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MBulli
2018-03-12 23:24:55 +01:00
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tex/chapters/realworld.tex
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@@ -17,26 +17,26 @@ The bivariate state estimation was calculated whenever a step was recognized, ab
\begin{figure}
\input{gfx/walk.tex}
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of the walk. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides an high error compared to the ground truth (solid black), while the BoxKDE approach (orange) does not. }
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of the walk. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides a high error compared to the ground truth (solid black), while the BoxKDE approach (orange) does not. }
\label{fig:realWorldMulti}
\end{figure}
%
Fig.~\ref{fig:realWorldMulti} illustrates a frequently occurring situation, where the particle set splits apart, due to uncertain measurements and multiple possible walking directions.
\figref{fig:realWorldMulti} illustrates a frequently occurring situation, where the particle set splits apart, due to uncertain measurements and multiple possible walking directions.
This results in a bimodal posterior distribution, which reaches its maximum distances between the modes at \SI{13.4}{\second} (black dotted line).
Thus estimating the most probable state over time using the weighted-average results in the blue line, describing the pedestrian's position to be somewhere outside the building (light green area).
In contrast, the here proposed method (orange line) is able to retrieve a good estimate compared to the ground truth path shown by the black solid line.
Due to a right turn, the distribution gets unimodal after \SI{20.8}{\second}.
This happens since the lower red particles are walking against a wall and are punished with a low weight.
This happens since the lower red particles are walking against a wall, and therefore are punished with a low weight.
This example highlights the main benefits using our approach.
While being fast enough to be computed in real time, the proposed method reduces the estimation error of the state in this situation, as it is possible to distinguish the two modes of the density.
It is clearly visible, that this enables the system to recover the real state if multimodalities arise.
However, in situations with highly uncertain measurements, the estimation error could further increase since the real estimate is not equal to the best estimate, \ie{} the real position of the pedestrian.
The error over time for different estimation methods of the complete walk can be seen in fig. \ref{fig:realWorldTime}.
The error over time for different estimation methods of the complete walk can be seen in \figref{fig:realWorldTime}.
It is given by calculating the distance between estimation and ground truth at a specific time $t$.
Estimates provided by simply choosing the maximum particle stand out the most.
As one could have expected beforehand, this method provides many strong peaks through continuously jumping between single particles.
As expected beforehand, this method provides many strong peaks through continuously jumping between single particles.
Additionally, in most real world scenarios many particles share the same weight and thus multiple highest-weighted particles exist.
\begin{figure}
@@ -45,7 +45,7 @@ Additionally, in most real world scenarios many particles share the same weight
\label{fig:realWorldTime}
\end{figure}
Further investigating fig. \ref{fig:realWorldTime}, the BoxKDE performs slightly better than the weighted-average.
Further investigating \figref{fig:realWorldTime}, the BoxKDE performs slightly better than the weighted-average.
However after deploying \SI{100} Monte Carlo runs, the difference becomes insignificant.
The main reason for this are again multimodalities caused by faulty or delayed measurements, especially when entering or leaving rooms.
Within our experiments the problem occurred due to slow and attenuated Wi-Fi signals inside thick-walled rooms.
@@ -54,7 +54,7 @@ Therefore, the average between the modes of the distribution is often closer to
With new measurements coming from the hallway or other parts of the building, the distribution and thus the estimation are able to recover.
Nevertheless, it can be seen that our approach is able to resolve multimodalities even under real world conditions.
It does not always provide the lowest error, since it depends more on an accurate sensor model than a weighted-average approach, but is very suitable as a good indicator about the real performance of a sensor fusion system.
It does not always provide the lowest error, since it depends more on an accurate sensor model than a weighted-average approach, but it is very suitable as a good indicator about the real performance of a sensor fusion system.
In the here shown examples we only searched for a global maxima, even though the BoxKDE approach opens a wide range of other possibilities for finding a best estimate.
%springt nicht so viel wie maximum