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@@ -32,7 +32,7 @@ As the Galaxy's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band
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Additionally, the Galaxy's barometer sensor provides fare more inaccurate and less frequent readings than the Nexus does.
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This results in a better localisation using the Nexus smartphone.
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The computation for both filtering and smoothing was done offline using the aforementioned \mbox{CONDENSATION} algorithm and multinomal (cumulative) resampling.
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For each path we deployed 10 MC runs using \SI{2500}{} particles and $500$ sample realisations for BS.
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For each path we deployed 10 MC runs using \SI{2500}{} particles. BS uses $500$ sample realisations drawn with a cumulative frequency.
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%However, the filter itself would be fast enough to run on the smartphone itself ($ \approx \SI{100}{\milli\second} $ per transition, single-core Intel\textsuperscript{\textregistered} Atom{\texttrademark} C2750).
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%The computational times of the different smoothing algorithm will be discussed later.
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Unless explicitly stated, the state was estimated using the weighted arithmetic mean of the particle set.
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@@ -57,11 +57,10 @@ Walking upstairs sets $ \mu_{\text{step}} = \SI{0.4}{\meter}$, $ \sigma_{\text{s
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%kurz zeigen das activity recognition was bringt
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\begin{figure}
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\input{gfx/activity/activity_over_time}
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\caption{activity recognition}
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\caption{The activities recognized for path 4. The misdetection in seg. 2 is cause by faulty pressure readings.}
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\label{fig:activityRecognition}
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\end{figure}
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By adding the activity recognition to the system of \cite{Ebner-16}, we are able to further improve the overall localisation results.
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The approximation error decreases by an average of \SI{XX}{\centimeter} for all 4 paths on 10 MC runs.
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By adding the activity recognition the approximation error of the filter decreases by an average of \SI{XX}{\centimeter} for all 4 paths.
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Due to this additional knowledge, the state transition samples mostly depending upon the current activity and therefore limits the possibility of false floor changes.
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Fig. \ref{fig:activityRecognition} shows the recognized activities for path 4 using the Nexus 6.
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Despite a short misdetection in seg. 2, caused by faulty pressure readings, the recognition can be considered to be very robust and accurate.
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@@ -73,7 +72,7 @@ Thus, we calculate only the positional error between estimation and ground truth
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%
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\begin{figure}
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\input{gfx/particles/particles}
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\caption{particles. green = avg50, black = avg. gnuplot zickt bei der legende}
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\caption{Comparison between the filtered and FBS particle set. Both have identical positions and are recorded at the same time step on path 4. The black dot indicates the estimation using the weighted arithmetic mean of all particles. The different colours represent the current weight of a certain particle.}
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\label{fig:particles}
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\end{figure}
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In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position.
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@@ -120,34 +119,37 @@ For better distinction, the path was divided into $10$ individual segments.
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%
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\begin{figure}
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\input{gfx/eval/lag_path4_comp/path4_lag_comp}
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\caption{Hier muss ich noch was schreiben. Bin aber seeeehr muede. Geh jetzt ins Bett. Nachti.}
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\caption{Estimation results on path 4 for the filter and both smoothers using fixed-lag smoothing with $\tau = 5$. For a better visualisation, the segments are divided using an outline of alternating grey levels. The corresponding segment-error can be seen in fig. \ref{fig:lag_error_path4}.}
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\label{fig:lag_comp_path4}
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\end{figure}
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\begin{figure}
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\input{gfx/eval/lag_path4_comp/error_timed}
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\caption{Hier muss ich noch was schreiben. Bin aber seeeehr muede. Geh jetzt ins Bett. Nachti.}
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\caption{Error development while walking along Path 4 using the Nexus 6. Especially in segments including floor changes, the error is reduced visibly by using smoothing methods.}
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\label{fig:lag_error_path4}
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\end{figure}
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%
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Again it can be observed, that both smoother enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 9).
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Besides the positional quality, also the timely error could be reduced clearly.
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The BS provides an overall approximation error of $\SI{4.86}{\meter}$ for the Galaxy and $\SI{2.97}{\meter}$ for the Nexus by filtering with $\SI{5.68}{\meter}$ and $\SI{3.15}{\meter}$ respectively.
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Whereas FBS ..
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Again it can be observed, that both smoother enable a better overall estimation especially in areas where the user is changing floors (cf. fig. \ref{fig:lag_error_path4} seg. 4, 7).
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Immediately after the first floor change, a long and straight walk down the hallway follows.
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While the Wi-Fi component pulls the pedestrian into the rooms on the right side, the actual walking route was located on the left side of the floor (see ground truth in fig. \ref{fig:lag_comp_path4} seg. 6).
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Here, the BS is able to slightly improve the path, whereas the FBS follows the filtering until the upcoming staircase provides the necessary information for adjustments.
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%It follows a critical area with high errors and multimodalities.
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%Due to an in-house exhibition during the time of recording, we had to leave the ground truth by a few meters and Wi-Fi was strongly attenuated.
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By looking at fig. \ref{fig:lag_comp_path4} seg. 9 it seems that both smoothing methods are highly improving the error.
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However, the approximation error in this area is similar to the filter and only the positional error decreases.
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This timely error is caused by a phenomenon we call Wi-Fi jump.
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Especially in seg. 8 and 9 a big crowd was gathered and highly attenuated the Wi-Fi signal.
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For an excessive amount of time, the absolute location estimated by the Wi-Fi component got stuck in the middle of seg. 8 and therefore delayed the estimation.
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The next viable measurements were then provided at the end of seg. 9.
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This suggests that the here presented smoothing transition is able to improve the estimated path visibly, but does not compensate for those jumps in a timely manner.
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Finally, the BS provides an approximation error alongside all paths of $\SI{6.48}{\meter}$ for the Galaxy and $\SI{4.47}{\meter}$ for the Nexus by filtering with $\SI{7.92}{\meter}$ and $\SI{5.50}{\meter}$ respectively.
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Whereas FBS improves the Galaxy's estimation from $\SI{7.73}{\meter}$ to $\SI{6.68}{\meter}$ and from $\SI{5.66}{\meter}$ to $\SI{4.80}{\meter}$ for the Nexus.
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As stated before, the main advantage of BS over FBS is the better computational time by just using a sub-set of particles for calculations.
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is not able to reduce the filtering error, obtaining $\SI{5.59}{\meter}$ using the Nexus and $\SI{3.12}{\meter}$ the Galaxy.
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%However, this does not mean, that the FBS is unpracticable for problems of fixed-lag smoothing.
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%By looking at the data in detail, high errors similar as seen in fig. \ref{fig:lag_error_path4} occur on path 3, which cause the estimation to behave more natural instead of walking the supposed path.
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%This phenomena could be observed for both smoothers respectively.
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%Also note the difference between this error, including timely information, and the positional error used before.
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%The median errors for all conducted walks are listed in table \ref{}.
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Similar to fixed-interval smoothing, decreasing the number of particles does not necessarily worsen the estimation.
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Reducing the number of particles down to $500$ does not necessarily worsen the estimation.
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In most cases smoothing compensates for this reduction and maintains the good results.
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%For example estimating path for using \SI{50}{particles} results in an approximation error for BS of \SI{}{\meter}.
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%lag vergrößern was passiert beschreiben
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Besides changing the number of particles, it is also possible the variate the lag.
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As one would expect, increasing the lag causes the smoothed estimation to approach the results provided by fixed-interval smoothing.
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This can be verified by looking at fig. \ref{}, which is a detailed view of segment XX of path 4 (cf. fig. \ref{fig:intcomp}).
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%This can be verified by looking at fig. \ref{}, which is a detailed view of segment XX of path 4 (cf. fig. \ref{fig:intcomp}).
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It is obvious that a lag of \SI{30}{} time steps has access to much more future observations and is therefore able to obtain such a result.
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Considering an update interval of \SI{500}{\milli\second}, a lag of \SI{30}{} would however mean that the smoother is \SI{15}{\second} behind the filter.
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Nevertheless, there are practical applications like accurately verifying hit checkpoints or continuously optimizing a recurring segment of the path.
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toni