiIndoorOutdoor}
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\end{figure}
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\reffig{fig:wifiIndoorOutdoor} depicts the to-be-expected issues by examining the signal strength
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values of the reference measurements for one \docAP{}.
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Even though the transmitter is only \SI{5}{\meter} away from the reference
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measurement (small box), the metallized windows attenuate the signal as much as \SI{50}{\meter}
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of corridor (wide rectangle). The model described in section \ref{sec:sigStrengthModel} will not be able
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to match such situations due to the lack of obstacle information.
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%
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We will thus look at various optimization strategies and the error between
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the resulting estimation model and our reference measurements:
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\begin{itemize}
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\item{
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{\em\noOptEmpiric{}} uses the same three empiric parameters \mTXP{}, \mPLE{}, \mWAF{} for each \docAPshort{} in combination
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with its position, which is well known from the floorplan.
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}
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\item{
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{\em\optParamsAllAP{}} is the same as above, except that the three parameters are optimized
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using the reference measurements (convex function). All transmitters share the same three parameters.
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}
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\item{
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{\em\optParamsEachAP{}} optimizes the three parameters per \docAP{} instead of using the same
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parameters for all. This still denotes a convex function per transmitter.
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}
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\item{
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{\em\optParamsPosEachAP{}} does not need any prior knowledge and will optimize all six parameters
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(3D position, \mTXP, \mPLE, \mWAF) based on the reference measurements (non-convex function).
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}
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\item{
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{\em\optPerFloor{}} and {\em\optPerRegion{}} are just like {\em \optParamsPosEachAP{}} except that
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there are several sub-models, each of which is optimized for one floor/region instead of the whole building.
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The chosen bounding boxes and resulting sub-models are depicted in \reffig{fig:modelBBoxes}.
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}
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\end{itemize}
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\reffig{fig:wifiModelError} shows the optimization results for all strategies which are as expected:
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The estimation error is indirectly proportional to the number of optimized parameters.
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However, while median- and average-errors are fine, maximal errors sometimes are relatively high.
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As depicted in \reffig{fig:wifiModelErrorMax}, even with {\em \optPerRegion{}}, some locations simply do not fit the model,
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and thus lead to high (local) errors.
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%
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Looking at the optimization results for \mTXP{}, \mPLE{} and \mWAF{} supports
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this finding. While the median for those values based on all optimized transmitters is totally sane
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(\SI{-42}{\decibel{}m}, \SI{2.4}, \SI{-6.0}{\decibel}), the minimum and maximum values are far beyond the physically possible range.
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The same holds for the estimated transmitter position when using {\em \optParamsPosEachAP{}}: The median
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distance between estimated and real position is $\sim$\SI{8}{\meter} and the maximum $\sim$\SI{27}{\meter}.
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For \SI{68}{\percent} of all installed transmitters, the estimated floor-number matched the real location.
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\newcommand{\tablefont}{\scriptsize}
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\begin{figure}
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\centering
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\begin{subfigure}{0.52\textwidth}
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\input{gfx2/wifi_model_error_0_95.tex}
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\end{subfigure}%
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\begin{subfigure}{0.47\textwidth}
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\centering
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\begin{tabular}{|l|c|c|c|c|}
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\hline
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& \tablefont 25 \% & \tablefont median & \tablefont 75 \% & \tablefont avg \\\hline
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\tablefont\noOptEmpiric{} & \tablefont\SI{2.5}{\decibel} & \tablefont\SI{5.6}{\decibel} & \tablefont\SI{9.3}{\decibel} & \tablefont\SI{6.5}{\decibel} \\\hline
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\tablefont\optParamsAllAP{} & \tablefont\SI{2.0}{\decibel} & \tablefont\SI{4.3}{\decibel} & \tablefont\SI{7.5}{\decibel} & \tablefont\SI{5.4}{\decibel} \\\hline
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\tablefont\optParamsEachAP{} & \tablefont\SI{1.6}{\decibel} & \tablefont\SI{3.3}{\decibel} & \tablefont\SI{6.2}{\decibel} & \tablefont\SI{4.4}{\decibel} \\\hline
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\tablefont\optParamsPosEachAP{} & \tablefont\SI{1.5}{\decibel} & \tablefont\SI{3.0}{\decibel} & \tablefont\SI{5.5}{\decibel} & \tablefont\SI{3.8}{\decibel} \\\hline
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\tablefont\optPerFloor{} & \tablefont\SI{0.7}{\decibel} & \tablefont\SI{1.6}{\decibel} & \tablefont\SI{3.3}{\decibel} & \tablefont\SI{2.6}{\decibel} \\\hline
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\tablefont\optPerRegion{} & \tablefont\SI{0.6}{\decibel} & \tablefont\SI{1.4}{\decibel} & \tablefont\SI{3.1}{\decibel} & \tablefont\SI{2.4}{\decibel} \\\hline
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\end{tabular}
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\vspace{8mm}
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\end{subfigure}
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\caption{
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Cumulative error distribution for all optimization strategies. The error results from the (absolute) difference
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between model predictions and real-world values for each reference measurement.
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The higher the number of variable parameters, the better the model resembles real-world conditions.
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}
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\label{fig:wifiModelError}
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\end{figure}
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\begin{figure}
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\centering
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\begin{subfigure}{0.32\textwidth}
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\centering
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\input{gfx2/wifiMaxErrorNN_opt0.tex}
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\caption{\em \noOptEmpiric{}}
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\label{fig:wifiModelErrorMaxA}
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\end{subfigure}
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\begin{subfigure}{0.32\textwidth}
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\centering
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\input{gfx2/wifiMaxErrorNN_opt3.tex}
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\caption{\em \optParamsPosEachAP{}}
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\label{fig:wifiModelErrorMaxB}
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\end{subfigure}
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\begin{subfigure}{0.32\textwidth}
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\centering
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\input{gfx2/wifiMaxErrorNN_opt5.tex}
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\caption{\em \optPerRegion{}}
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\label{fig:wifiModelErrorMaxC}
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\end{subfigure}
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\caption{
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Local maximum error between model estimation and reference measurements among all known transmitters.
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While optimization is able to reduce such errors, some local maxima remain due to overadaption.
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}
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\label{fig:wifiModelErrorMax}
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\end{figure}
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%\begin{figure}
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% \input{gfx/wifi_model_error_0_95.tex}
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% %\input{gfx/wifi_model_error_95_100.tex}
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% \caption{
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% Comparison between different optimization strategies by examining the error (in \decibel) at each reference measurement.
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% The higher the number of variable parameters, the better the model resembles real world conditions.
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% }
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% \label{fig:wifiModelError}
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%\end{figure}
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% statds:
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%TXP: cnt(34) min(-67.698959) max(4.299183) range(71.998146) med(-41.961170) avg(-41.659286) stdDev(17.742294)
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%EXP: cnt(34) min(0.932817) max(4.699000) range(3.766183) med(2.380410) avg(2.546959) stdDev(1.074687)
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%WAF: cnt(34) min(-27.764957) max(5.217187) range(32.982143) med(-5.921916) avg(-7.579522) stdDev(5.840527)
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%Pos: cnt(34) min(3.032438) max(26.767128) range(23.734690) med(7.342710) avg(8.571227) stdDev(4.801449)
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While {\em \optPerRegion{}} is able to overcome the indoor vs. outdoor issues depicted in
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\reffig{fig:wifiIndoorOutdoor}, by using a separate bounding box just for the outdoor area,
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it obviously requires a profound prior knowledge to correctly select the individual regions for the sub-model.
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%Such issues can only be fixed using more appropriate models that consider walls and other obstacles.
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% das ist wohl zu viel
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%\begin{figure}
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% \centering
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% \input{gfx/wifiOptApPosDifference.tex}
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% \caption{zu viel, oder?}
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%\end{figure}
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% -------------------------------- number of fingerprints -------------------------------- %
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\hspace{3mm} % HACK...
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As we try to minimize the system's setup time as much as possible, we need to determine
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the amount of necessary reference measurements for the optimization to produce robust model parameters.
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Depending on the chosen model, and thus the number of to-be-optimized parameters, more measurements will be required.
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While there was almost no difference between using 121 or 30 reference measurements for
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{\em \optParamsAllAP{}} and {\em \optParamsEachAP{}}
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(average error changed from \SIrange{5.3}{5.4}{\decibel} and \SIrange{4.5}{5.0}{\decibel}, respectively),
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{\em \optPerRegion{}} is highly affected
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(average error changed from \SIrange{2.0}{6.2}{\decibel}), as it needs at least a certain number of measurements within each
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region for the optimization to converge.
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\begin{figure}
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\centering
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\begin{subfigure}{0.49\textwidth}
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\input{gfx2/wifi_model_error_num_fingerprints_method_5_0_90.tex}
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\end{subfigure}
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\begin{subfigure}{0.49\textwidth}
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\input{gfx2/wifi_model_error_num_fingerprints_method_5_90_100.tex}
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\end{subfigure}
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\caption{
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Impact of reducing the number of reference measurements for optimizing {\em \optPerRegion{}}.
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The cumulative error distribution is determined by comparing its signal strength prediction against all 121 measurements.
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While using only \SI{50}{\percent} of the 121 scans has barely an impact on the error,
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30 measurements (\SI{25}{\percent}) are clearly insufficient.
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}
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\label{fig:wifiNumFingerprints}
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\end{figure}
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%\begin{figure}[b]
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% \input{gfx/wifi_model_error_num_fingerprints_method_5_0_90.tex}
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% \input{gfx/wifi_model_error_num_fingerprints_method_5_90_100.tex}
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% \caption{%
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% Impact of reducing the number of reference measurements during optimization on {\em \optPerRegion{}}.
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% The model's cumulative error distribution is determined by comparing the its signal strength prediction against all 121 measurements.
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% While using only \SI{50}{\percent} of the 121 scans has barely an impact on the error,
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% 30 measurements (\SI{25}{\percent}) are clearly insufficient.
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% }%
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% \label{fig:wifiNumFingerprints}%
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%\end{figure}
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\reffig{fig:wifiNumFingerprints} depicts the impact of reducing the number of reference measurements
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during the optimization process for the {\em \optPerRegion{}} strategy.
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The error is determined by using the (absolute) difference between expected signal strength and
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the optimized model's corresponding prediction for all of the 121 reference measurements.
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%
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Considering only 60 of the 121 scans (\SI{50}{\percent}) yields a slightly increasing model error but still provides good results.
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While using only \SI{25}{\percent} of the reference measurements increases the error rapidly,
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for \SI{75}{\percent} of the 121 considered error-values, the estimation is still better than using just empiric values without optimization.
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%The extremely large outlier depicted in the right half of figure \ref{fig:wifiNumFingerprints} (red line) relates to one
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%sub-model with only one assigned reference measurement, where the optimized result is unable to predict values
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%for the rest of the sub-model's region. \todo{versteht man das?}
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Additionally we examined the impact of skipping reference measurements for difficult locations,
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like staircases surrounded by steel-enforced concrete. While this slightly decreases the
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estimation error for all other positions (hallway, etc.) as expected, the error within the skipped locations is dramatically
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increasing (see right half of \reffig{fig:wifiNumFingerprints}). It is thus highly recommended
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to also perform reference measurements for locations, that are expected to strongly deviate (signal strength)
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from their surroundings.
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%leaving out fingerprints for model 1
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% 25%: cnt(1128) min(0.007439) max(27.804710) range(27.797272) med(4.404236) avg(5.449720) stdDev(4.470373)
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% 50%: cnt(1128) min(0.006027) max(27.732193) range(27.726166) med(4.367859) avg(5.437861) stdDev(4.475426)
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% 100%: cnt(1128) min(0.000282) max(27.705376) range(27.705093) med(4.272881) avg(5.411202) stdDev(4.493495)
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% noStair%: cnt(1128) min(0.000801) max(27.209221) range(27.208420) med(4.333328) avg(5.459918) stdDev(4.459484)
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%leaving out fingerprints for model 2
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% 25%: cnt(1128) min(0.000320) max(29.752560) range(29.752239) med(3.837357) avg(5.027578) stdDev(4.617191)
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% 50%: cnt(1128) min(0.015305) max(34.152130) range(34.136826) med(3.627090) avg(4.635868) stdDev(4.135866)
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% 100%: cnt(1128) min(0.000488) max(25.687740) range(25.687252) med(3.319756) avg(4.441193) stdDev(3.912525)
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% noStair%: cnt(1128) min(0.017693) max(25.687740) range(25.670048) med(3.304321) avg(4.507620) stdDev(3.957071)
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%leaving out fingerprints for model 3
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% 25%: cnt(1128) min(0.003242) max(39.470978) range(39.467735) med(3.371758) avg(4.977330) stdDev(5.213937)
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% 50%: cnt(1128) min(0.002808) max(30.113415) range(30.110607) med(2.941238) avg(4.015042) stdDev(3.696969)
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% 100%: cnt(1128) min(0.000557) max(16.813850) range(16.813293) med(3.056915) avg(3.813013) stdDev(3.062580)
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% noStair%: cnt(1128) min(0.002518) max(30.370636) range(30.368118) med(3.016884) avg(3.983101) stdDev(3.508327)
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%leaving out fingerprints for model 4
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% 25%: cnt(1128) min(0.000000) max(62.233345) range(62.233345) med(2.502831) avg(5.432897) stdDev(8.664582)
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% 50%: cnt(1128) min(0.000000) max(56.843803) range(56.843803) med(1.543137) avg(2.937506) stdDev(4.417061)
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% 100%: cnt(1128) min(0.000046) max(33.175812) range(33.175766) med(1.537933) avg(2.441976) stdDev(2.793499)
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% noStair%: cnt(1128) min(0.000000) max(62.233345) range(62.233345) med(1.493668) avg(2.744918) stdDev(4.428092)
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%leaving out fingerprints for model 5
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% 25%: cnt(1128) min(0.000000) max(62.620842) range(62.620842) med(2.140709) avg(6.257105) stdDev(11.638572)
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% 50%: cnt(1128) min(0.000000) max(57.371948) range(57.371948) med(1.357452) avg(2.982217) stdDev(5.877471)
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% 100%: cnt(1128) min(0.000000) max(14.837151) range(14.837151) med(1.251358) avg(1.989277) stdDev(2.189072)
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% noStair%: cnt(1128) min(0.000000) max(62.233345) range(62.233345) med(1.143669) avg(2.316189) stdDev(4.164822)
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% -------------------------------- wifi walk error -------------------------------- %
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\subsection{\docWIFI{} location estimation error}
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\label{sec:evalWifiMeter}
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Having optimized several signal strength prediction models, we can now examine the resulting localization
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accuracy (in \meter) for each. For now, this will just cover the \docWIFI{} component itself.
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The impact of fusing additional sensors and a adding prior knowledge provided by a transition model will be evaluated later.
|
|
|
|
|
|
%Using the optimized model setups and the measurements $\mRssiVec$ determined by scanning for nearby \docAPshort{}s,
|
|
%we can directly perform a location estimation by rewriting \refeq{eq:wifiProb}:
|
|
%For each of the discussed optimization strategies we can now determine the resulting localization accuracy.
|
|
The position $\mPosVec{}$ within the building that best fits some \docWIFI{} signal strength measurements $\mRssiVec$ received by the smartphone
|
|
is the one that maximizes $p(\mPosVec \mid \mRssiVec)$.
|
|
Omitting prior knowledge and normalization, this can be rewritten as:
|
|
|
|
\begin{equation}
|
|
p(\mPosVec \mid \mRssiVec) =
|
|
\frac{p(\mRssiVec \mid \mPosVec) p(\mPosVec)}{p(\mRssiVec)}
|
|
\propto p(\mRssiVec \mid \mPosVec),\enskip
|
|
p(\mPosVec) = p(\mRssiVec) = \text{const}
|
|
.
|
|
\label{eq:wifiBayes}
|
|
\end{equation}
|
|
|
|
Following \refeq{eq:wifiObs} and \refeq{eq:wifiProb}, the best
|
|
location $\mPosVec^*$ given $\mRssiVec$ is the one that satisfies
|
|
|
|
\begin{equation}
|
|
\mPosVec^* = \argmax_{\mPosVec}
|
|
\prod_{\mRssi_{i} \in \mRssiVec{}}
|
|
\mathcal{N}(\mRssi_i \mid \mu_{i,\mPosVec}, \sigma^2)
|
|
\enskip.
|
|
\label{eq:bestWiFiPos}
|
|
\end{equation}
|
|
|
|
In \refeq{eq:bestWiFiPos} $\mu_{i,\mPosVec}$ is the signal strength for \docAP{} $i$,
|
|
installed at location $\mPosVec$, returned from the to-be-examined prediction model.
|
|
For all comparisons, we use a constant uncertainty of $\sigma = \SI{8}{\decibel}$,
|
|
which is an empirical choice based on prior experiments.
|
|
|
|
The quality of the estimated location is determined by using the Euclidean distance between estimation
|
|
$\mPosVec^*$ and the pedestrian's ground truth position at the time the scan $\mRssiVec$
|
|
has been received.
|
|
|
|
|
|
|
|
We therefore conducted 13 walks on 5 different paths within our building,
|
|
each of which is defined by connecting marker points at well known positions
|
|
(see \reffig{fig:allWalks}).
|
|
Whenever the pedestrian reached such a marker, the current time was recorded.
|
|
Due to constant walking speeds, the ground-truth for any timestamp can be approximated
|
|
using linear interpolation between adjacent markers.
|
|
|
|
% walked paths
|
|
\begin{figure}
|
|
\centering
|
|
\input{gfx2/all_walks.tex}
|
|
\caption{
|
|
Overview of all conducted paths, each starting at the denoted rectangle.
|
|
Outdoor areas are marked in green.
|
|
The length of the paths is as follows:
|
|
path 1: \SI{207}{\meter}, path 2: \SI{138}{\meter}, path 3: \SI{86}{\meter}, path 4: \SI{140}{\meter},
|
|
and path 5: \SI{97}{\meter}.
|
|
}
|
|
\label{fig:allWalks}
|
|
\end{figure}
|
|
|
|
\begin{figure}
|
|
\centering
|
|
% error gfx
|
|
\begin{subfigure}{0.52\textwidth}
|
|
\centering
|
|
\input{gfx2/modelPerformance_meter.tex}
|
|
\end{subfigure}
|
|
% table
|
|
%5.98767 9.23025 14.4272 11.9649
|
|
%6.53764 9.01424 12.8797 12.0121
|
|
%6.85665 9.82203 13.8528 12.9988
|
|
%5.35629 8.5921 14.8037 11.9996
|
|
%4.30191 6.91534 14.0746 11.948
|
|
%4.26189 6.35975 11.5646 10.7466
|
|
\begin{subfigure}{0.47\textwidth}
|
|
\footnotesize
|
|
\centering
|
|
\begin{tabular}{|l|c|c|c|c|}
|
|
\hline
|
|
& \tablefont\SI{25}{\percent} & \tablefont median & \tablefont\SI{75}{\percent} & \tablefont avg \\\hline
|
|
\tablefont\noOptEmpiric{} & \tablefont\SI{6.0}{\meter} & \tablefont\SI{9.2}{\meter} & \tablefont\SI{14.4}{\meter} & \tablefont\SI{11.9}{\meter} \\\hline
|
|
\tablefont\optParamsAllAP{} & \tablefont\SI{6.5}{\meter} & \tablefont\SI{9.0}{\meter} & \tablefont\SI{12.8}{\meter} & \tablefont\SI{12.0}{\meter} \\\hline
|
|
\tablefont\optParamsEachAP{} & \tablefont\SI{6.8}{\meter} & \tablefont\SI{9.8}{\meter} & \tablefont\SI{13.8}{\meter} & \tablefont\SI{13.0}{\meter} \\\hline
|
|
\tablefont\optParamsPosEachAP{} & \tablefont\SI{5.4}{\meter} & \tablefont\SI{8.6}{\meter} & \tablefont\SI{14.8}{\meter} & \tablefont\SI{12.0}{\meter} \\\hline
|
|
\tablefont\optPerFloor{} & \tablefont\SI{4.3}{\meter} & \tablefont\SI{6.9}{\meter} & \tablefont\SI{14.0}{\meter} & \tablefont\SI{11.9}{\meter} \\\hline
|
|
\tablefont\optPerRegion{} & \tablefont\SI{4.2}{\meter} & \tablefont\SI{6.5}{\meter} & \tablefont\SI{11.6}{\meter} & \tablefont\SI{10.7}{\meter} \\\hline
|
|
\end{tabular}
|
|
\vspace{7mm}
|
|
\end{subfigure}
|
|
\caption {
|
|
Cumulative error distribution between walked ground truth and \docWIFI{}-only location estimation using \refeq{eq:bestWiFiPos}.
|
|
%depending on the signal strength prediction model.
|
|
All models suffer from several (extremely) high errors that relate to bad \docWIFI{}
|
|
coverage e.g. within outdoor areas (see \reffig{fig:wifiIndoorOutdoor}). This negatively affects the average and 75th
|
|
percentile. The strategies {\em \optParamsAllAP{}} and {\em \optParamsEachAP{}} sometimes suffered from overadaption,
|
|
indicated by increased error values for the 25th percentile.
|
|
}
|
|
\label{fig:modelPerformance}
|
|
\end{figure}
|
|
|
|
%To estimate the overall performance of the prediction models, we compare the position estimation
|
|
%for each \docWIFI{} measurement within the recorded paths (3756 \docAPshort{} scans in total)
|
|
%against the corresponding ground-truth, which indicates the absolute 3D error in meter.
|
|
The position estimation for each \docWIFI{} measurement within the recorded walks (3756 scans in total)
|
|
is compared against its corresponding ground-truth, indicating the 3D distance error.
|
|
The resulting cumulative error distribution can be seen in \reffig{fig:modelPerformance}.
|
|
The quality of the location estimation directly scales with the quality of the signal strength prediction model.
|
|
However, as discussed earlier, the maximal estimation error might increase for some setups.
|
|
%
|
|
Either due to multimodalities, where more than one area matches the recent
|
|
\docWIFI{} observation, or optimization yielded an overadaption where the average signal
|
|
strength prediction error is small, but the maximum error is dramatically increased for some regions.
|
|
|
|
|
|
|
|
% -------------------------------- plots indicating walk issues -------------------------------- %
|
|
|
|
\begin{figure}
|
|
\centering
|
|
\input{gfx2/wifiMultimodality.tex}
|
|
\caption{
|
|
\docWIFI{}-only location probability for three distinct scans where
|
|
higher color intensities denote a higher likelihood for \refeq{eq:bestWiFiPos}.
|
|
The first scan (left, green) depicts a best-case scenario, where the region around the ground truth (black rectangle) is highly probable.
|
|
Often, other locations are just as likely as the ground truth (2nd scan, blue),
|
|
or the location with the highest probability is far from the actual ground truth (3rd scan, right, red).
|
|
}
|
|
\label{fig:wifiMultimodality}
|
|
\end{figure}
|
|
|
|
\reffig{fig:wifiMultimodality} depicts aforementioned issues of multimodal (blue) or wrong (red) location
|
|
estimations. Filtering (\refeq{eq:recursiveDensity}) thus is highly recommended, as minor errors are compensated
|
|
using other sensors or a movement model that prevents the estimation from leaping within the building.
|
|
However, if wrong sensor values are observed for longer time periods, even filtering will produce erroneous
|
|
results and might get stranded (density is trapped e.g. within a room),
|
|
as the movement model is constrained by the actual floorplan.
|
|
|
|
|
|
% -------------------------------- other distributions, unseen APs, etc -------------------------------- %
|
|
|
|
\hspace{3mm}%hack
|
|
|
|
To reduce the amount of such misclassifications, where other locations within the building are
|
|
as likely as the pedestrian's actual location, we examined various approaches.
|
|
Unfortunately, most of which did not provide a viable enhancement under all conditions for the performed walks.
|
|
|
|
%\commentByFrank{ja, eig gehoert das vor in die theorie, aber da es so kurz ist und vorne immer die ueberleitung kaputt macht
|
|
%oder anderen dingen vorgreifen wuerde, steht es hier}
|
|
The misclassification-rate is determined by counting the amount of (random) locations within
|
|
the building that produce a similar probability \refeq{eq:wifiProb} compared to the actual ground-truth
|
|
position.
|
|
|
|
One possibility to dissolve such an equal \docWIFI{}-likelihood between two (or more) locations is,
|
|
to not only consider the \docAPshort{}s seen by the smartphone, but also the \docAPshort{}s not seen
|
|
by the smartphone. This additional information can be used to rule out all locations where this unseen
|
|
\docAP{} should have be received (high signal strength from the prediction model).
|
|
% There might be an \docAP{} that should be visible at the other locations. However,
|
|
%as the Smartphone did not see this \docAPshort{} the other location can be ruled out.
|
|
While this works in theory, evaluations revealed several issues:
|
|
|
|
\begin{itemize}
|
|
|
|
\item{
|
|
There is a chance that even a nearby \docAPshort{} is unseen during a scan due to packet collisions or
|
|
temporal effects within the surrounding. It thus might make sense to opt-out other locations
|
|
only, if at least two \docAPshort{}s are missing. On the other hand, this obviously demands for (at least)
|
|
two \docAPshort{}s to actually be different between the two locations, and requires a lot of permanently
|
|
installed transmitters to work out.
|
|
}
|
|
|
|
\item{
|
|
Furthermore, this requires the signal strength prediction model to be fairly accurate. Within our testing
|
|
walks, several places are surrounded by concrete walls, which cause a harsh, local drop in signal strength.
|
|
The models used within this work will not accurately predict the signal strength for such locations.
|
|
%%Including \docAPshort{}s unseen by the Smartphone thus often increases the estimation error instead
|
|
%%of fixing the multimodality.
|
|
}
|
|
|
|
\end{itemize}
|
|
|
|
To sum up, while some situations e.g. outdoors could be improved,
|
|
many other situations are deteriorated, especially when some transmitters are (temporarily)
|
|
attenuated by ambient conditions like concrete walls.
|
|
|
|
We therefore examined variations of the probability calculation from \refeq{eq:wifiProb}.
|
|
Contrary to the results shown in \cite{PotentialRisks}, removing weak \docAPshort{}s from $\mRssiVec{}$
|
|
did not work out. While some estimations were improved, the overall error increased
|
|
for our walks, as there are many situations where only a handful \docAP{}s can be seen.
|
|
Removing this (valid) information will increase the error for such situations.
|
|
|
|
However, incorporating additional knowledge provided by virtual \docAP{}s (see section \ref{sec:vap}) mitigated this issues.
|
|
If e.g. only one out of six virtual networks is seen, this observation is likely to be erroneous, no matter
|
|
what the corresponding signal strength indicates.
|
|
As those occasions are relatively seldom, the impact is a minor one.
|
|
Nevertheless, depending on the used prediction model, a handful of major estimation errors were prevented.
|
|
Additionally, among all examined models and walks, there was none where this approached lead to increased error values.
|
|
|
|
%This approach improved the location estimation especially
|
|
%for areas where a transmitter was hardly seen within the reference measurements and its optimization is thus
|
|
%expected to be inaccurate.
|
|
|
|
Using a smaller $\sigma$ or a stricter exponential distribution for the model vs. scan comparison in \refeq{eq:wifiProb}
|
|
had a positive effect on the misclassification error for some of the walks, but also slightly increased the overall estimation error.
|
|
%(see figure \ref{fig:normalVsExponential}).
|
|
Due to those negative side-effects, the final localization system (\refeq{eq:recursiveDensity}) is unlikely to profit from such changes.
|
|
|
|
%\todo{ueberleitung OK?}
|
|
|
|
% braucht zu viel platz
|
|
%\begin{figure}
|
|
% \input{gfx/wifiCompare_normalVsExp_cross.tex}
|
|
% \input{gfx/wifiCompare_normalVsExp_meter.tex}
|
|
% \caption{
|
|
% Comparison between normal- (black) and exponential-distribution (red) for \refeq{eq:wifiProb}.
|
|
% While misclassifications are slightly reduced (upper chart),
|
|
% the median error between ground-truth and estimation (lower chart) increases by
|
|
% about \SI{1}{\meter}.
|
|
% }
|
|
% \label{fig:normalVsExponential}
|
|
%\end{figure}
|
|
|
|
|
|
|
|
%\todo{
|
|
% erwähnen??? sigma je nach signalstärke anpassen bringt leider auch nichts. wenn man das aber macht,
|
|
% dann: fuer grosse signalstaerken ein grosses sigma! andersrum gehts nach hinten los!
|
|
%}
|
|
|
|
|
|
|
|
|
|
% -------------------------------- final system -------------------------------- %
|
|
|
|
\subsection{Filtered location estimation error}
|
|
\label{sec:evalFiltered}
|
|
|
|
After examining the \docWIFI{} component on its own, we will now analyze the impact of previously discussed model
|
|
optimizations on our smartphone-based indoor localization system described in section \ref{sec:system}, based on
|
|
\refeq{eq:recursiveDensity}.
|
|
|
|
Due to transition constraints from the building's floorplan, we expect the
|
|
posterior density to often get stuck when the \docWIFI{} component provides erroneous estimations
|
|
due to bad signal strength predictions or observations (see \reffig{fig:wifiMultimodality}):
|
|
|
|
A pedestrian walks along a hallway, but bad model values indicate that his most likely position
|
|
is within a room right next to the hallway.
|
|
If the density (described by the particles) is dragged (completely) into this room,
|
|
the IMU indicates no change in direction (pedestrian walks straight),
|
|
and the room has only one single door, the density is trapped within this room.
|
|
%
|
|
While such problems can often be solved by simply using more particles to describe the posterior,
|
|
smartphone use-cases are usually performance- and battery limited.
|
|
|
|
As particle filtering from \refeq{eq:recursiveDensity} is a random process with varying output,
|
|
we calculated each combination of the {\em 13 walks and six optimization strategies},
|
|
25 times, using 5000, 7500 and 10000 particles resulting in 75 runs per walk, 975 per strategy and 5850 in total.
|
|
%
|
|
\reffig{fig:overallSystemError} depicts the cumulative error distribution per optimization strategy,
|
|
resulting from all executions for each conducted walk.
|
|
|
|
While most values represent the expected results (more optimization yields better results),
|
|
the values for {\em \optParamsAllAP{}} and {\em \optPerRegion{}} do not.
|
|
The increased error for both strategies can be explained by having a closer look at the walked
|
|
paths and relates to exceptional regions like outdoors. In both cases there is some sort of model overadaption.
|
|
%
|
|
As mentioned earlier, a single, simple model is unable to accurately estimate the signal strength for both
|
|
buildings and adjacent outdoor regions. Due to metallized glass (see \reffig{fig:wifiIndoorOutdoor}), in- and
|
|
outdoor conditions strongly differ. The model's optimization
|
|
builds a compromise among all locations and renders indoor places unnecessarily bad: Previous
|
|
discussions showed that outdoor regions do not provide viable \docWIFI{} signals at all. It thus makes sense
|
|
to just omit badly covered regions from the model optimization process, as the filter's evaluation will simply
|
|
omit \docWIFI{} when the quality is insufficient (see section \ref{sec:wifiQuality}).
|
|
|
|
%
|
|
While {\em \optPerRegion{}} does not suffer from such issues due to separated optimization regions for in- and outdoor,
|
|
its increased error relates to movements between such adjacent regions, as there often is a huge model difference.
|
|
While this difference is perfectly fine, as it also exists within real-world conditions,
|
|
the filtering process suffers at such model-boundaries:
|
|
The model prevents the particles from moving e.g. from inside the building towards outdoor regions, as the
|
|
outdoor-model does not yet match. Due to sensor delays and issues with the absolute heading near in- and outdoor boundaries
|
|
(metal-framed doors) the error is slightly increased and retained for some time until the density stabilizes itself.
|
|
|
|
Especially for {\em path 1}, the particle-filter often got stuck within the upper right outdoor area between both buildings
|
|
(see \reffig{fig:final}). Using the empirical parameters, \SI{40}{\percent} of all runs for this path got stuck at this location.
|
|
{\em \optParamsAllAP{}} already reduced the risk to \SI{20}{\percent} and all other optimization strategies did not get stuck at all.
|
|
Increasing the number of particles from 5000 to 10000 indicated only a minor increase in accuracy and slightly decreased
|
|
the risk of getting stuck. For battery- and performance-constrained use-cases on the smartphone 5000 thus seems to be sufficient.
|
|
|
|
Issues while moving from the inside out or vice versa, should also be mitigated by incorporating the smartphone's GPS sensor.
|
|
However, within our testing walks, the GPS did rarely provide accurate measurements, as the outdoor-time often was too short
|
|
for the sensor to receive a valid fix. The accuracy indicated by the GPS usually was $\ge \SI{50}{\meter}$ and thus
|
|
did not provide useful information.
|
|
|
|
However, comparing the error results within \reffig{fig:modelPerformance} and \reffig{fig:overallSystemError}, one can
|
|
denote the positive impact of fusing multiple sensors with a transition model based on the building's
|
|
actual floorplan. Even within outdoor regions and staircases that suffer from erroneous \docWIFI{} estimations due to a bad
|
|
signal strength coverage. The quality metric described in section \ref{sec:wifiQuality} was able to detect such
|
|
cases and \docWIFI{} was temporarily ignored. The remaining sensors, like the IMU, and the floorplan were able to
|
|
keep the pedestrian's heading until the signal quality reached sane levels again.
|
|
|
|
\begin{figure}
|
|
\centering
|
|
\begin{subfigure}{0.49\textwidth}
|
|
\input{gfx2/overall-system-error.tex}
|
|
\end{subfigure}
|
|
%
|
|
\begin{subfigure}{0.50\textwidth}
|
|
%OVERALL:2.62158 5.13701 11.1822 9.00261
|
|
%OVERALL:2.92524 6.00231 12.4425 10.6983
|
|
%OVERALL:1.98318 3.99259 7.92429 5.81281
|
|
%OVERALL:1.8647 3.86918 7.10482 5.62054
|
|
%OVERALL:1.60847 3.15739 6.13963 4.79148
|
|
%OVERALL:1.63617 3.34828 6.5379 5.12281
|
|
\footnotesize
|
|
\centering
|
|
\setlength{\tabcolsep}{0.25em} % for the horizontal padding
|
|
\begin{tabular}{|l|c|c|c|c|c|}
|
|
|
|
\hline
|
|
& \tablefont\SI{25}{\percent} & \tablefont median & \tablefont\SI{75}{\percent} & \tablefont avg & \tablefont stuck \\\hline
|
|
\tablefont\noOptEmpiric{} & \tablefont\SI{2.6}{\meter} & \tablefont\SI{5.1}{\meter} & \tablefont\SI{11.2}{\meter} & \tablefont\SI{9.0}{\meter} & \tablefont\SI{22}{\percent} \\\hline
|
|
\tablefont\optParamsAllAP{} & \tablefont\SI{2.9}{\meter} & \tablefont\SI{6.0}{\meter} & \tablefont\SI{12.4}{\meter} & \tablefont\SI{10.7}{\meter} & \tablefont\SI{15}{\percent} \\\hline
|
|
\tablefont\optParamsEachAP{} & \tablefont\SI{1.9}{\meter} & \tablefont\SI{4.0}{\meter} & \tablefont\SI{7.9}{\meter} & \tablefont\SI{5.8}{\meter} & \tablefont\SI{5}{\percent} \\\hline
|
|
\tablefont\optParamsPosEachAP{} & \tablefont\SI{1.9}{\meter} & \tablefont\SI{3.9}{\meter} & \tablefont\SI{7.1}{\meter} & \tablefont\SI{5.6}{\meter} & \tablefont\SI{5}{\percent} \\\hline
|
|
\tablefont\optPerFloor{} & \tablefont\SI{1.6}{\meter} & \tablefont\SI{3.2}{\meter} & \tablefont\SI{6.1}{\meter} & \tablefont\SI{4.8}{\meter} & \tablefont\SI{4}{\percent} \\\hline
|
|
\tablefont\optPerRegion{} & \tablefont\SI{1.6}{\meter} & \tablefont\SI{3.3}{\meter} & \tablefont\SI{6.5}{\meter} & \tablefont\SI{5.0}{\meter} & \tablefont\SI{4}{\percent} \\\hline
|
|
\end{tabular}
|
|
\setlength{\tabcolsep}{1.0em} % reset the horizontal padding
|
|
\vspace{9.0mm}
|
|
\end{subfigure}
|
|
%
|
|
\caption{
|
|
Cumulative error distribution for each model when used within the final localization system from \refeq{eq:recursiveDensity}.
|
|
Especially {\em \optParamsAllAP{}} suffered from overadaption and thus provided worse results. Compared to just using \docWIFI{}
|
|
(\reffig{fig:modelPerformance}) the error difference between the models now is much more distinct.
|
|
Starting from {\em \optParamsEachAP{}} the system rarely gets stuck and provides a viable accuracy.
|
|
}
|
|
\label{fig:overallSystemError}
|
|
\end{figure}
|
|
|
|
|
|
Finally, \reffig{fig:final} depicts all of the previously discussed improvements and issues by examining {\em path 1}
|
|
from \reffig{fig:allWalks}.
|
|
For better visibility within path- and error-plots, the unfiltered estimations were smoothed, using a moving average of
|
|
ten consecutive values ($\approx \SI{7}{\second}$). As can be seen, optimizing the \docWIFI{} model yields an improvement
|
|
for indoor situations, as the estimation is closer to the ground truth, and the starting position (indicated by the rectangle)
|
|
is more accurate.
|
|
For the depicted walk, the error outdoors is increased, as the likeliest position is shifted. Adding
|
|
the particle filter (\refeq{eq:recursiveDensity}) on top of the optimized model, fixes this issue. What cannot be seen
|
|
within the figure: while the likeliest position is deteriorated by the optimization, the likelihood of the region around
|
|
the pedestrian's ground truth is actually increased. Thus, combined with transition model and other sensors, the system
|
|
is able to stay right on track. The filter fails for {\em \noOptEmpiric}, as one \docAPshort{} near the entry of the second
|
|
building prevents the density from entering, due to a very high difference between model and real-world conditions.
|
|
|
|
\begin{figure}
|
|
%\begin{subfigure}{0.49\textwidth}
|
|
% \centering
|
|
% \input{gfx/final3D.tex}
|
|
%\end{subfigure}
|
|
%\begin{subfigure}{0.49\textwidth}
|
|
% \centering
|
|
% \input{gfx/final2D.tex}
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%\end{subfigure}
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\begin{subfigure}{0.99\textwidth}
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\centering
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\input{gfx/final3D.tex}
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\end{subfigure}
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\\\vspace{4mm}
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\begin{subfigure}{0.48\textwidth}
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\centering
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\input{gfx/final2D-a.tex}
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\end{subfigure}
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\begin{subfigure}{0.48\textwidth}
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\centering
|
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\input{gfx/final2D-b.tex}
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\end{subfigure}
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\\
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\begin{subfigure}{0.99\textwidth}
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\input{gfx/final-error.tex}
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\end{subfigure}
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\caption{
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Detailed analysis of the \docWIFI{} error for {\em \noOptEmpiric{}} (unoptimized) and {\em \optPerFloor{}}
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using {\em path 1} (see \reffig{fig:allWalks}). While optimization reduces the error indoors, the error outdoors
|
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is increased (bold line). A particle filter (PF, \refeq{eq:recursiveDensity}) on top of the optimized model
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|
takes \SI{5}{\second} to initialize the starting-position (rectangles), fixes the outdoor-issue and
|
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improves indoor situations. A filter on top of {\em \noOptEmpiric{}} got stuck right before
|
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entering the 2nd building. Both, the filtered and unfiltered version of {\em \noOptEmpiric{}}
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are dragged into the 2nd floor in the middle of the walk.
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}
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\label{fig:final}
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\end{figure}
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% results
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% 5000 particles
|
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%
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% model empiric
|
|
% |path1a(5.76715@100%) |path1b(3.73881@4%) |toni-all-1a(6.1505@76%) |toni-all-1b(4.60639@40%) |path2a(7.35355@28%) |path2b(7.4316@0%) |toni-all-2a(10.7068@44%) |toni-all-2b(7.4323@28%) |toni-inst-1b(4.60685@0%) |toni-inst-2a(3.83979@0%) |toni-inst-2b(3.98889@0%) |toni-inst-3a(4.70925@0%) |toni-inst-3b(4.40971@0%) | OVERALL:(5.12463@24%)
|
|
% model opt 1
|
|
% |path1a(17.6635@56%) |path1b(9.41882@24%)|toni-all-1a(4.06972@0%) |toni-all-1b(3.83157@0%) |path2a(6.92405@16%) |path2b(8.6365@16%) |toni-all-2a(11.6348@48%) |toni-all-2b(12.029@76%) |toni-inst-1b(5.07535@0%) |toni-inst-2a(4.45517@0%) |toni-inst-2b(3.99025@0%) |toni-inst-3a(8.28201@8%) |toni-inst-3b(5.57021@20%) | OVERALL:(6.57212@20%)
|
|
% model opt 2
|
|
% |path1a(2.01602@0%) |path1b(2.90237@0%) |toni-all-1a(2.80293@0%) |toni-all-1b(1.99745@0%) |path2a(5.39013@4%) |path2b(8.13855@0%) |toni-all-2a(9.7462@40%) |toni-all-2b(9.28677@44%) |toni-inst-1b(4.5305@0%) |toni-inst-2a(4.28726@0%) |toni-inst-2b(4.03041@0%) |toni-inst-3a(4.26278@4%) |toni-inst-3b(5.63394@24%) | OVERALL:(4.07822@8%)
|
|
% model opt 3
|
|
% |path1a(1.74623@0%) |path1b(2.61609@0%) |toni-all-1a(2.49372@0%) |toni-all-1b(1.90326@0%) |path2a(5.07957@4%) |path2b(7.73973@8%) |toni-all-2a(10.2793@48%) |toni-all-2b(6.48194@16%) |toni-inst-1b(5.73752@4%) |toni-inst-2a(3.76165@0%) |toni-inst-2b(3.51509@0%) |toni-inst-3a(6.06681@16%) |toni-inst-3b(5.27748@24%) | OVERALL:(3.94786@9%)
|
|
% model per floor
|
|
% |path1a(1.76139@0%) |path1b(2.22047@0%) |toni-all-1a(2.10094@0%) |toni-all-1b(1.62287@0%) |path2a(5.50715@16%) |path2b(7.1257@0%) |toni-all-2a(10.5138@48%) |toni-all-2b(6.72044@20%) |toni-inst-1b(3.77885@0%) |toni-inst-2a(2.23669@0%) |toni-inst-2b(3.20604@0%) |toni-inst-3a(2.46891@0%) |toni-inst-3b(2.73366@0%) | OVERALL:(3.22315@6%)
|
|
% model per bbox
|
|
% |path1a(1.80033@0%) |path1b(2.32875@0%) |toni-all-1a(2.17754@0%) |toni-all-1b(1.6697@0%) |path2a(6.38772@16%) |path2b(5.84004@0%) |toni-all-2a(9.67635@36%) |toni-all-2b(8.3282@24%) |toni-inst-1b(4.11891@0%) |toni-inst-2a(2.64016@0%) |toni-inst-2b(3.36297@0%) |toni-inst-3a(2.15568@0%) |toni-inst-3b(2.98047@0%) | OVERALL:(3.40679@5%)
|
|
%
|
|
%
|
|
% 7500 particles
|
|
% model empiric
|
|
% |path1a(8.23256@100%) |path1b(3.91532@0%) |toni-all-1a(7.0666@80%) |toni-all-1b(5.35225@48%) |path2a(6.5708@16%) |path2b(7.53023@0%) |toni-all-2a(10.6246@40%) |toni-all-2b(6.63087@4%) |toni-inst-1b(4.76934@0%) |toni-inst-2a(3.82903@0%) |toni-inst-2b(4.00339@0%) |toni-inst-3a(3.85417@4%) |toni-inst-3b(4.47613@0%) | OVERALL:(5.23337@22%)
|
|
% model opt 1
|
|
% |path1a(10.3959@36%) |path1b(8.37674@16%)|toni-all-1a(3.96164@0%) |toni-all-1b(4.24675@4%) |path2a(6.02912@8%) |path2b(8.1804@0%) |toni-all-2a(12.4277@48%) |toni-all-2b(10.4748@56%) |toni-inst-1b(5.49874@4%) |toni-inst-2a(4.09279@0%) |toni-inst-2b(3.87762@0%) |toni-inst-3a(5.10456@0%) |toni-inst-3b(4.52029@4%) | OVERALL:(5.97832@13%)
|
|
% model opt 2
|
|
% |path1a(2.04657@0%) |path1b(2.82853@0%) |toni-all-1a(2.93467@0%) |toni-all-1b(1.98463@0%) |path2a(4.66513@8%) |path2b(8.19959@0%) |toni-all-2a(8.34246@12%) |toni-all-2b(7.2456@12%) |toni-inst-1b(4.72651@0%) |toni-inst-2a(4.00208@0%) |toni-inst-2b(3.94811@0%) |toni-inst-3a(3.74498@0%) |toni-inst-3b(5.15519@16%) | OVERALL:(3.99594@3%)
|
|
% model opt 3
|
|
% |path1a(1.82148@0%) |path1b(2.7664@0%) |toni-all-1a(2.46073@0%) |toni-all-1b(1.93273@0%) |path2a(5.15394@4%) |path2b(7.53562@0%) |toni-all-2a(8.43582@20%) |toni-all-2b(6.01557@8%) |toni-inst-1b(5.47576@0%) |toni-inst-2a(3.44451@0%) |toni-inst-2b(3.6069@0%) |toni-inst-3a(4.84921@4%) |toni-inst-3b(5.62456@8%) | OVERALL:(3.88747@3%)
|
|
% model per floor
|
|
% |path1a(1.79881@0%) |path1b(2.1456@0%) |toni-all-1a(2.17125@0%) |toni-all-1b(1.63247@0%) |path2a(5.37789@8%) |path2b(6.79701@0%) |toni-all-2a(9.29407@32%) |toni-all-2b(6.28292@8%) |toni-inst-1b(3.79967@0%) |toni-inst-2a(2.24007@0%) |toni-inst-2b(3.15768@0%) |toni-inst-3a(2.17671@0%) |toni-inst-3b(2.83445@0%) | OVERALL:(3.16559@3%)
|
|
% model per bbox
|
|
% |path1a(1.77473@0%) |path1b(2.2609@0%) |toni-all-1a(2.06814@4%) |toni-all-1b(1.6841@0%) |path2a(6.48652@4%) |path2b(5.79359@0%) |toni-all-2a(9.40116@24%) |toni-all-2b(7.21382@16%) |toni-inst-1b(3.82829@0%) |toni-inst-2a(2.47975@0%) |toni-inst-2b(3.35265@0%) |toni-inst-3a(2.20058@0%) |toni-inst-3b(2.86407@0%) | OVERALL:(3.3381@3%)
|
|
%
|
|
% 10000 particles
|
|
% model empiric
|
|
% |path1a(6.43082@100%) |path1b(3.58544@0%) |toni-all-1a(6.92747@76%) |toni-all-1b(5.81139@72%) |path2a(5.12683@4%) |path2b(7.91078@0%) |toni-all-2a(10.3958@16%) |toni-all-2b(7.09186@8%) |toni-inst-1b(4.45815@0%) |toni-inst-2a(4.077@0%) |toni-inst-2b(4.02524@0%) |toni-inst-3a(3.35953@0%) |toni-inst-3b(4.40318@0%) | OVERALL:(5.06224@21%)
|
|
% model opt 1
|
|
% |path1a(6.47262@16%) |path1b(6.04852@12%)|toni-all-1a(3.97276@0%) |toni-all-1b(3.62778@0%) |path2a(5.48776@8%) |path2b(8.21965@0%) |toni-all-2a(11.3175@44%) |toni-all-2b(11.4499@60%) |toni-inst-1b(5.19827@0%) |toni-inst-2a(4.1351@0%) |toni-inst-2b(3.90291@0%) |toni-inst-3a(4.58096@8%) |toni-inst-3b(4.62723@4%) | OVERALL:(5.47998@11%)
|
|
% model opt 2
|
|
% |path1a(2.15007@0%) |path1b(2.80157@0%) |toni-all-1a(2.70849@0%) |toni-all-1b(1.8937@0%) |path2a(4.13743@0%) |path2b(8.20317@0%) |toni-all-2a(7.86448@12%) |toni-all-2b(7.41533@12%) |toni-inst-1b(4.54459@0%) |toni-inst-2a(4.17614@0%) |toni-inst-2b(3.90311@0%) |toni-inst-3a(3.846@4%) |toni-inst-3b(4.84665@8%) | OVERALL:(3.89883@2%)
|
|
% model opt 3
|
|
% |path1a(1.79085@0%) |path1b(2.64892@0%) |toni-all-1a(2.33085@0%) |toni-all-1b(1.9533@0%) |path2a(4.40712@4%) |path2b(7.815@0%) |toni-all-2a(8.97738@28%) |toni-all-2b(5.87188@0%) |toni-inst-1b(4.93315@0%) |toni-inst-2a(3.53349@0%) |toni-inst-2b(3.60056@0%) |toni-inst-3a(5.57379@8%) |toni-inst-3b(4.49996@4%) | OVERALL:(3.78756@3%)
|
|
% model per floor
|
|
% |path1a(1.7498@0%) |path1b(2.11555@0%) |toni-all-1a(1.89388@0%) |toni-all-1b(1.61323@0%) |path2a(5.06884@0%) |path2b(6.7157@0%) |toni-all-2a(9.54228@36%) |toni-all-2b(6.7699@24%) |toni-inst-1b(3.84709@0%) |toni-inst-2a(2.2789@0%) |toni-inst-2b(3.17625@0%) |toni-inst-3a(2.13417@0%) |toni-inst-3b(2.59095@0%) | OVERALL:(3.08506@4%)
|
|
% model per bbox
|
|
% |path1a(1.73406@0%) |path1b(2.30577@0%) |toni-all-1a(2.01979@0%) |toni-all-1b(1.64225@0%) |path2a(6.30713@12%) |path2b(6.02961@0%) |toni-all-2a(9.70206@20%) |toni-all-2b(6.55847@8%) |toni-inst-1b(3.93324@0%) |toni-inst-2a(2.459@0%) |toni-inst-2b(3.3522@0%) |toni-inst-3a(2.13783@0%) |toni-inst-3b(2.63231@0%) | OVERALL:(3.29408@3%)
|
|
|
|
% all combined
|
|
% model empiric
|
|
% |path1a(6.72661@100%) |path1b(3.74113@1%) |toni-all-1a(6.69696@77%) |toni-all-1b(5.26661@53%) |path2a(6.11286@16%) |path2b(7.63154@0%) |toni-all-2a(10.5765@33%) |toni-all-2b(7.0506@13%) |toni-inst-1b(4.61087@0%) |toni-inst-2a(3.91375@0%) |toni-inst-2b(4.00372@0%) |toni-inst-3a(3.89586@1%) |toni-inst-3b(4.43552@0%) | OVERALL:(5.13701@22%)
|
|
% model opt 1
|
|
% |path1a(10.0538@36%) |path1b(7.96075@17%)|toni-all-1a(3.99762@0%) |toni-all-1b(3.89137@1%) |path2a(6.08714@10%) |path2b(8.33165@5%) |toni-all-2a(11.7481@46%) |toni-all-2b(11.2068@64%) |toni-inst-1b(5.25558@1%) |toni-inst-2a(4.23255@0%) |toni-inst-2b(3.92269@0%) |toni-inst-3a(5.62327@5%) |toni-inst-3b(4.82302@9%) | OVERALL:(6.00231@15%)
|
|
% model opt 2
|
|
% |path1a(2.07273@0%) |path1b(2.84622@0%) |toni-all-1a(2.81671@0%) |toni-all-1b(1.9553@0%) |path2a(4.66453@4%) |path2b(8.17561@0%) |toni-all-2a(8.60702@21%) |toni-all-2b(7.68813@22%) |toni-inst-1b(4.59132@0%) |toni-inst-2a(4.15243@0%) |toni-inst-2b(3.96315@0%) |toni-inst-3a(3.96402@2%) |toni-inst-3b(5.16219@16%) | OVERALL:(3.99259@5%)
|
|
% model opt 3
|
|
% |path1a(1.78819@0%) |path1b(2.67775@0%) |toni-all-1a(2.43527@0%) |toni-all-1b(1.92948@0%) |path2a(4.90009@4%) |path2b(7.70505@2%) |toni-all-2a(9.16313@32%) |toni-all-2b(6.10436@8%) |toni-inst-1b(5.37191@1%) |toni-inst-2a(3.57332@0%) |toni-inst-2b(3.57426@0%) |toni-inst-3a(5.4337@9%) |toni-inst-3b(5.12685@12%) | OVERALL:(3.86918@5%)
|
|
% model per floor
|
|
% |path1a(1.77029@0%) |path1b(2.16265@0%) |toni-all-1a(2.05043@0%) |toni-all-1b(1.62289@0%) |path2a(5.29536@8%) |path2b(6.88344@0%) |toni-all-2a(9.75416@38%) |toni-all-2b(6.57473@17%) |toni-inst-1b(3.80742@0%) |toni-inst-2a(2.25183@0%) |toni-inst-2b(3.18067@0%) |toni-inst-3a(2.24992@0%) |toni-inst-3b(2.72835@0%) | OVERALL:(3.15739@4%)
|
|
% model per bbox
|
|
% |path1a(1.76908@0%) |path1b(2.30081@0%) |toni-all-1a(2.09503@1%) |toni-all-1b(1.66411@0%) |path2a(6.39346@10%) |path2b(5.8772@0%) |toni-all-2a(9.59953@26%) |toni-all-2b(7.06924@16%) |toni-inst-1b(3.96094@0%) |toni-inst-2a(2.51694@0%) |toni-inst-2b(3.3549@0%) |toni-inst-3a(2.1656@0%) |toni-inst-3b(2.81547@0%) | OVERALL:(3.34847@4%)
|
|
|
|
|
|
% REAL WALKS
|
|
|
|
%\todo{obwohl das angepasste modell doch recht gut laeuft und der fehler recht klein wird, sind immernoch stellen dabei,
|
|
%wo es einfach nicht gut passt, unguenstige mehrdeutigkeiten vorliegen, oder regionen einfach nicht passen wie sie sollten.
|
|
%das liegt teils auch daran, dass die fingerprints drehend aufgenommen wurden und beim laufen nach hinten durch den
|
|
%menschen abgeschottet wird. auch zeitlicher verzug kann ein problem darstellen.}
|
|
|
|
%\todo{
|
|
% wenn ich beim fingerprinten einen AP an einer stelle NICHT gesehen habe,
|
|
% ist das auch eine aussage für die model optimierung.. da kann dann sicher keine signatlstaerke > -90 an der stelle raus kommen
|
|
%}
|
|
|
|
|
|
%ware das grid-model nicht da, wuerde der outdoor teil richtig schlecht laufen,
|
|
%weil das wlan hier absolut ungenau ist.. da die partikel aber aufgrund des vorherigen
|
|
%walks schon recht dicht beisamen sind, kittet das das ganze sehr gut.
|
|
%kann man testen, indem man z.B. weniger resampling macht und mehr alte partikel aufhebt.
|
|
%geht sofort kaputt sobald man aus dem gebäude raus kommt
|
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% was ist das??
|
|
%\input{gfx/wifi-opt-error-hist-methods.tex}
|
|
%\input{gfx/wifi-opt-error-hist-stair-outdoor.tex}
|
|
%outdoor hat insgesamt nicht all zu viel einfluss, da die meisten APs
|
|
%an den outdoor punkten kaum gesehen werden. auf einzelne APs kann
|
|
%der einfluss jedoch recht groß sein, siehe den fingerprint plot von
|
|
%dem einen ausgewählten AP
|
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%\todo{anfaenglich falsches heading ist gift, wegen rel. heading, weil sich dann alles verlaeuft. fix: anfaenglich große heading variation erlauben}
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%\todo{NICHT MEHR AKTUELL: abs-head ist in der observation besser, weil es beim resampling mehr bringt und dafuer srogt, dass die richtigen geloescht werden!}
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|