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added missing legend to gfx

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fixed some typos and refactored some sentences
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FrankE
2016-02-15 17:11:03 +01:00
parent ac542ba634
commit 54ab3d8dbe
9 changed files with 124 additions and 75 deletions
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9
tex/chapters/sensors.tex
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@@ -36,10 +36,10 @@
%
In \refeq{eq:baroTransition}, $b$ denotes the usual pressure change in $\frac{\text{hPa}}{\text{m}}$.
The evaluation, following the transition, compares the predicted relative pressure with the observed
one using a normal distribution utilizing the previously estimated $\sigma_\text{baro}$:
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}).
p(\mObsVec_t \mid \mStateVec_t)_\text{baro} = \mathcal{N}(\mObs_t^{\mObsPressure} \mid \mState_t^{\mStatePressure}, \sigma_\text{baro}^2).
\label{eq:baroEval}
\end{equation}
@@ -59,7 +59,8 @@
P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF,
\end{equation}
%
The probability to measure this prediction given a location is:
Assuming statistical independence of all \docAPshort{}s,
the probability to measure their predictions at a given location is:
%
\begin{equation}
\mProb(\mObsVec_t \mid \mStateVec_t)_\text{wifi} =
@@ -82,7 +83,7 @@
\subsection{Step- \& Turn-Detection}
Step- and turn-detection uses the smartphone's IMU and is implemented as described in \cite{Ebner-15}.
Step- and turn-detection use the smartphone's IMU and are implemented as described in \cite{Ebner-15}.
%
However, a big disadvantage of using the state transition as proposal distribution is the high possibility of sample
impoverishment due to a small measurement noise. This happens since accurate observations result in high peaks