IPIN2018/tex/chapters/relatedwork.tex

\section{Related Work}
\label{sec:relatedWork}

We consider indoor localization to be a time-sequential, non-linear and non-Gaussian state estimation problem. 
Such problems are often solved by using Bayesian filters, which update the state estimation recursively
with every new incoming measurement. 
A powerful method to obtain numerical results for this approach are particle filters.

In context of indoor localisation, particle filter approximate a probability distribution describing the pedestrian's possible whereabouts by using a set of weighted random samples (particles).
Here, new particles are drawn according to some importance distribution, often represented by the state transition, which models the dynamics of the system.
Those particles are then weighted by the state evaluation given different sensor measurements.
A resampling step is deployed to prevent that only a small number of particles have a signifcant weight \cite{chen2003bayesian}.
Most localisation approaches differ mainly in how the transition and evaluation steps are implemented and the available sensors are incorporated \cite{Fetzer-16, Ebner-16, Hilsenbeck2014}.
Additionally, within this paper we present a method, which is designed to run solely on a commercial smartphone.

In its most basic form, the state transition is given by.. einfach distanz und heading.. intersection with walls usw.

\todo{nochmal mit frank klären was wir jetzt GENAU machen.}

These disadvantages can be avoided by using spatial models
like indoor graphs. Besonders geometric spatial models sind beliebt

\todo{kurz auf voronoi eingehen mit neueren papern und dann auf grid basierte eingehen. schreiben das wir in previous work auch solche benutzt haben, aber das problem ist halt der gigantische speicheraufwand. deshalb haben wir uns für triangle based entscheiden, die erstellung ist einfacher, die verfahren sind aus der spieletheorie bekannt und erfolgreich im einatz. natürlich ist das ganze ein wenig rechenaufwendiger, da nun bla und blub gemacht werden muss, jedoch ist das laufen realisischer und nicht auf 45 grad winkel begrenzt. es wird also eine höhere genaugikeit erwartet, bei stark reduzierten speicher und zugrifssbedarf auf das netz.}

%eval - wifi, fingerprinting
The outcomes of the state evaluation process depend highly on the used sensors. 
Most smartphone-based systems are using received signal strength indications (RSSI) given by Wi-Fi or Bluetooth as a source for absolute positioning information. 
At this, one can mainly differ between fingerprinting and signal-strength prediction model based solutions \cite{Ebner-17}.
Indoor localization using Wi-Fi fingerprints was first addressed by \cite{radar}. 
During a one-time offline-phase, a multitude of reference measurements are conducted. 
During the online-phase the pedestrian's location is then inferred by comparing those prior measurements against live readings.
Based on this pioneering work, many further improvements where made within this field of research \cite{PropagationModelling, ProbabilisticWlan, meng11}. 
However, despite a very high accuracy up to \SI{1}{\meter}, fingerprinting approaches suffer from tremendous setup- and maintenance times. 
Using robots instead of human workforce might thus be a viable choice, still this seems not to be a valid option for old buildings with limited accessibility due to uneven grounds and small stairs.
 
%wifi, signal strength 
Signal strength prediction models are a well-established field of research to determine signal strengths for arbitrary locations by using an estimation model instead of real measurements.
While many of them are intended for outdoor and line-of-sight purposes \cite{PredictingRFCoverage, empiricalPathLossModel}, they are often applied to indoor use-cases as well \cite{Ebner-17, farid2013recent}.
Besides their solid performance in many different localization solutions, a complex scenario requires a equally complex signal strength prediction model.
As described in section 1, historical buildings represent such a scenario and thus the model has to take many different constraints into account.
An example is the wall-attenuation-factor model \cite{PathLossPredictionModelsForIndoor}. 
It introduces an additional parameter to the well-known log distance model \cite{IntroductionToRadio}, that considers obstacles between (line-of-sight) the AP and the location in question by attenuating the signal with a constant value. 
Depending on the use-case, this value describes the number and type of walls, ceilings, floors etc. between both positions. 
For obstacles, this requires an intersection-test of each obstacle with the line-of-sight, which is costly for larger buildings. 
Thus \cite{Ebner-17} suggests to only consider floors/ceilings, what can be calculated without intersection checks and allows for real-time use-cases running on smartphones.

%wifi optimization
To further reduce the setup-time, \cite{WithoutThePain} introduces an approach that works without any prior knowledge.
They use a genetic optimization algorithm to estimate the parameters for a signal strength prediction, including the access points (AP) position, and the pedestrian's locations during the walk.
The estimated parameters can be refined using additional walks.
Within this work we present a similar optimization approach for estimating the AP's location in 3D. 
However, instead of taking multiple measuring walks, the locations are optimized based only on some reference measurements, what further decreases the setup-time.
Additionally, we will show that such an optimization scheme can partly compensate for the above abolished intersection-tests.

%immpf
Besides well chosen probabilistic models, the system's performance is also highly affected by handling problems which are based on the nature of particle filter.
They are often caused by restrictive assumptions about the dynamic system, like the aforementioned sample impoverishment. 
The authors of \cite{Sun2013} handled the problem by using an adaptive number of particles instead of a fixed one. 
The key idea is to choose a small number of samples if the distribution is focused on a small part of the state space and a large number of particles if the distribution is much more spread out and requires a higher diversity of samples.
The problem of sample impoverishment is then encountered by adapting the number of particles depend upon the systems current uncertainty \cite{Fetzer-17}.

In practice sample impoverishment is often a problem of environmental restrictions and system dynamics.
Therefore, the method above fails, since it is not able to propagate new particles into the state space due to environmental restrictions e.g. walls or ceilings.
In \cite{Fetzer-17} we deployed an interacting multiple model particle filter (IMMPF) to solve sample impoverishment in such restrictive scenarios. 
We combine two particle filter using a non-trivial Markov switching process, depending upon the Kullback-Leibler divergence between both.
However, deploying a IMMPF is in many cases not necessary and produces additional processing overhead.
Thus a much simpler, but very heuristic method is presented within this paper. 

%estimation
Finally, as the name recursive state estimation says, it requires to find the most probable state within the state space, to provide the "best estimate" of the underlying problem.
In the discrete manner of a particle representation this is often done by providing a single value, also known as sample statistic, to serve as a best guess \cite{Bullmann-18}. 
Examples are the weighted-average over all particles or the particle with the highest weight.
However in complex scenarios like a multimodal representation of the posterior, such methods fail to provide an accurate statement about the most probable state.
Thus, in \cite{Bullmann-18} we present a rapid computation scheme of kernel density estimates (KDE).
Recovering the probability density function using an efficient KDE algorithm yields a promising approach to solve the state estimation problem in a more profound way.