87 lines
6.9 KiB
TeX
87 lines
6.9 KiB
TeX
\section{Related Work}
|
|
\label{sec:relatedWork}
|
|
|
|
|
|
Like mentioned before, most state-of-the-art systems use recursive state estimators like Kalman- and particle filters.
|
|
They differ mainly by the used sensors, their probabilistic models and how environmental information is incorporated.
|
|
For example \cite{Li2015} recently presented an approach combining methods of pedestrian dead reckoning (PDR), \docWIFI{}
|
|
fingerprinting and magnetic matching using a Kalman filter. While providing good results, fingerprinting methods
|
|
require an extensive offline calibration phase. Therefore, many other systems like \cite{Fang09} or \cite{Ebner-15}
|
|
use signal strength prediction models like the log-distance model or wall-attenuation-factor model.
|
|
Additionally, the sensors noise is not always Gaussian or satisfies the central limit theorem, what makes the
|
|
usage of Kalman filters 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}, \cite{Gu2009} or \cite{Khaleghi2013}.
|
|
|
|
However, within this work, we use 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
|
|
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{Woodman08-PLF, Blanchert09-IFF, Koeping14-ILU}.
|
|
However, as \cite{Nurminen13-PSI} already stated, it "gives more probability to a short step".
|
|
An additional drawback of these approaches is that for every transition an intersection-test
|
|
must be executed and thus often yields a high computational complexity.
|
|
|
|
These disadvantages can be avoided by using spatial models like indoor graphs.
|
|
Here, two main classes can be distinguished: symbolic and geometric spatial models \cite{Afyouni2012}.
|
|
Especially geometric spatial models (coordinate-based approaches) are very popular, since they integrate metric properties to provide highly accurate location and distance information.
|
|
One of the most common environmental representations in indoor localization literature is the Voronoi diagram \cite{Liao2003}.
|
|
It represents the topological skeleton of the building's floorplan as an irregular tessellation of space.
|
|
This drastically removes degrees of freedom from the map, and results in a low complexity.
|
|
|
|
In the work of \cite{Nurminen2014} a Voronoi diagram is used to approximate the human movement.
|
|
It is assumed that the pedestrian can be anywhere on the topological links.
|
|
The probabilities of changing to the next link are proportional to the total link lengths.
|
|
However, for highly accurate localisation in large-scale buildings, this network of one-dimensional
|
|
curves is not suitable \cite{Afyouni2012}.
|
|
Therefore, \cite{Hilsenbeck2014} searches for large open spaces (e.g. a lobby) and extends the Voronoi diagram
|
|
by adding those two-dimensional areas.
|
|
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. Similar to \cite{Ebner-15}, they provide a state transition model that selects
|
|
an edge and a node from the graph according to a sampled distance and heading.
|
|
|
|
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.
|
|
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)
|
|
or the behaviour of a pedestrian at this particular position (e.g. jumping or running).
|
|
|
|
A similar approach is presented in \cite{Li2010}, \cite{Ebner-15} and is also used within this work.
|
|
By assuming that the floorplan is given beforehand, the occupied cells can be removed.
|
|
The remaining cells are described by their centre/bounding-box and represent all free spaces in the indoor environment.
|
|
A graph is defined by using the centres as nodes and connecting direct neighbours with edges.
|
|
|
|
In order to enable floor changes, some approaches suggest to simply connect the nodes at staircases \cite{Ebner-15, Hilsenbeck2014}.
|
|
However, as mentioned before changing the floor in a discrete manner does not resemble real-world conditions.
|
|
Therefore, \cite{GarciaPuyol2014} presented a stepwise floor change based on a hexagonal gridded-graph.
|
|
We introduce a similar approach for square-shaped grids.
|
|
|
|
All this allows a wide range of possibilities for modelling the pedestrian's movement, while only sampling valid locations.
|
|
In virtual environments like video games and simulations, the human motion is often modelled using graphs and path finding techniques.
|
|
Here, the goal is not only to provide a shortest path, but also the least-cost path, most natural path or least-dangerous path.
|
|
For example, \cite{Bandi2000} uses an A* algorithm to search a 3D gridded environment for the shortest path to a goal.
|
|
An additional smoothing procedure is performed to make the path more natural.
|
|
They are considering foot span, body dimensions and obstacle dimensions when determining whether an obstacle is surmountable.
|
|
However, many of this information is difficult to ascertain in real-time or imply additional effort in real-world environments.
|
|
Therefore, more realistic simulation models, mainly for evacuation simulation, are just using a simple shortest path on regularly
|
|
tessellated graphs \cite{Sun2011, tan2014agent}. A more costly, yet promising approach is shown by \cite{Brogan2003}. They use a
|
|
data set of previously recorded walks to create a model of realistic human walking paths.
|
|
|
|
Finally, it seems that currently none of the localisation system approaches are using realistic walking paths as additional
|
|
source of information to provide a more targeted and robust movement. Most common systems are sampling a new state only in
|
|
regard of the user's heading and speed using one of the above mentioned indoor graphs.
|
|
|
|
|
|
|
|
|