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final version paper

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toni
2017-05-12 16:37:19 +02:00
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14
tex/chapters/method.tex
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@@ -82,7 +82,7 @@ Further, the number of particles in each mode can be selected independently of t
Algorithm \ref{alg:immpf} shows the complete IMMPF procedure in detail.
As prior knowledge, $M$ initial probabilities $P(m_1 \mid \mObsVec_{1})$ and initial distributions $p(\mStateVec_{1} \mid m_1, \mObsVec_{1})$ providing a particle set $\{W^i_{1}, \vec{X}^i_{1} \}_{i=1}^N$ are available.
The mixing step requires that the independently running filtering processes are all finished.
A new iteration $t$ is initiated by the mixing step (line 1 to 7) and requires that the independently running filters (line 8 to 15) have all finished processing within the previous iteration $t-1$.
\begin{algorithm}[t]
\caption{IMMPF Algorithm}
@@ -118,9 +118,9 @@ Within the IMMPF we utilize the restrictive graph-based filter as the \textit{do
Due to its robustness and good diversity the simple, more permissive filter, is then used as \textit{support} for possible sample impoverishment.
The names dominant and support are now applied as synonyms for the respective filters used as modes within the IMMPF.
As a reminder, both filters (modes) are running in parallel for the entire estimation life cycle.
If we recognize that the dominant filter diverges from the supporting filter and thus got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter.
As seen before, the Markov transition matrix $\Pi_t$ provides the probability $P(m_{t+1} \mid m_t)$ for transitioning between modes.
As a reminder, both filters (modes) are running in parallel for the entire IMMPF life cycle.
If we recognize that the dominant filter diverges from the supporting filter and thus probably got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter.
As seen before, the Markov transition matrix $\Pi_t$ provides the probability $P(m_{t+1} \mid m_t)$ for transitioning between both modes.
%In our approach those modes are the dominant graph-based filter and the supporting simple filter.
The dominant filter's probability to draw particles from its own posterior is given by the positive exponential distribution
%
@@ -135,11 +135,11 @@ If the Kullback-Leibler divergence $D_{\text{KL}}$ increases to a certain point,
$\lambda$ depends highly on the respective filter models and is therefore chosen heuristically.
In most cases $\lambda$ tends to be somewhere between $0.01$ and $0.10$.
However, \eqref{equ:KLD} only works reliable if the measurement noise is within reasonable limits, because the support filter using the simple transition depends solely on them.
However, \eqref{equ:KLD} only works reliably if the measurement noise is within reasonable limits, because the support filter using the simple transition depends solely on them.
Especially \docWIFI{} serves as the main source for estimation and thus attenuated or bad \docWIFI{} readings are causing bad estimation results for the supporting filter.
This further leads to a growing $D_{\text{KL}}$, even if the dominant filter provides a good position estimation.
In such scenarios a lower diversity and higher focus of the particle set, as given by the dominant filter, is required.
We achieves this by introducing a \docWIFI{} quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa.
We achieve this by introducing a \docWIFI{} quality factor, allowing the support filter to pick particles from the dominant filter and prevent the later from doing it vice versa.
The quality factor is defined by
%
\begin{equation}
@@ -182,7 +182,7 @@ Considering the measures \eqref{equ:KLD} and \eqref{eq:wifiQuality} presented ab
This matrix is the centrepiece of our approach.
It is responsible for controlling and satisfying the need of diversity and the need of focus for the whole localisation approach.
How $\Pi_t$ works is straightforward.
If the dominant graph-based filter suffers from sample impoverishment (get stuck or lose track), the probability in $[\Pi_t]_{12} = (1 - f(D_{\text{KL}}))$ increases with diverging support filter.
If the dominant graph-based filter suffers from sample impoverishment (get stuck or lost track), the probability in $[\Pi_t]_{12} = (1 - f(D_{\text{KL}}))$ increases with diverging support filter.
Consequently, the number of particles, the dominant filter draws from the supporting filter, also increases by $[\Pi_t]_{12} \cdot 100\%$.
Similar behaviour applies to the \docWIFI{} quality factor $q(\mObsVec_t^{\mRssiVec_\text{wifi}})$.
If the quality is low, the supporting filter regains focus by obtaining particles from the dominant's posterior.