84 lines
6.8 KiB
TeX
84 lines
6.8 KiB
TeX
\section{Related Work}
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\label{sec:relatedWork}
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Like mentioned before, most state-of-the-art systems use recursive state estimators like Kalman- and particle filters.
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They differ mainly by the used sensors, their probabilistic models and how environmental information is incorporated.
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For example \cite{Li2015} recently presented an approach combining methods of pedestrian dead reckoning (PDR), \docWIFI{}
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fingerprinting and magnetic matching using a Kalman filter. While providing good results, fingerprinting methods
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require an extensive offline calibration phase. Therefore, many other systems like \cite{Fang09} or \cite{Ebner-15}
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use signal strength prediction models like the log-distance or wall-attenuation-factor model.
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Additionally, the sensors noise is not always Gaussian or satisfies the central limit theorem. Using
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Kalman filters is therefore problematic \cite{sarkka2013bayesian, Nurminen2014}.
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All this shows, that sensor models differ in many ways and are a subject in itself.
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A good discussion on different sensor models can be found in \cite{Yang2015} or \cite{Khaleghi2013}.
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However, within this work, we use simple models, configured using a handful of empirically chosen parameters and
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address their inaccuracies by harnessing prior information like the pedestrian's desired destination. Therefore,
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instead of examining different sensors and their contribution to the localisation process, we will focus
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on the state transition and how to incorporate environmental and navigational knowledge.
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A widely used and easy method for modelling the movement of a pedestrian, is the prediction of a new position
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using both, a walking direction and a to-be-walked distance, starting from the previous position.
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If the line-of-sight between the new and the old position intersects a wall, the probability for this
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transition is set to zero \cite{Blanchert09-IFF, Koeping14-ILU}.
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However, as \cite{Nurminen13-PSI} already stated, it "gives more probability to a short step".
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An additional drawback of these approaches is that for every transition an intersection-test
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must be executed and thus often yields a high computational complexity.
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These disadvantages can be avoided by using spatial models like indoor graphs.
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Here, two main classes can be distinguished: symbolic and geometric spatial models \cite{Afyouni2012}.
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Especially geometric spatial models (coordinate-based approaches) are very popular, since they integrate metric properties to provide highly accurate location and distance information.
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One of the most common environmental representations in indoor localization literature is the Voronoi diagram \cite{Liao2003}.
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It represents the topological skeleton of the building's floorplan as an irregular tessellation of space.
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This drastically removes degrees of freedom from the map, and results in a low complexity.
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In the work of \cite{Nurminen2014} a Voronoi diagram is used to approximate the human movement.
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It is assumed that the user can be anywhere on the topological links.
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The probabilities of changing to the next link are proportional to the total link lengths.
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However, for accurate localisation in large-scale buildings, this network of one-dimensional curves is not suitable \cite{Afyouni2012}.
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Therefore, \cite{Hilsenbeck2014} searches for large open spaces (e.g. a lobby) and extends the Voronoi diagram by adding those two-dimensional areas.
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The final graph is then created by sampling nodes in regular intervals across the links and filling up the open spaces in a tessellated manner.
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Similar to \cite{Ebner-15}, they provide a transition model that selects an edge and a node from the graph according to a sampled distance and heading.
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Nevertheless, most corridors are still represented by just one topological link.
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While the complexity is reduced, it does not allow arbitrary movements and leads to suboptimal trajectories.
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Far more flexible and variable geometric spatial models are regularly tessellated approaches e.g. based on grids.
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Those techniques are trivially implemented, but yet very powerful.
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In \cite{Afyouni2012}, a square-shaped or hexagonal grid covers the entire map.
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Especially in the area of simultaneous localisation and mapping (SLAM), so-called occupancy-grid approaches are
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very popular \cite{elfes1989using, Thrun2003}.
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Occupancy grids assign a high probability to cells within the accessible space.
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Likewise, cells occupied by obstacles or walls are less likely.
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Additionally, every grid cell is able to hold some context information about the environment (e.g. elevators or stairs)
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or the behaviour of a pedestrian at this particular position (e.g. jumping or running).
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A similar approach, presented in \cite{Li2010}, \cite{Ebner-15}, is also used within this work.
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Assuming the floorplan is given beforehand, occupied cells can be removed.
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The remaining cells are described by their centre/bounding-box and represent free spaces within the environment.
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A graph is defined by using the centres as nodes and connecting direct neighbours with edges.
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In order to enable floor changes, some approaches suggest to simply connect the nodes at staircases \cite{Ebner-15, Hilsenbeck2014}.
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However, as mentioned before changing the floor in a discrete manner does not resemble real-world conditions.
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Therefore, \cite{GarciaPuyol2014} presented a stepwise floor change based on a hexagonal gridded-graph.
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We introduce a similar approach for square-shaped grids.
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All this allows a wide range of possibilities for modelling the pedestrian's movement, while only sampling valid locations.
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In virtual environments like video games and simulations, the human motion is often modelled using graphs and path finding techniques.
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Here, the goal is not only to provide a shortest path, but also the least-cost path, most natural path or least-dangerous path.
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For example, \cite{Bandi2000} uses an A*-algorithm to search a 3D gridded environment for the shortest path to a goal.
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An additional smoothing procedure is performed to make the path more natural.
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They are considering foot span, body dimensions and obstacle dimensions when determining whether an obstacle is surmountable.
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However, many of this information is difficult to ascertain in real-time or imply additional effort in real-world environments.
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Therefore, more realistic simulation models, mainly for evacuation simulation, are just using a simple shortest path on regularly
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tessellated graphs \cite{tan2014agent}. A more costly, yet promising approach is shown by \cite{Brogan2003}. They use a
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data set of previously recorded walks to create a model of realistic human walking paths.
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Finally, it seems that currently none of the localisation system approaches are using realistic walking paths as additional
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source of information to provide a more targeted and robust movement. Most common systems are sampling a new state only in
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regard of the user's heading and speed using one of the above mentioned indoor graphs.
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