\section{Introduction}

%It is well known, that signals given by Global Navigation Satellite Systems (GNSS) like the Global Positioning System (GPS) do not move easily through solid objects. Therefore, they work best in outdoor environments, when the device has a clear line of sight to the sky. 
%Obviously, GNSS are of no practical use in the context of indoor localisation.  

Determining a position indoors is a challenging task. 
Besides the complex architecture of many buildings, high accuracy needs to be achieved, especially for buildings with many small separated areas like shopping malls or office blocks.
In recent years, many different systems were presented to meet those requirements. 
Especially \docWIFI{} positioning and pedestrian dead reckoning (PDR) are very popular solutions. 
Approaches based on PDR try to estimate the current position given the previous position and thus require an initial state. 
However, this allows for cumulative errors and leads to an erroneous position estimation within a very short period. 
By incorporating the absolute position information of \docWIFI{} this drift can be corrected.
Additional improvements can be achieved by using environmental information about walls and obstacles provided by a floor map.

In most cases, probabilistic methods are used to incorporate those highly different sensor types. 
Here, a probability distribution describes the pedestrian's possible whereabouts and therefore the uncertainty of the system. 
Drawing 
%\commentByLukas{Drawing samples oder sampling} 
from a probability distribution and
%\commentByLukas{Willst du hier das Samplen erwaehnen? Es kommt so ein bisschen aus dem Nichts und man kann es gerade nur schwer einordnen} 
%\commentByToni{Ich möchte hier auf Monte Carlo ueberleiten. Warum macht man das ueberhaupt? Ich finde das umschreibt das ganz gut. alles andere kostet nur unfassbar viel platz wie ich finde.}
%\commentByFrank{vlt als Kompromiss einfach etwas umstellen/kuerzen: Describing/Modelling (multimodal) probability densities analytically is in most cases...}
finding an analytical solution for densities is in most cases a difficult task, especially in case of time sequential, non-linear and non-Gaussian models. 
Due to the high complexity of the human movement, we consider indoor localisation as such.

Bayesian filters solve such problems by updating the state estimation recursively with every new incoming measurement. 
A broad class to obtain numerical results for this approach are Monte Carlo (MC) methods, where a set of random samples is used to approximate the underlying probability distribution. 
By applying the time sequential hidden Markov process of Bayes filtering, one of the most important MC techniques results: particle filtering. 
Here, a set of weighted random samples is used to solve the state estimation process.

Based on this general methodology, many different approaches for estimating a position in indoor environments have been developed. 
All these approaches differ mainly in how the dynamics are modelled in the transition step and how a specific sensor measurement can be used for evaluation. 
For example, recent approaches are using a graph-based structure to consider environmental restrictions (walking through walls) and the characteristics of human movements (walking speed) within the transition model \cite{Ebner-15, Nurminen2014, Hilsenbeck2014}. 
The evaluation model is mostly separated into any number of sensor models, each representing the probability for a noisy measurement in regard to the current position. 
For example, a barometer can be used to determine the probability of being on a certain floor \cite{Binghao13-UBI}. 
%Another example that demonstrates the big differences between single approaches is the large number of sensor models using Wi-Fi signal strengths. There are fingerprinting methods, which require an extensive offline calibration phase, signal strength prediction models like the log-distance model or wall-attenuation-factor model and many others \cite{Ville09, Fang09, Ebner:Thesis:2013}.

Despite the many advances made in the last years, nearly all systems suffer from more or less the same problems.
As mentioned before, PDR suffers from an accumulating bias,
the signal of \docWIFI{} becomes attenuated by walls
%\commentByFrank{falls noch platz ist: noch mehr nachteile :P \docWIFI{} location estimation strongly depends on the quality of the signal-strength estimation model (oder fingerprinting) and the way the smartphone is held}
and the barometric pressure is highly affected by weather patterns and humidity
%\commentByFrank{spontane fenster/tuer oeffnung}
\cite{Binghao13-UBI}. 
This is the reason for the use of statistical methods in the first place. Nevertheless, there are even more profound problems regarding the whole position estimation procedure. 

Current transition models, which aim to approximate the movement, are still very restrictive and unable to handle unforeseen events. 
Faulty sensor measurements, like a falsely detected turn, can cause the estimation to lose track.
For example by recognising a turn too soon and walking into a room instead of another big hallway. 
Due to this, the filter needs some time to recover, which again takes a while because of the restrictive model (e.g. no walking through walls and only realistic walking speed). 
This temporal delay worsens the estimation immensely. 
A solution to recover from such filter divergences faster, involves methods to re-initialize the filtering procedure \cite{Nurminen2014}. 
However, even this cannot completely prevent delays. 
Another reason for possible time delays are slow sensor updates. 
For example, most mobile devices restrict the \docWIFI{} module to update only every few seconds, to save on battery. 
%
\begin{figure}[t]
	\centering
	\def\svgwidth{0.9\columnwidth}
  \input{gfx/multimodalpath.eps_tex}
	\caption[An example of the occurrence of a multimodal distribution.]{
	An example of the occurrence of a multimodal distribution.
	At time $t-1$ the floor is separated by a wall and the distribution (coloured circle), splits apart.
	The approximated position (green line) is estimated somewhere in-between. After a right turn, the distribution slowly starts to recover its unimodality.}
	\label{fig:multimodalPath}
\end{figure}
%
Further critical problems arise from multimodal distributions. 
Those are caused by multiple possible position estimates. 
Fig. \ref{fig:multimodalPath} illustrates an example where a floor is separated by a wall.
Due to inaccurate measurements and a PDR approach for evaluating the movement, the distribution splits apart. 
Depending on the chosen estimator, the approximated position might be located somewhere in-between as seen in fig. \ref{fig:multimodalPath}.
Only after the pedestrian turns right, the distribution is again unimodal, since moving through walls is impossible. 
As one can imagine, this can lead to serious problems in big indoor environments. 
Such a situation can be improved by incorporating future measurements (e.g. the right turn)
%or predictive information (e.g. the most likely path)
to the filtering procedure \cite{Ebner-16}. 
However, standard filtering methods are not able to use any future information and the possibilities to make a distant forecast are also limited \cite{robotics, Doucet11:ATO, chen2003bayesian}.

One promising way to deal with these problems is smoothing. 
Smoothing methods are able to make use of future measurements for computing their estimation. 
By running backwards in time, they are also able to remove multimodalities and improve the overall localisation result.
Since the problem of navigation, especially the representation of complex movement patterns, results in a non-linear and non-Gaussian state space, this work focuses mainly on smoothing techniques based on the broad class of MC methods, namely
%Of course, this excludes linear procedures like Kalman filtering.
forward-backward smoothing \cite{doucet2000} and backward simulation \cite{Godsill04:MCS}.

Within this work, we investigate the benefits and drawbacks of those techniques using a conventional localisation system \cite{Ebner-16}. 
We provide both fixed-lag and fixed-interval smoothing as well as a novel approach for incorporating them easily within the localisation procedure. 
%Additionally, we enrich the state transition model with an activity recognition to distinguish between walking, standing and walking stairs.
The main goal is to solve the above-mentioned problems and to investigate new possibilities for even more advanced systems.
All of our contributions are supported by an extensive experimental evaluation.


%\commentByLukas{In der Einleitung sollte an einer Stelle ganz klar die Contributions der Arbeit herausgestellt werden. Vielleicht irgendwie sowas: The contributions of this work are as follows:Firstly, we extend current smoothing methods for indoor localisation to resolve multimodalities during the state estimation process. Secondly, we incorporate the knowledge of the user's destination as a-priori knowledge. Thirdly, we enrich the state transition model with an activity recognition to distinguish between walking, standing and walking stairs. All of our contributions are supported by an extensive experimental evaluation. }

%\commentByToni{Steht doch direkt einen Absatz drueber nur halt kein plakatives "The contributions of " steht. Nur das Smoothing ist die Contribution meiner Meinung nach. Das prior knowledge ist ausm fusion paper. lediglich die activity rec fehlte. habe es ergänzt :). da bin ich mir aber noch nicht sicher... es wird ja nicht wirklich evaluiert sondern eher als "gegeben" angesehen. vielleicht dann auch eher so beschreiben?}
%\commentByFrank{finds gut so}



