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% intro
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\todo{reihenfolge so jetzt klar?}
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\commentByFrank{reihenfolge so jetzt klar?}
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Within our experiments we will first have a look at model optimizations to reduce the error
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between model predictions and real-world conditions.
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Hereafter we examine the resulting accuracy when using the optimized models for localization
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@@ -14,7 +14,7 @@
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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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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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%
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@@ -65,7 +65,7 @@
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\input{gfx2/model-bboxes.tex}
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\caption{
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Each distinct floor-color denotes one model (7 in total) for {\em \optPerRegion{}}.
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Often, more than one bounding box is needed to approximate the region's shape.
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Often more than one bounding box is needed to approximate 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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@@ -106,7 +106,7 @@
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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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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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@@ -141,10 +141,10 @@
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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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\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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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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@@ -300,8 +300,8 @@
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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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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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@@ -348,7 +348,7 @@
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\todo{uebergang jetzt besser?}
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Having optimized several signal strength prediction models, we can now examine the resulting localization
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accuracy for each one. For now, this will just cover the \docWIFI{} component itself.
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accuracy for each. For now, this will just cover the \docWIFI{} component itself.
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The impact of adding additional sensors and a transition model will be evaluated later.
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@@ -379,9 +379,9 @@
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\label{eq:bestWiFiPos}
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\end{equation}
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Within \refeq{eq:bestWiFiPos} $\mu_{i,\mPosVec}$ is the signal strength for \docAP{} $i$,
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In \refeq{eq:bestWiFiPos} $\mu_{i,\mPosVec}$ is the signal strength for \docAP{} $i$,
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installed at location $\mPosVec$, returned from the to-be-examined prediction model.
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For all comparisons we use a constant uncertainty of $\sigma = \SI{8}{\decibel}$.
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For all comparisons, we use a constant uncertainty of $\sigma = \SI{8}{\decibel}$.
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The quality of the estimated location is determined by using the Euclidean distance between estimation
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$\mPosVec^*$ and the pedestrian's ground truth position at the time the scan $\mRssiVec$
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@@ -401,7 +401,7 @@
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\centering
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\input{gfx2/all_walks.tex}
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\caption{
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Overview of all conducted paths.
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Overview of all conducted paths, each starting at the denoted rectangle.
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Outdoor areas are marked in green.
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}
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\label{fig:allWalks}
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@@ -455,7 +455,7 @@
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The quality of the location estimation directly scales with the quality of the signal strength prediction model.
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However, as discussed earlier, the maximal estimation error might increase for some setups.
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%
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This is either due to multimodalities, where more than one area matches the recent
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Either due to multimodalities, where more than one area matches the recent
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\docWIFI{} observation, or optimization yielded an overadaption where the average signal
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strength prediction error is small, but the maximum error is dramatically increased for some regions.
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@@ -487,7 +487,7 @@
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\hspace{3mm}%hack
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To reduce the amount such of misclassifications, where other locations within the building are
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To reduce the amount of such misclassifications, where other locations within the building are
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as likely as the pedestrian's actual location, we examined various approaches.
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Unfortunately, most of which did not provide a viable enhancement under all conditions for the performed walks.
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@@ -525,18 +525,18 @@
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\end{itemize}
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To sum up, while some situations, e.g. outdoors, could be improved,
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To sum up, while some situations e.g. outdoors could be improved,
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many other situations are deteriorated, especially when some transmitters are (temporarily)
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attenuated by ambient conditions like concrete walls.
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We therefore examined variations of the probability calculation from \refeq{eq:wifiProb}.
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Despite the results show in \cite{PotentialRisks}, removing weak \docAPshort{}s from $\mRssiVec{}$
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yielded similar results. While some estimations were improved, the overall error increased
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Contrary to the results shown in \cite{PotentialRisks}, removing weak \docAPshort{}s from $\mRssiVec{}$
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did not work out. While some estimations were improved, the overall error increased
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for our walks, as there are many situations where only a handful \docAP{}s can be seen.
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Removing this (valid) information will highly increase the error for such situations.
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Removing this (valid) information will increase the error for such situations.
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Incorporating additional knowledge provided by virtual \docAP{}s (see section \ref{sec:vap}) mitigated this issues.
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If only one out of six virtual networks is observed, this observation is likely to be erroneous, no matter
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However, incorporating additional knowledge provided by virtual \docAP{}s (see section \ref{sec:vap}) mitigated this issues.
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If only one out of six virtual networks is seen, this observation is likely to be erroneous, no matter
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what the corresponding signal strength indicates. This approach improved the location estimation especially
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for areas where a transmitter was hardly seen within the reference measurements and its optimization is thus
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expected to be inaccurate.
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@@ -546,7 +546,7 @@
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%(see figure \ref{fig:normalVsExponential}).
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Due to those negative side-effects, the final localization system (\refeq{eq:recursiveDensity}) is unlikely to profit from such changes.
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\todo{ueberleitung OK?}
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%\todo{ueberleitung OK?}
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% braucht zu viel platz
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%\begin{figure}
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@@ -597,7 +597,7 @@
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25 times, using 5000, 7500 and 10000 particles resulting in 75 runs per walk, 975 per strategy and 5850 in total.
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%
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\reffig{fig:overallSystemError} depicts the cumulative error distribution per optimization strategy,
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resulting from all executions for each walk conducted with the smartphone.
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resulting from all executions for each conducted walk.
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While most values represent the expected results (more optimization yields better results),
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the values for {\em \optParamsAllAP{}} and {\em \optPerRegion{}} do not.
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@@ -622,15 +622,15 @@
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(metal-framed doors) the error is slightly increased and retained for some time until the density stabilizes itself.
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Especially for {\em path 1}, the particle-filter often got stuck within the upper right outdoor area between both buildings
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(see \reffig{fig:allWalks}). Using the empirical parameters, \SI{40}{\percent} of all runs for this path got stuck at this location.
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(see \reffig{fig:final}). Using the empirical parameters, \SI{40}{\percent} of all runs for this path got stuck at this location.
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{\em \optParamsAllAP{}} already reduced the risk to \SI{20}{\percent} and all other optimization strategies did not get stuck at all.
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Additionally increasing the number of particles from 5000 to 10000 indicated only a minor increase in accuracy and slightly decreased
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the risk of getting stuck. For battery- and performance-constrained use-cases on the smartphone 5000 thus seems to be a sufficient.
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Increasing the number of particles from 5000 to 10000 indicated only a minor increase in accuracy and slightly decreased
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the risk of getting stuck. For battery- and performance-constrained use-cases on the smartphone 5000 thus seems to be sufficient.
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Issues while moving from the inside out, or vice versa, should also be mitigated by incorporating the smartphone's GPS sensor.
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Issues while moving from the inside out or vice versa, should also be mitigated by incorporating the smartphone's GPS sensor.
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However, within our testing walks, the GPS did rarely provide accurate measurements, as the outdoor-time often was too short
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for the sensor to receive a valid fix. The accuracy indicated by the GPS usually was $\ge \SI{50}{\meter}$ and thus
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did not provide usefull information.
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did not provide useful information.
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However, comparing the error results within \reffig{fig:modelPerformance} and \reffig{fig:overallSystemError}, one can
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denote the positive impact of fusing multiple sensors with a transition model based on the building's
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@@ -672,7 +672,7 @@
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\caption{
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Cumulative error distribution for each model when used within the final localization system from \refeq{eq:recursiveDensity}.
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Especially {\em \optParamsAllAP{}} suffered from overadaption and thus provided worse results. Compared to just using \docWIFI{}
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(\reffig{fig:modelPerformance}) the error difference between the models now is much more pronounced.
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(\reffig{fig:modelPerformance}) the error difference between the models now is much more distinct.
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Starting from {\em \optParamsEachAP{}} the system rarely gets stuck and provides a viable accuracy.
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}
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\label{fig:overallSystemError}
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@@ -681,16 +681,16 @@
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Finally, \reffig{fig:final} depicts all of the previously discussed improvements and issues by examining {\em path 1}
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from \reffig{fig:allWalks}.
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For better visibility within path- and error-plots, the non filtered estimations were smoothed using a moving average of
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For better visibility within path- and error-plots, the unfiltered estimations were smoothed, using a moving average of
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ten consecutive values ($\approx \SI{7}{\second}$). As can be seen, optimizing the \docWIFI{} model yields an improvement
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for indoor situations, as the estimation is closer to the ground truth, and the starting position (indicated by the rectangle)
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is more accurate.
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For the depicted walk, the error outdoors is increased, as the likeliest position is shifted. Adding
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the particle filter (\refeq{eq:recursiveDensity}) on top of the optimized model fixes this issue. What cannot be seen
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within the images: while the likeliest position is deteriorated by the optimization, the likelihood of the region around
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the pedestrian's ground truth actually is increased. Thus, combined with transition model and other sensors, the system
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the particle filter (\refeq{eq:recursiveDensity}) on top of the optimized model, fixes this issue. What cannot be seen
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within the figure: while the likeliest position is deteriorated by the optimization, the likelihood of the region around
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the pedestrian's ground truth is actually increased. Thus, combined with transition model and other sensors, the system
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is able to stay right on track. The filter fails for {\em \noOptEmpiric}, as one \docAPshort{} near the entry of the second
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building prevents the density from entering due to a very high difference between model and real-world conditions.
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building prevents the density from entering, due to a very high difference between model and real-world conditions.
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\begin{figure}
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\begin{subfigure}{0.49\textwidth}
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