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changes by toni

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Toni
2016-02-29 12:03:57 +01:00
parent 6ef06459cb
commit cabf60c851
5 changed files with 26 additions and 29 deletions
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14
tex/chapters/sensors.tex
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@@ -9,9 +9,9 @@
However, due to noisy sensors, more than one reading is required to estimate the relative base.
Harnessing the usual setup time of a navigation-system (route calculation, user checking the route, etc.)
we use the average of all barometer readings during this timeframe as estimated base $\overline{\mObsPressure}$.
Moreover, it is often necessary to omit some initial sensors readings, as the smartphone's sensor needs some time
to settle. Besides, we use the setup timeframe to estimate the sensors uncertainty $\sigma_\text{baro}$ for later
use within the evaluation. Fig. \ref{fig:baroSetupError} depicts actual sensor-readings including aforementioned
Moreover, it is often necessary to omit some initial sensor readings, as the smartphone's sensor needs some time
to settle. Besides, we use the setup timeframe to estimate the sensor's uncertainty $\sigma_\text{baro}$ for later
use within the evaluation step. Fig. \ref{fig:baroSetupError} depicts actual sensor readings including aforementioned
error conditions.
%
\begin{figure}
@@ -31,7 +31,7 @@
\Delta z = \mState_{t-1}^{z} - \mState_{t}^z
,\enskip
b \in \R
.
\enspace .
\label{eq:baroTransition}
\end{equation}
%
@@ -40,7 +40,7 @@
one using a normal distribution with the previously estimated $\sigma_\text{baro}$:
%
\begin{equation}
p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2).
p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2) \enspace.
\label{eq:baroEval}
\end{equation}
%
@@ -55,7 +55,7 @@
\docAPshort{} and the number of floors $\Delta f$ between the \docAPshort{} and the state-in-question:
%
\begin{equation}
P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF,
P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace ,
\end{equation}
%
Assuming statistical independence of all \docAPshort{}s,
@@ -63,7 +63,7 @@
%
\begin{equation}
\mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} =
\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2).
\prod\limits_{i=1}^{n} \mathcal{N}(\mRssi_\text{wifi}^{i} \mid P_{r}(\mMdlDist_{i}, \Delta{f_{i}}), \sigma_{\text{wifi}}^2) \enspace .
\label{eq:wifiTotal}
\end{equation}
%