24 lines
1.9 KiB
TeX
24 lines
1.9 KiB
TeX
\subsection{Fixed-lag smoothing}
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Within \cite{fetzer-16} we added an additional smoothing step to the localisation procedure.
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In contrast to normal filtering, smoothing methods are able to incorporate future measurements instead of just using current and past data.
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Therefore, they are able to compute probability distributions in the form of $p(\mStateVec_t \mid \mObsVec_{1:T})$.
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Especially interesting for real-time applications is the so-called fixed-lag smoothing.
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In fixed-lag smoothing, one tries to estimate the current state, given measurements up to a time $t + \tau$, where $\tau$ is a predefined lag.
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By running backwards in time, they are able to remove multimodalities and improve the overall localisation result.
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We can distinguish between two different smoothing algorithms: Forward-backward smoothing \cite{doucet2000} and backward simulation \cite{Godsill04:MCS}.
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Both perform very similar and are reweighting possible states based on a smoothing transition model.
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The smoothing transition model calculates the probability of being in a state $\vec{q}_{t+1}$ in regard to previous states and the pedestrian's walking behaviour.
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Therefore, we compare the distance, angle and height between $\vec{q}_{t+1}$ and $\vec{q}_{t}$ in regard to the measurements gettered at time $t$.
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The resulting likelihood is then used for reweighting.
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%By writing
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%\begin{equation}
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%p(\vec{q}_{t+1} \mid \vec{q}_t, \mObsVec_t)_{\text{step}} = \mathcal{N}(\Delta d_t \mid \mu_{\text{step}}, \sigma_{\text{step}}^2)
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%\label{eq:smoothingTransDistance}
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%\end{equation}
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%we receive a statement about how likely it is to cover a distance $\Delta d_t$ between two states $\vec{q}_{t+1}$ and $\vec{q}_{t}$.
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%In the easiest case, $\Delta d_t$ is the euclidean distance between two states.
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%The average step length $\mu_{\text{step}}$ is based on the pedestrian's walking speed and $\sigma_{\text{step}}^2$ denotes the step length's variance.
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