FHWS/Fusion2016
Archived
3
0
Fork 0
Code Issues 1 Pull Requests Releases Wiki Activity

updated tex. sensors done.

Browse Source
This commit is contained in:
Toni
2016-02-12 15:40:52 +01:00
parent f0215731ce
commit 6b02336277
6 changed files with 40 additions and 54 deletions
Download Patch File Download Diff File Expand all files Collapse all files

11
tex/chapters/system.tex
View File

@@ -28,14 +28,14 @@ It should be noted, that we also include the current observation $\mObsVec_{t}$
Containing all relevant sensor measurements to evaluate the current state, the observation vector is defined as follows:
%
\begin{equation}
\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{ib}, \mObsHeading, \mObsPressure) \enspace,
\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{ib}, \mObsHeading, \mObsSteps, \mObsPressure) \enspace,
\end{equation}
%
where $\mRssiVec_\text{wifi}$ is the Wi-Fi and $\mRssiVec_\text{ib}$ the iBeacon signal strength vector.
The information, if a step or turn was detected, is given as a Boolean value.
\commentByToni{Wie sieht die Observation nun genau aus? Fehlt da nicht Step und Turn?}
Finally, $\mObsPressure$ is the relative barometric pressure referring to some fixed point in time.
For incorporating the highly different sensor types, one should refer to the process of probabilistic sensor fusion \cite{}.
Finally, $\mObsPressure$ is the relative barometric pressure with respect to some fixed point in time.
For incorporating the highly different sensor types, one should refer to the process of probabilistic sensor fusion \cite{Khaleghi2013}.
By assuming statistical independence of all sensor models, the probability density of the state evaluation is given by
%
\begin{equation}
@@ -51,6 +51,9 @@ By assuming statistical independence of all sensor models, the probability densi
Here, every single component refers to a probabilistic sensor model.
The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$, whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for iBeacons and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for Wi-Fi.
\todo{art unseres particle filters hier einfuehren. transition als proposal. dann kann man spaeter bei step und turn besser begruenden warum wir es in die transition ziehen.}
It is well known that finding analytic solutions for densities is very difficult and they only exit in rare cases.
Therefore, numerical solutions like Gaussian filters or the broad class of Monte Carlo methods are deployed \cite{sarkka2013bayesian}.
Since we assume that indoor localisation is a time-sequential, non-linear and non-Gaussian process, a particle filter for approximating the posterior distribution is chosen.
Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t})$ is used as proposal distribution, what is also known as CONDENSATION algorithm \cite{Isard98:CCD}.