405 lines
29 KiB
TeX
405 lines
29 KiB
TeX
\section{Experiments}
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\subsection{Hardware Setup}
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%\begin{itemize}
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% \item Pixel 2XL Android P liefert RSSI und FTM
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% \item 4 Intel NUCS mit selbstgebauten Antennen (Auf Ibrahim verweisen aber auch genau erläutern, eventl mit Bild)
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% \item Gebäude erläutern. Bürogebäude in Industriegebiet. Holzhaus. Gebäude war Leer um eine optimale menschenleere Umgebung zu schaffen. Größe XxX. -> Bild mit AP Positionen (gerne von unten linken wo ergebnisse drauf sind, spart platz)
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% \item FH Gebäude erläutern. -> Bild mit AP Positionen (gerne von unten linken wo ergebnisse drauf sind, spart platz)
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% \item Zweites Gebäude weil: Verhält es sich in einem anderen Gebäude genauso? Also AP's ähnlich positionieren, aber andere umgebung (wände, räume usw.).
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% \item Position wurde auf einem Stockwerk geschätzt, also nur 2D.
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% \item Nuc steht auf einem Tisch
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% \item die messungen kommen immer gleichzeitig von ftm und rssi. dadurch ist die sampelrate die gleiche und wir können besser vergleichen
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%\end{itemize}
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%
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%
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%Mapping zwischen AP-MAC und Position ist gegeben.
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%In Android Q könnte man LCI am Ap hinterlegen um die AP-Pos dynamisch zu erfragen.
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%Praktische Einschräkungen: Da Wifi Scans nur selten möglich sind, können neue FTM APs nicht leicht erkannt werden.
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%AUßerdem muss per Reflection ScanResults für bereits bekannte APs MAC erzeugt werden.
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%Für eine parktische Anwendung wäre es nochtwenig, dass neue APs automatisch on the fly erkannt werden können.
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In all our experiments we used a Google Pixel 2 XL and Google Pixel 3a smartphone, both running Android~9.
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Google introduced official ranging APIs based on FTM for supported devices with Android~9.
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Also starting with Android~9, Google limited the number of network scans to four every two minutes.
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This limitation renders the commonly used network scanning API virtually unusable for measuring RSSI values for localization purposes.
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However, the new FTM ranging API has no rate limit.
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Additionally, the new FTM API also provides RSSI values, thus with each measurement the signal strength and distance to one AP can be simultaneously obtained.
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In our experiments every \SI{200}{ms} a FTM measurement to every known access point is queried.
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This does not guarantee that distance measurements for every access point are available at that frequency.
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Due to blocked sight or harsh environmental conditions the measurements can fail.
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According to our observations Android issues eight FTM measurements for a single ranging request.
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The API returns various values, \eg mean distance, standard deviation, RSSI, number of attempted measurements, and the number of successful measurements.
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It is not documented how Android aggregates the eight measurements, but it is assumed that the arithmetic mean is calculated on the distance.
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The list of access points is statically stored in the application and known beforehand.
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With Android~10 it is possible to transfer the AP position dynamically using the location configuration information protocol.
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This allows a more flexible applications as access point can be added or modified dynamically without updating the client application.
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In some cases we noticed that Android did not provide FTM measurements for intervals about three up to five seconds for unknown reasons, although multiple APs were clearly in reach.
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Due to the rarity of this problem we decided to repeat these faulty experiment runs.
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% TODO welche Daten liefert Android. Wie die konkret gemessene Distanz entshtet ist nicht bekannt. Android teilt mit wieviele FTM Messungen erfolgreich waren z.b. 7/8. etc.
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% TODO Linux kernel version; intel firmware version
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The access points are Intel NUCs running a patched Linux to enable FTM support.
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In total we're using eight APs based on Intel WiFi cards.
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Four of them are based on Intel Dualband-Wireless-AC~8260 cards configured as described by \etal{Ibrahim} \cite{ibrahim2018verification}.
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The remaining four are based on Intel Wireless-AC~9462 modules and run a recent Linux kernel 5.3.7 where the iwlwifi driver and hostapd are already prepared to support FTM.
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However, the driver still requires small manual changes, as a global boolean flag needs to be set to activate the FTM related code.
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In addition, the firmware of the card returns that the chip is not calibrated for FTM.
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As a consequence the driver disables FTM responder functionality.
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Overriding this check, however, allows to use the chip as responder and FTM measurements can be performed reliable.
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At this point it is not clear to us what the exact purpose of the flag is.
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While it indicates that the card is not calibrated accuracy of the measurements are sufficient as shown in our experiments.
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Due to regulatory limitations both wireless cards can only be configured as access points in the \SI{2.4}{GHz} frequency band.
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To improve the signal quality and strength we connected two external consumer grade omni directional antennas to the wireless cards and attached them to the case of the Intel NUC.
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The antennas have an antenna gain of \SI{2}{dBi} as specified by the manufacturer.
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We used a \SI{10}{cm} coaxial cable to connect the antennas to the cards, which is practically the shortest cable possible to limit the additional signal propagation delay.
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\subsection{Verification FTM Performance in LOS Scenario}
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%\begin{itemize}
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% \item AP position strategy
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% \item DoP plot
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% \item wieviel APs sichtbar sind, wie kommen die Ranges, welche Parameter machen was und bedeuten was
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% \item Einfluss der Wände; warum starke Abschwächungen
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% \item Welche Platzierung wäre besser; Warum nicht möglich?
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% \item Daher Proabilistic Ansatz weil viele Messungen fehlen oder stark schwanken
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% \item Mehr APs bringen was?
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% \item Bildergrid und Video
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%\end{itemize}
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The first experiment evaluates the indoor precision and accuracy of FTM distance measurements given different hardware configurations.
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While \etal{Ibrahim} \cite{ibrahim2018verification} already verified the precision of the \intelOld card in great detail, our setup differs from theirs and requires anew evaluation.
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In contrast to \etal{Ibrahim} we use smartphones as receivers and two different cards with different firmware versions as senders.
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Additionally, it is unclear how the external antennas affect the measurements.
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For these reasons we did a static distance measurement experimental setup to confirm that the combination of Pixel devices and Intel cards provide reliable values.
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\begin{figure}[ht]
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\centering
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\newcolumntype{c}{>{\footnotesize}l} % HACK: Inkscape erzeugt ein tablular und ignoriert die font size
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\input{gfx/DistMeasExpLOS.pdf_tex}
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\caption{Experimental setup in the main hallway of our university building. Every \SI{2}{m} 140 FTM measurements were recorded from the smartphone (Green) to the responder (Blue). The AP is close to a stair } % TODO Das mit der Treppe besser erklären
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\label{fig:LosDistExp}
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\end{figure}
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Our test setup consist of $10$ measurement points evenly spaced at a distance of \SI{2}{m} on a straight line.
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The closest point to the AP is \SI{2}{m} away and the furthest \SI{20}{m}.
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The setup is shown in \autoref{fig:LosDistExp}.
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At every point each phone is placed on a stand.
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Around 140 FTM measurements are recorded, which corresponds to a measure period of \SI{30}{s} per point.
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The APs and the phones are placed on an empty cardboard box on a metal stand to allow some distance between the metal and the phone.
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The phones laid flat on the box.
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Both the APs and the phones are located at \SI{1.05}{m} above the floor.
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While recording measurements for \SI{30}{s} at a single point is not realistic in a dynamic positioning system, it allows us to evaluate the statistical properties of the method.
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The whole experiment was deployed in the hallway of our university.
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Each distance measurement is performed with every hardware combination.
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On the receiving side we used the Google \pixelOld and \pixelNew.
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On the sending side we used the \intelBoth with internal and external \SI{2}{dBi} omnidirectional antennas.
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The antenna geometry and properties of the internal antenna are unknown.
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In total there are eight phone AP combinations.
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% TODO Table mit mean dist err, median dist err und mean RSSI
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% Erkenntnis 1: 9462 bessere schätzung, weniger Messungen die zu kurz sind; 8260 viele Messungen bei <16m sind zu kurz; Zusammenhang mit 15m wegen Sampling Rate?
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% Erkenntnis 2: Unterschied der Antennen bei RSSI minimal langweilig;
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% Erkenntnis 3: Antenne vs FTM: Keine Aussage möglich
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% Erkenntnis 4: Unterschied zwischen Pixel 2 und 3 ist nicht erkennbar
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\autoref{fig:DistMeasMeanNucPixel}~\subref{fig:DistMeasMeanNucPixel:a} shows the average measured distance per smartphone in respect to the ground truth distance.
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Likewise, \autoref{fig:DistMeasMeanNucPixel}~\subref{fig:DistMeasMeanNucPixel:b} depicts the average measured distance per access point.
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The corresponding values of these figures are shown in \autoref{tab:distvalues}.
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We compute the mean over the 140 FTM measurements denoted as $\bar{d}$ and its standard deviation.
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Because $\bar{d}$ can be larger or smaller than the true distance we use the difference between $\bar{d}$ and the true distance as error metric.
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However, when its necessary to quantify the error regardless of its direction the absolute difference is used.
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Interestingly, both the wireless cards and the Pixel devices exhibit some similar tendency regarding the measurement error.
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As seen in \autoref{fig:DistMeasMeanNucPixel}~\subref{fig:DistMeasMeanNucPixel:a} the \pixelOld tends to underestimate the distance.
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Only at \SI{6}{m} and \SI{10}{m} the estimated distance is slightly larger compared to the true distance.
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The overall error is mostly negative and the mean absolute error is $\SI{1}{m}$.
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Contrarily, the \pixelNew tends to overestimate the distance compared to the groundtruth distance.
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Here the mean absolute error is $\SI{1.4}{m}$.
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However, at the \SI{16}{m} mark the measured mean distance of the \pixelNew significantly increases.
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Computing the mean absolute error only in the interval of $[\SI{2}{m}, \SI{16}{m}]$ reduces the \pixelNew error to $\SI{0.6986}{m}$, at the same time the \pixelOld error changes negligible.
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While on average the standard deviation of the distance measurements are quite similar for both devices, the standard deviation for the \pixelNew is more stable.
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At \SI{16}{m} the \pixelOld stops to underestimate the distance and the measurements at \SI{18}{m} and \SI{20}{m} are quite close to the true distance.
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In contrast, the \pixelNew starts to increasingly overestimate the true distance which results in large error values ($\approx \SI{4}{m}$).
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The same behavior is observable for the \intelBoth cards.
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Again at \SI{16}{m} both cards start to overestimate the true distance.
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For distances smaller than \SI{16}{m} the \intelOld also underestimates the distance with a mean absolute error of \SI{1.11}{m} in that range.
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Like the \pixelNew the error increases for larger distances, however, somewhat smaller with $\approx \SI{2}{m}$.
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In total the \intelNew card tends to provide an accurate distance estimate but has some outliers at \SI{6}{m} and \SI{10}{m} but never underestimates the true distance.
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While the mean distance over many measurements is relevant for stationary measure points, in our scenario a pedestrian is moving with the smartphone.
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Therefore, only one or a few measurements can be observed at a given position.
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A more expressive visualization for this scenario is given with the CDF graph in \autoref{fig:DistMeasMeanNucPixel}~\subref{fig:DistMeasMeanNucPixel:c} which allows to reason about the underlying error distribution.
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Most striking is the curve of the \intelOld and \pixelOld combination with internal antenna (red dashed line).
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Firstly, about 80\% of the measurements have a negative error, \ie underestimate the true distance.
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Secondly, the curve indicates that the error distribution is a Gaussian mixture distribution with two modes at \SI{-3.201}{m} and \SI{0.0879}{m}, whereas the mode at \SI{-3.201}{m} provides about 60\% of the probability mass.
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The multimodality is greatly reduced by using the external antenna (orange dashed line), but still about 70\% of the measurements are smaller than the true distance.
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This indicates that the performance of this particular device combination could be improved by adding a constant factor of around \SI{1}{m}.
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However, using the same card together with the \pixelNew (red line) the error is already much smaller and only a small portion is negative.
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In this case no constant offset would significantly improve the measurements.
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Surprisingly, the error distribution of the \intelOld and \pixelNew combination with added external antennas (orange line) dramatically changes compared to the internal antenna.
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There are more negative error values and large positive errors are introduced, which where non-existent with the internal antenna setup.
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As a result no clear recommendation to either use the internal or external antennas with the \intelOld can be stated.
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While the external antenna significantly reduces negative errors of the \pixelOld it introduces large positive errors for the \pixelNew.
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At the same time the \pixelOld would perform reasonable well without external antennas.
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Underestimated distances are somewhat surprising, as only overestimated distances are expected with time based methods.
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Furthermore, underestimated measurements could result in negative distances which are hard to reason about.
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Therefore, one possible argument to choose the external antennas is to reduce the negative error while accepting some more positive errors.
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In the case of the \intelNew card the effect of the antennas is marginal.
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The error of the \pixelOld (blue dashed line) is primarily positive and mostly less than \SI{3}{m}.
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Using external antennas actually worsened the measurements producing much more negative errors.
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Note that this behavior is on the contrary to the error distributions of the \intelOld card.
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In contrast, the error of the \pixelNew with the \intelNew card is changes only insignificant with the antennas.
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While 50\% of the error is smaller than \SI{1.5}{m} with the external antenna (light green line), the error is smaller than \SI{2.5}{m} in the same range for the internal antenna (blue line).
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%TODO RSSI erwähnen
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In sum, with these results no clear tendency could be observed whether to use the internal or external antennas to reduce the error of the FTM measurements.
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Of course this is only true for this specific experiment, for different environmental conditions or sender and receiver positions the results may vary.
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More significant is the choice of the particular wireless card.
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Here, the \intelNew mainly gives better results compared to the \intelOld, \ie most of the errors are positive and in a range of up to \SI{5}{m}.
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Both the \pixelBoth produce similar results, but the \pixelOld tends to underestimate the distance more compared to the \pixelNew.
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Opposed to \etal{Ibrahim} \cite{ibrahim2018verification} findings no single constant offset which significantly improves the measurements across all device combinations could be found in our tests.
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However, the overall error of the device combinations is reasonable small and its distribution is mostly Gaussian-like, which justifies the basic applicability of the technique and devices for indoor positioning.
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\begin{figure}[ht]
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\centering
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\subfloat[]{\label{fig:DistMeasMeanNucPixel:a}\includegraphics[]{MeanDistPixel.pdf}}\hspace{0.5cm}
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\subfloat[]{\label{fig:DistMeasMeanNucPixel:b}\includegraphics[]{MeanDistIntel.pdf}}
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\par\medskip
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\subfloat[]{\label{fig:DistMeasMeanNucPixel:c}\includegraphics[]{DistErrorCdf.pdf}}
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\caption{\textbf{(a)} \textbf{(b)} the mean distance per smartphone and per access point, respectively. \textbf{(c)} the CDF of the measurement error for each device combination.}
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\label{fig:DistMeasMeanNucPixel}
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\end{figure}
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% Smartphones und Intel cards in einer table
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\begin{table}[ht]
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\renewcommand{\arraystretch}{1.2}
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\caption{The mean distance $\bar{d}$, standard deviation $\sigma$ and the error for each groundtruth point grouped by device. The error equals to $\bar{d}-\text{GT}$. All values are in meter.}
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\resizebox{\textwidth}{!}{%
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\begin{tabular}{@{}RRRRcRRRcRRRRcRRR@{}}
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\toprule
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\theadbf{GT} & \multicolumn{3}{c}{\bfseries Pixel 2 XL} & \phantom{a} & \multicolumn{3}{c}{\bfseries Pixel 3a} & \phantom{a} & \multicolumn{3}{c}{\bfseries AC 8260} & \phantom{a} & \multicolumn{3}{c}{\bfseries AC 9462} \\ \cmidrule{2-4} \cmidrule{6-8} \cmidrule{10-12} \cmidrule{14-16}
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~ & \thead{$\bar{d}$} & \thead{$\sigma$} & \thead{error} && \thead{$\bar{d}$} & \thead{$\sigma$} & \thead{error} && \thead{$\bar{d}$} & \thead{$\sigma$} & \thead{error} && \thead{$\bar{d}$} & \thead{$\sigma$} & \thead{error} \\ \midrule
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2 & 0.032 & 1.615 & -1.968 && 2.472 & 1.165 & 0.472 && 0.221 & 1.460 & -1.779 && 2.282 & 1.724 & 0.282 \\
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4 & 2.645 & 1.834 & -1.355 && 3.976 & 1.755 & -0.024 && 2.175 & 0.541 & -1.825 && 4.446 & 1.973 & 0.446 \\
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6 & 6.577 & 1.780 & 0.577 && 6.605 & 1.978 & 0.605 && 5.599 & 0.876 & -0.401 && 7.583 & 1.922 & 1.583 \\
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8 & 6.861 & 1.506 & -1.139 && 8.780 & 1.510 & 0.780 && 7.041 & 1.562 & -0.959 && 8.601 & 1.715 & 0.601 \\
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10 & 10.454 & 2.176 & 0.454 && 11.520 & 1.522 & 1.520 && 9.916 & 1.787 & -0.084 && 12.058 & 1.247 & 2.058 \\
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12 & 10.342 & 1.875 & -1.658 && 12.096 & 1.582 & 0.096 && 10.055 & 1.478 & -1.945 && 12.384 & 1.506 & 0.384 \\
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14 & 12.866 & 2.309 & -1.134 && 14.327 & 1.870 & 0.327 && 12.312 & 2.110 & -1.688 && 14.882 & 1.182 & 0.882 \\
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16 & 15.992 & 0.879 & -0.008 && 17.765 & 1.488 & 1.765 && 16.223 & 1.005 & 0.223 && 17.534 & 1.710 & 1.534 \\
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18 & 18.962 & 1.491 & 0.962 && 22.569 & 1.458 & 4.569 && 20.341 & 2.417 & 2.341 && 21.190 & 2.589 & 3.190 \\
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20 & 20.742 & 1.318 & 0.742 && 24.058 & 1.820 & 4.058 && 22.001 & 2.920 & 2.001 && 22.799 & 1.853 & 2.799 \\
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\bottomrule
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\end{tabular}}
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\label{tab:distvalues}
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\end{table}
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\subsection{Range Measurements in NLOS Scenario}
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%Während der posionierung ist an gewissen stellen eine systematische abweichung zum gt aufgefallen dies trat immer an zwei stellen auf, daraus folgender die hypthese das es irgendwie an dieser gegebenheit liegen muss. als folge daraus ist dann eben entstanden das wir die brandschutztüren gesehen haben und dann eine experiment aufgebaut haben um die hypthese zu messen, inwiefern sich die türen oder besser gesagt wie sich unterschiedliche wandmateriellien, insbesondere wenn diese so extrem wie hier sind, auf die FTM Messungen auswirken.
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%
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%rssi grafik lassen wir weg (bst2rssi.png) und schreiben das nur im text. müssen ja nur den sprung von 7 auf 8 beschreiben. interessanter sind die FTM Plots mit der Streuung (bst2ftm.png)
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During the analysis of the recorded data of the test walks presented below systematic and reproducible deviations of the estimated position to the groundtruth were found.
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These effects increased the error significantly and are bound to specific locations in the building.
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It is likely that environmental factors of the building at these locations affect the FTM distance measurement process.
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%Therefore, environmental factors of the building structure at these locations are likely to affect the FTM distance measurements.
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While it is well known that the environment will affect measurements, especially indoors, it is nevertheless interesting to analyses the underlying cause.
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It was noticed that the ranging measurements to one access point suddenly started to heavily overestimate the true distance.
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This effect occurs as soon as the pedestrians walks by a fire door.
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These heavy doors are about \SI{12}{cm} thick and made of metal.
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In the case of a fire outbreak these doors are automatically closed, but normally they are not closed and tucked away between walls.
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Whenever such fire door is in the line of sight between the access point and the smartphone the ranging error increases significantly.
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\begin{figure}[ht]
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\centering
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\begin{minipage}{.5\textwidth}
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\centering
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\subfloat[]{\label{fig:BSTExp:a}\includegraphics[width=\textwidth]{VersuchsaufbauBST1.png}}
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\end{minipage}%
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\begin{minipage}{.5\textwidth}
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\centering
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\subfloat[]{\label{fig:BSTExp:b}\includegraphics[width=0.8\textwidth]{VersuchsaufbauBST2.png}}
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\end{minipage}\par\medskip
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\caption{Test setups to evaluate the impact of fire doors (red lines) compared to regular walls (black lines). In \textbf{(a)} the measurement points are placed on a circle to keep the distance constant. The setup of \textbf{(b)} allows more measurement points. }
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\label{fig:BSTExp}
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\end{figure}
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To quantify the impact of these fire doors on the FTM measurement we created two test setups as seen schematically in \autoref{fig:BSTExp}.
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In the first experiment, as shown in \autoref{fig:BSTExp:a}, we used the same access point position as in the test walks of the next section.
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We placed seven measurement points onto a circle so that most of these points are located in the main hallway.
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The radius of the circle is \SI{10}{m} and measure point 1 to 3 are located in the shadow of the fire door while points 4 to 7 are not.
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At every point we placed the \pixelOld on a metal stand \SI{1.05}{m} above the floor and recored FTM distance measurements for \SI{60}{s} with one measurement every \SI{200}{ms}, which results in around 255 successful distance measurements per point.
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%Note that this number is the mean of all successful measurements and the theoretical number of total measurements should be 300.
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Note that this number differs from the theoretical possible 300 measurements because some measurements fail due to NLOS.
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\begin{figure}[ht]
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\centering
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\subfloat[]{\label{fig:Bst1Results:a}\includegraphics[]{BSTPlot1.pdf}}\hspace{0.25cm}
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\subfloat[]{\label{fig:Bst1Results:b}\includegraphics[]{BSTPlot1Rssi.pdf}}
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\caption{Results for test setup as seen in \figref{fig:BSTExp:a}. \textbf{(a)} While the true distance (black line) is constant the mean measured distance (blue line) is not. At point 2 a bimodal distribution of measurements is apparent. If only the larger mode is used the error decreases monotonously (dashed cyan line). \textbf{(b)} Corresponding RSSI values at each measurement point.}
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\label{fig:Bst1Results}
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\end{figure}
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The distance measurement results are depicted in \autoref{fig:Bst1Results:a}.
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The error in the shadow area is larger compared to the points not shadowed by the fire door.
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While the mean distances at point 1 and 2 are off by around \SI{10}{m} the error decreases monotonously for the following points.
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Point 5 to 7 are not affected by the fire wall with a mean error of \SI{0.8}{m}.
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But the deviation at point 4, which signal path is quite close to the door, is somewhat larger.
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The distribution of the distances recorded at point 2 has two modes at \SI{16.55}{m} and \SI{34.12}{m}, which are clearly visible in the plot.
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This bimodal distribution increases the mean distance significantly, if, instead of the mean, the distance at the larger mode (\SI{16.55}{m}) is used, then the overall curve is monotonously decreasing (cyan dashed line).
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The mean RSSI, as shown in \autoref{fig:Bst1Results:b}, exhibits the same tendency as the mean distance.
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At points 1, 2 and 3 the RSSI is decreasing with a minimum at point 4 and stable for the remaining points.
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This suggest that the RSSI correlates somewhat with the measured distances in this scenario, except at point 4 where the RSSI is stronger than every other point.
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However, this could be caused by measurement inaccuracy of the smartphone chip and might be a nonrecurring outlier.
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The RSSI compared to FTM measurements have insignificant small variance in this test and very stable.
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Notice that point 2, 3, 5 and 6 are located near stairways with massive metal railings.
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It is expected that the stairways also add measurement noise, however, we still included them deliberately in this test setup as they are nonetheless of real interest because they also appear in the test walks.
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In order to evaluate the effect of the fire door exclusively, we build a second test setup at a corner office located next to a fire door on the same floor.
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As seen in \autoref{fig:BSTExp:b} the measurement points are placed parallel to the wall, due to structural limitations it was not possible to keep the distance to the AP constant.
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The groundtruth was obtained by carefully measuring the distances to walls and taking the line of sight distance from a true to scale map.
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\begin{figure}[ht]
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\centering
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\subfloat[]{\label{fig:Bst2Results:a}\includegraphics[]{BSTPlot2.pdf}}\hspace{0.25cm}
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\subfloat[]{\label{fig:Bst2Results:b}\includegraphics[]{BSTPlot2Rssi.pdf}}
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\label{fig:Bst2Results}
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\caption{Results for setup as seen in \figref{fig:BSTExp:b}. While the groundtruth distance only varies slightly (black line) the mean measured distance (blue line) varies greatly depending on the relative position to the fire door.}
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\end{figure}
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\subsection{Positioning Environment}
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\begin{itemize}
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\item Beschreibe Gebäude - inkl HLS Räume!
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\item beschreibe ground truth pfade
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\item access point positionen mit DOP analyse
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\item wie sind wir gelaufen / testbedingungen... wie wurde GT gemessen usw. app etc pp.
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\end{itemize}
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All experiments were done in our university building.
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The before mentioned Intel NUCs were deployed, because the existing WiFi infrastructure does not support the FTM protocol.
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While the positions of the access points where chosen with localization in mind, the actual positions mimic the placement of access points for network infrastructure.
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In contrast to regular stationary access points which are usually mounted on walls or ceilings, our Intel NUCs were placed on tables for practical reasons.
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\subsection{Results for Multilateration}
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zunächst wird das einfachste und nahliegendste verfahren untersucht um die performance von ftm und rssi gegenüberzustellen.
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Figure 3 rote Bereiche - Heizung Lüftung Sanitär (HLS) Räume schirmen Radio Signale komplett ab! Wenn man dahinter steht, bekommt man gar nichts mehr vom AP mit. Wenn man sich nun die AP positionen ansieht, welche wir gewählt haben, fällt auf das wir Idioten sind. Anhand eine Triangulation Loc + Fehler Plots erklären.
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\begin{itemize}
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\item Parameter einführen und erklären
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\item Unterschied FTM und RSSI bei diesem Verfahren
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\item Positioning Error
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\item Wie sieht der geschätzte Pfad aus
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\item FTM ist nicht wie erwartet mega viel besser als RSSI. die simple literation glättet einfach gar nichts, weswegen... (hier begründung einfügen)
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\item DOP Grafik -> später vom particel filter referenzieren.
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\end{itemize}
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wir bekommen hier also das gefühl, das ftm irgendwie besser sein muss, aber können es noch nicht wirklich nutzen. weshalb nun der probabilistische approach angesehen wird.
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\subsection{Results for Probabilistic Approach}
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multilateration verfügt über keinerlei glättung, das einfach probablistische verfahren bietet das. verlgeicht man fig. x und fig. y kann man das schön sehen.
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\begin{itemize}
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\item Parameter einführen und erklären
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\item Unterschied FTM und RSSI bei diesem Verfahren
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\item Positioning Error
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\item Wie sieht der geschätzte Pfad aus
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\item FTM setzt sich langsam ab und wird ein gutes stück besser als Rssi
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\end{itemize}
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\subsection{Results for Particle Filtering}
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der einsatz der probablistischen methode sieht weitaus besser azs als multilateration weil wir eine glättung der daten ermöglichen. es fehlt aber informationen über die vergangenheit. der particle filter bietet das.
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\begin{itemize}
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\item Parameter einführen und erklären
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\subitem filter updated pro neuer messung. kann man natürlich auch anders machen. nachdem wir aber eine so simple transition haben, ist es egal.
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\item Unterschied FTM und RSSI bei diesem Verfahren
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\item Positioning Error
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\item Wie sieht der geschätzte Pfad aus
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\item Hier werden die Ergebnisse langsam richtig gut. Also FTM ist weitaus besser als RSSI. Warum ist das so? (Filter hat die Vergangenheit mit drin, FTM ist somit auf Dauer stabiler und streut deswegen nicht so stark wie RSSI).
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\end{itemize}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=1\textwidth]{Path2_Walk0_FTM.png}
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\caption{Path 2 FTM, Pixel 2 mean 4.94778 stdDev 2.49081 median 4.88544 count 249 }
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\end{figure}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=1\textwidth]{Path2_Walk0_FTM_Error.png}
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\caption{Path 2 Error FTM, Pixel 2 }
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\end{figure}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=1\textwidth]{Path2_Walk0_RSSI.png}
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\caption{Path 2 RSSI, Pixel 2 mean 5.33965 stdDev 2.68662 median 5.22802 count 249}
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\end{figure}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=1\textwidth]{Path2_Walk0_RSSI_Error.png}
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\caption{Path 2 Error RSSI, Pixel 2}
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\end{figure}
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\begin{figure}[ht]
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\centering
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\includegraphics[width=1\textwidth]{Path2_Walk0_FTM_RSSI_Error.png}
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\caption{Path 2 Error FTM / RSSI, Pixel 2}
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\end{figure}
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\subsection{Comparison and Discussion}
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Hier vergleichen wie sich die einzelen Verfahren untereinander unterscheiden und welche Vor / Nachteile sie haben. Jeweils für RSSI und FTM. (Vorher haben wir RSSI und FTM gegenübergestellt innerhalb der Verfahren und jetzt stellen wir die einzelnen Verfahren gegenüber und diskutieren deren Unterschied in Bezug auf die WI-Fi methoden)
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\begin{itemize}
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\item multilateration ist an sich schon ein schlechtes verfahren, man kann aber sehen das ftm schon etwas besser wird. verfolgt man den gedanken über die weiteren verfahren, sieht man schnell wie sich FTM von der Leistung her absetzt und durch die besseren verfahren auch eine besser lokalisiierungsleistung bringt.
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\item Tabelle, wo alle Ergebnisse nochmal zusammen sind.
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\item Wichtige Erkenntnisse:
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\subitem wenn man sehr nah dran ist, ist die messung nicht wirklich gut bei FTM.
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\subitem FTM ist vom setup weitaus einfacher als rssi, weil es die dämpfung etc. pp nicht so wichtig nimmt.
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\end{itemize}
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