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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/grid.tex
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@@ -38,14 +38,14 @@
%\commentByFrank{eingefuehrt}
and walking along adjacent nodes into a given walking-direction $\gHead$ until a distance $\gDist$ is
reached \cite{Ebner-15}.
Both, heading and distance, are supplied by the current sensor readings $\mObsVec_{t}$
Both, heading and distance, are supplied by the previous sensor readings $\mObsVec_{t-1}$
and thus reflect the pedestrian's real heading and walking speed including uncertainty.
Working with relative sensor readings, the state's heading is updated during each transition:
%
\begin{align}
\gHead &= \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_t^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
\gDist &= \mObs_t^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2)
.
\gHead &= \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_{t-1}^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
\gDist &= \mObs_{t-1}^{\mObsSteps} \cdot \mStepSize + \mathcal{N}(0, \sigma_{\gDist}^2)
\enspace .
\end{align}
%\commentByFrank{fixed. war das falsche makro in (2) und dem satz darunter. das delta musste weg. der state hat ein absolutes heading. step-size als variable}
%
@@ -60,7 +60,7 @@
connected to a vertex $\mVertexA$, and, hereafter, randomly draw the to-be-walked edge
depending on those probabilities. This step is repeated until the sum
of the length of all used edges exceeds $d$. The latter depends on the number of
detected steps $\mObs_t^{\mObsSteps}$ and the pedestrian's step-size $\mStepSize$.
detected steps $\mObs_{t-1}^{\mObsSteps}$ and the pedestrian's step-size $\mStepSize$.
%\commentByFrank{step-size als variable}
To quantify the improvement prior knowledge is able to provide,
@@ -68,7 +68,7 @@
just based on its deviation from the currently estimated heading $\gHead$:
%
\begin{equation}
p(\mEdgeAB) = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{dev}^2).
p(\mEdgeAB) = p(\mEdgeAB \mid \gHead) = \mathcal{N} (\angle \mEdgeAB \mid \gHead, \sigma_\text{dev}^2) \enspace .
\label{eq:transSimple}
\end{equation}
%
@@ -210,7 +210,7 @@
%
To route the pedestrian towards his desired target, a modified version
of Dijkstra's algorithm is used. Instead of calculating the shortest path from the start to the end,
the direction is inverted and the calculated terminates as soon as every single node was evaluated.
the direction is inverted and the calculation terminates as soon as every single node was evaluated.
Hereafter, every node in the grid knows the distance and shortest path to the pedestrian's target.
To get realistic path suggestions, we use the importance-factors to adjust the edge-weight

14
tex/chapters/introduction.tex
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@@ -20,7 +20,7 @@ This combination of highly different sensor types is also known as sensor fusion
Here, probabilistic methods like particle- or Kalman filters are often used to approximate a probability density describing the pedestrian's possible whereabouts.
This procedure can be separated into two probabilistic models:
The transition model, which represents the dynamics of the pedestrian and predicts his next accessible locations, and the evaluation model, which estimates the probability for the position also corresponding to
The transition model, which represents the dynamics of the pedestrian and predicts his next accessible locations, and the evaluation model, which estimates the probability for the position corresponding to
recent sensor measurements.
%Therefore, the most accurate position is represented by a peak of the probability distribution.
In our previous work we were able to present such a localisation system based on all the sensors mentioned above, including the phone's barometer \cite{Ebner-15}.
@@ -28,12 +28,11 @@ In our previous work we were able to present such a localisation system based on
%In pedestrian navigation, the human movement is subject to the characteristics of walking speed and -direction.
%Additionally, environmental restrictions need to be considered as well, for example, walking through walls is impossible.
%Therefore, incorporating environmental knowledge is a necessary and gainful step.
Incorporating environmental knowledge is a necessary and gainful step.
For example walking through walls is impossible.
Incorporating environmental knowledge is a necessary and gainful step e.g. walking through walls is impossible.
Like other systems, we are using a graph-based approach to sample only valid movements.
The unique feature of our approach is the way how human movement is modelled.
This is done by using random walks on a graph, which are based on the heading of the pedestrian.
Despite very good results, the system presented in \cite{Ebner-15} suffers from two drawbacks, we want to solve within this work.
Despite very good results, the system presented in \cite{Ebner-15} suffers from two drawbacks, we attempt to solve within this work.
First, the transition model of our previous approach uses discrete floor-changes.
Although the overall system provides viable results, it does not resemble real-world floor changes.
@@ -49,10 +48,9 @@ is not smoothly spread. The heading-change of our new approach is solely control
During the random walk, matching edges are sampled according to their deviation from this change.
To improve the complex problem of localising a person indoors, prior knowledge given by a navigation system can be used.
Such applications are used to navigate a user to his desired destination.
This limits the unpredictability of human movement to a certain degree.
Such applications are utilized to navigate a user to his desired destination, limiting the unpredictability of human movement to a certain degree.
So, based on this assumption, the destination is known beforehand and the starting point is the user's currently estimated position.
Regarding a graph-based transition model, one could suggest to use the shortest route between start and destination as the user's most-likely-to-walk path.
Regarding a graph-based transition model, one could suggest to use the shortest route between start and destination as the user's most likely to walk path.
By incorporating this prior knowledge into the state transition step, a new state can be sampled in a more targeted manner.
However, for regularly tessellated (grid) graphs, as used in \cite{Ebner-15}, this would lead to unnatural paths e.g.
directly adhering to walls.
@@ -61,7 +59,7 @@ Therefore, we present a novel approach that detects walls using an inverted grap
Since areas near walls are less likely to be chosen for walking, a probabilistic weight is assigned to every node of the graph.
This allows a variety of options for integrating additional knowledge about the environment and enables us to address another problem:
Entering or leaving rooms is very unlikely as only a few nodes are representing doors and allow doing so.
Entering or leaving rooms is very unlikely as only a few nodes are representing doors and allow of doing so.
This can be tackled by making such areas more likely.
Therefore, a novel approach for detecting doors using the inverted graph is presented within this work.
%\commentByFrank{auch hier vlt das inverted erstmal noch weg lassen wegen platz}

10
tex/chapters/relatedwork.tex
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@@ -13,12 +13,12 @@ Kalman filters is therefore problematic \cite{sarkka2013bayesian, Nurminen2014}.
All this shows, that sensor models differ in many ways and are a subject in itself.
A good discussion on different sensor models can be found in \cite{Yang2015} or \cite{Khaleghi2013}.
However, within this work, we use simple models, configured using a handful of empirically chosen parameters and
However, within this work, we utilize simple models, configured using a handful of empirically chosen parameters and
address their inaccuracies by harnessing prior information like the pedestrian's desired destination. Therefore,
instead of examining different sensors and their contribution to the localisation process, we will focus
on the state transition and how to incorporate environmental and navigational knowledge.
A widely used and easy method for modelling the movement of a pedestrian, is the prediction of a new position
A widely used and straightforward method for modelling the movement of a pedestrian, is the prediction of a new position
using both, a walking direction and a to-be-walked distance, starting from the previous position.
If the line-of-sight between the new and the old position intersects a wall, the probability for this
transition is set to zero \cite{Blanchert09-IFF, Koeping14-ILU}.
@@ -45,15 +45,15 @@ Nevertheless, most corridors are still represented by just one topological link.
While the complexity is reduced, it does not allow arbitrary movements and leads to suboptimal trajectories.
Far more flexible and variable geometric spatial models are regularly tessellated approaches e.g. based on grids.
Those techniques are trivially implemented, but yet very powerful.
In \cite{Afyouni2012}, a square-shaped or hexagonal grid covers the entire map.
In \cite{Afyouni2012} a square-shaped or hexagonal grid covers the entire map.
Especially in the area of simultaneous localisation and mapping (SLAM), so-called occupancy-grid approaches are
very popular \cite{elfes1989using, Thrun2003}.
Occupancy grids assign a high probability to cells within the accessible space.
Likewise, cells occupied by obstacles or walls are less likely.
Additionally, every grid cell is able to hold some context information about the environment (e.g. elevators or stairs)
Every grid cell is able to hold some context information about the environment (e.g. elevators or stairs)
or the behaviour of a pedestrian at this particular position (e.g. jumping or running).
A similar approach, presented in \cite{Li2010}, \cite{Ebner-15}, is also used within this work.
A similar approach, presented in \cite{Li2010}, is also used within this work.
Assuming the floorplan is given beforehand, occupied cells can be removed.
The remaining cells are described by their centre/bounding-box and represent free spaces within the environment.
A graph is defined by using the centres as nodes and connecting direct neighbours with edges.

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}
%

3
tex/chapters/system.tex
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@@ -62,7 +62,6 @@
Therefore, numerical solutions like Gaussian filters or the broad class of Monte Carlo methods are deployed \cite{sarkka2013bayesian}.
Since we assume indoor localisation to be a time-sequential, non-linear and non-Gaussian process,
a particle filter is chosen as approximation of the posterior distribution.
Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ is used as proposal distribution,
what is also known as CONDENSATION algorithm \cite{Isard98:CCD}.
Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ is used as proposal distribution, also known as CONDENSATION algorithm \cite{Isard98:CCD}.