first draft introduction, as far is toni can write.

tex/chapters/introduction.tex

@@ -1,54 +1,41 @@
 \section{Introduction}
 
 Sensor fusion approaches are often based upon probabilistic descriptions like particle filters, using samples to represent the distribution of a dynamical system. 
-To update the system recursively in time, probabilistic sensor models process the noise measurements and a state transition function provides the system's dynamics. 
+To update the system recursively in time, probabilistic sensor models process the noisy measurements and a state transition function provides the system's dynamics. 
 Therefore a sample or particle is a representation of one possible system state, e.g. the position of a pedestrian within a building. 
 In most real world scenarios one is then interested in finding the most probable state within the state space, to provide the "best estimate" of the underlying problem.  
-In the discrete manner of a sample representation this is often done by calculating a single value, also known as sample statistic, to serve as a "best guess". 
+In the discrete manner of a sample representation this is often done by providing a single value, also known as sample statistic, to serve as a "best guess". 
-This values is often calculated by means of simple parametric point estimators, e.g. using weighted-average of all samples or that one sample with the highest overall weight \cite{}. 
+This value is then calculated by means of simple parametric point estimators, e.g. the weighted-average over all samples, the sample with the highest weight or by assuming other parametric statistics like normal distributions \cite{}. 
 %da muss es doch noch andere methoden geben... verflixt und zugenäht... aber grundsätzlich ist ein weighted average doch ein point estimator? (https://www.statlect.com/fundamentals-of-statistics/point-estimation)
+%Für related work brauchen wir hier definitiv quellen. einige berechnen ja auch https://en.wikipedia.org/wiki/Sample_mean_and_covariance oder nehmen eine gewisse verteilung für die sample menge and und berechnen dort die parameter
 
-%multimodalities... 
+While such methods are computational fast and suitable most of the time, it is not uncommon that they fail to recover the state in more complex scenarios.
+Especially time-sequential, non-linear and non-Gaussian state spaces, depending upon a high number of different sensor types, frequently suffer from a multimodal representation of the posterior distribution.  
+As a result, those techniques are not able to provide an accurate statement about the most probable state, rather causing misleading or false outcomes. 
+For example in a localization scenario where a bimodal distribution represents the current posterior, a reliable position estimation is more likely to be at one of the modes, instead of somewhere in-between.  
+Additionally, in most practical scenarios the sample size and therefore the resolution is limited, causing the variance of the sample based estimate to be high \cite{Verma2003}.
+
+It is obvious, that a computation of the full posterior could solve the above, but finding such an analytical solution is an intractable problem, what is the reason for applying a sample representation in the first place. 
+Another promising way is to recover the probability density function from the sample set itself, by using a non-parametric estimator like a kernel density estimation (KDE). 
+With this, it is easy to find the "real" most probable state and thus to avoid the aforementioned drawbacks.
+However, non-parametric estimators tend to consume a large amount of computational time, which renders them unpractical for real time scenarios.
+Nevertheless, the availability of a fast processing density estimate might improve the accuracy of today's sensor fusion systems without sacrificing their real time capability.
+
+\commentByToni{Der nachfolgende Satz ist ziemlich wichtig. Find ich aktuell noch nicht gut. Allgemein sollte ihr jetzt noch ca eine viertel Seite ein wenig die Methode grob beschrieben werden.
+The basic idea ...
+We formalize this ...
+Our experiments support our ..
+}
+
+In this paper, a novel approximation approach for rapid computation of the KDE is presented.
+%Therefore, this paper presents a novel approximation approach for rapid computation of the KDE. 
+%In this paper, a well known approximation of the Gaussian filter is used to speed up the computation of the KDE. 
 
  
 
-%interested in the most proper state within the state space of the dynamic system
-%echte antwort computationel complex deswegen %weighted-average -> problem multimodal; sample mit höhsten wert -> springt viel rum 
-%-> Density -> KDE
-
-%Egal auf welchem Weg das sample set entstanden ist, am ende muss ein verwertbarer wert rauskommen. irgendein 
-
-After calculating 
 
 
 
-In real world scenarios 
-
-
-%find the state that describs our probleme the best 
-%
-
-%  ... in many real world scenarios an estimate of the problem state is required e.g. the position of a pedestrian within a building... 
-%this is often done by calculating the weighted-average of all samples or 
-
-%however multimodalities. 
-
-% in the optimal case 
-
-bessere entscheidung kde raus machen, als einfach nur 
-
-to receive this information 
-
-based upon a set of descrete samples
-
-%for this purpose parameteric estimators like ... are often used in real time scenarios because of their low complexity and short computatinal time.
-
-% however, 
-non parameteric estimators like kde 
-
- 
-
-\cite{Deinzer01-CIV}
 % KDE wellknown nonparametic estimation method
 % Flexibility is paid with slow speed
 % Finding optimal bandwidth

tex/egbib.bib

@@ -2880,3 +2880,14 @@ year = {2003}
     year={2017, submitted},
 }
 
+@inproceedings{Verma2003,
+author = {Verma, Vandi and Thrun, Sebastian and Simmons, Reid},
+doi = {10.1.1.68.4380},
+booktitle={Proc. of the International Joint Conference on Artificial Intelligence (IJCAI)}, 
+pages = {976--984},
+title = {{Variable resolution particle filter}},
+year = {2003}
+}
+
+
+