\section{Experiments}

All upcoming experiments were carried out on four floors of a \SI{77}{m} x \SI{55}{m} sized faculty building. 
It includes several staircases and elevators and has a ceiling height of about \SI{3}{m}. 
Nevertheless, the grid was generated for the complete campus and thus outdoor areas like the courtyard are also walkable.
As Wi-Fi is attenuated by obstacles and walls, it does not provide a consistent quality over the complete building. 
In fig. \ref{} we illustrate the quality obtained by the wall attenuation factor model presented earlier.
Here, green indicates a high coverage and thus a good quality for localisation, while red does the opposite.
To obtain this information we measured Wi-Fi at $666$ different points and interpolated the results as described in \cite{}.
As mentioned before, we omit any time-consuming calibration processes and use the same values for all access-points. That would be $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}, \mWAF_{\text{wifi}} = \SI{8}{\dB}$.
The position of the access-points (about five per floor) is known beforehand. 
Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures.

We arranged three distinct walks (see also fig. \ref{}).
The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only. 
The computation was done offline as described in algorithm \ref{}. 
For each walk we deployed $xx$ MC runs using 5000 Particles.
Instead of an initial position and heading, all walks start with a uniform distribution (random position and heading) as prior.
For the  filtering we used $\sigma_\text{wifi} = 8.0$ as uncertainties, both growing with each measurement's age.
While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically. 
The step size $\mStepSize$ for the transition was configured to be \SI{70}{\centimeter} with an allowed derivation of \SI{10}{\percent}. The heading deviation was set to \SI{25}{\degree}. 

KLD with normal dist and kernel density drawing from grid.


The ground truth is measured by recording a timestamp at marked spots on the walking route. When passing a marker, the pedestrian clicked a button on the smartphone application. 
Between two consecutive points, a constant movement speed is assumed.
Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for error measurements. 
The approximation error is then calculated by comparing the interpolated ground truth position with the current estimation \cite{Fetzer2016OMC}.





% allgemeine infos über pfade und gebäude. wo 
% bild: mit pfaden drauf und eventl. wifi qualität in jeweiligen bereichen? (kann frank das)

% gewählte parameter (auch mal die optimieren wifi parameter testen)

% wie für die kld gezogen? begründen warum wir nun keine parzenschätzung machen (weil ähnliche ergebnisse)

% ground truth

% maß für die streuung der verteilung (diversity von partikeln)

% zeigen das es stucken verhindert (eventl. hier eine andere aufnahme die mitten drinnen stecken bleibt)
% bild: stucken im raum + nicht mehr stucken im raum

% zeigen das schlechtes wi-fi (zu hohe diversity) behoben wird. 
% bild: lauf auf der rechten seite des gebäudes zeige mit und ohne wifi faktor (schlechtes wifi einzeichnen)

% zeigen das immpf nicht viel schlechter als normaler pf (ohne stucken) ist. 
% bild: er schafft es nicht die treppe rauf + er schafft es immpf + er schafft es normal filter

% gegenüberstellung aller pfade und werte in tabelle
