added section recursive state estimation, and 3/4 of related work

2016-04-19 07:45:23 +02:00
parent db2b9dd461
commit 8d29605121
3 changed files with 55 additions and 63 deletions
--- a/tex/chapters/relatedwork.tex
+++ b/tex/chapters/relatedwork.tex
@@ -18,16 +18,20 @@ On the other hand, fixed-interval smoothing requires all observations until time
 The origin of MC smoothing can be traced back to Genshiro Kitagawa. 
 In his work \cite{kitagawa1996monte} he presented the simplest form of smoothing as an extension to the particle filter. 
 This algorithm is often called the filter-smoother since it runs online and a smoothing is provided while filtering. 
-This approach can produce an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with computational complexity of only $\mathcal{O}(N)$.
-\commentByFrank{kleines n?}
-However, it gives a poor representation of previous states \cite{Doucet11:ATO}.
-\commentByFrank{wenn noch platz, einen satz mehr dazu warum es schlecht ist?}
+This approach uses the particle filter steps to update weighted paths $\{(\vec{q}_{1:t}^i , w^i_t)\}^N_{i=1}$, producing an accurate approximation of the filtering posterior $p(\vec{q}_{t} \mid  \vec{o}_{1:t})$ with a computational complexity of only $\mathcal{O}(N)$.
+However, it gives a poor representation of previous states due a monotonic decrease of distinct particles caused by resampling of each weighted path \cite{Doucet11:ATO}.
 Based on this, more advanced methods like the forward-backward smoother \cite{doucet2000} and backward simulation \cite{Godsill04:MCS} were developed.
 Both methods are running backwards in time to reweight a set of particles recursively by using future observations. 
 Algorithmic details will be shown in section \ref{sec:smoothing}.

 %wo werden diese eingesetzt, paar beispiele. offline, online 
-In recent years, smoothing gets attention mainly in the field of computer vision and ... Here, ...
+In recent years, smoothing gets attention mainly in other areas as indoor localisation. 
+The early work of \cite{isard1998smoothing} demonstrates the possibilities of smoothing for visual tracking.
+They used a combination of the CONDENSATION particle filter with a forward-backward smoother. 
+Based on this pioneering approach, many different solutions for visual and multi-target tracking have been developed \cite{Perez2004}.
+For example, in \cite{Platzer:2008} a particle smoother is used to reduce multimodalities in a blood flow simulation for human vessels. Or \cite{} 
+
+

 Nevertheless, their are some promising approach for indoor localisation systems as well. For example ...

--- a/tex/chapters/system.tex
+++ b/tex/chapters/system.tex
@@ -1,11 +1,8 @@
 \section{Recursive State Estimation}

-	\commentByFrank{schon mal kopiert, dass es da ist.}
-	\commentByFrank{die neue activity in die observation eingebaut}
-	\commentByFrank{magst du hier auch gleich smoothing ansprechen? denke es würde sinn machen weils ja zum kompletten systemablauf gehört und den hatten wir hier ja immer drin. oder was meinst du?}
-
-	We consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem. 
-	Using a recursive Bayes filter that satisfies the Markov property, the posterior distribution at time $t$ can be written as
+As mentioned before, most smoothing methods require a preceding filtering. 
+In our previous work \cite{Ebner-16}, we consider indoor localisation as a time-sequential, non-linear and non-Gaussian state estimation problem. 
+Therefore, a Bayes filter that satisfies the Markov property is used to calculate the posterior, which is given by
 	%
 	\begin{equation}
 		\arraycolsep=1.2pt
@@ -13,40 +10,33 @@
 			&p(\mStateVec_{t} \mid \mObsVec_{1:t}) \propto\\ 
 				&\underbrace{p(\mObsVec_{t} \mid \mStateVec_{t})}_{\text{evaluation}}
 				\int \underbrace{p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})}_{\text{transition}}
-				\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}} \enspace,
+				\underbrace{p(\mStateVec_{t-1} \mid \mObsVec_{1:t-1})d\vec{q}_{t-1}}_{\text{recursion}} \enspace.
 		\end{array}
 		\label{equ:bayesInt}
 	\end{equation}
 	%
-	where $\mObsVec_{1:t} = \mObsVec_{1}, \mObsVec_{1}, ..., \mObsVec_{t}$ is a series of observations up to time $t$. 
-	The hidden state $\mStateVec$ is given by
+Here, the previous observation $\mObsVec_{t-1}$ is included into the state transition \cite{Koeping14-PSA}. 
+For approximating eq. \eqref{equ:bayesInt} by means of MC methods, the transition is used as proposal distribution, also known as CONDENSATION algorithm \cite{isard1998smoothing}.
+
+In context of indoor localisation, the hidden state $\mStateVec$ is defined as follows:
 	\begin{equation}
 		\mStateVec = (x, y, z, \mStateHeading, \mStatePressure),\enskip
 		x, y, z, \mStateHeading, \mStatePressure \in \R \enspace,
 	\end{equation}
 	%
-	where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the
-	relative atmospheric pressure prediction in hectopascal (hPa).
-	\commentByFrank{hier einfach kuerzen und aufs fusion paper verweisen? auch wenn das noch ned durch ist?}
-	The recursive part of the density estimation contains all information up to time $t-1$.
-	Furthermore, the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ models the pedestrian's movement as described in section \ref{sec:trans}. 
-	%It should be noted, that we also include the current observation $\mObsVec_{t}$ in it.
-	As proven in \cite{Koeping14-PSA}, we may include the observation $\mObsVec_{t-1}$ into the state transition. 
-
-	Containing all relevant sensor measurements to evaluate the current state, the observation vector is defined as follows:
+where $x, y, z$ represent the position in 3D space, $\mStateHeading$ the user's heading and $\mStatePressure$ the relative atmospheric pressure prediction in hectopascal (hPa). Further, the observation is given by
 	%
 	\begin{equation}
-		\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{ib}, \mObsHeading, \mObsSteps, \mObsPressure, \mObsActivity) \enspace,
+		\mObsVec = (\mRssiVec_\text{wifi}, \mRssiVec_\text{ib}, \mObsHeading, \mObsSteps, \mObsPressure, x) \enspace,
 	\end{equation}
 	%
-	where $\mRssiVec_\text{wifi}$ and $\mRssiVec_\text{ib}$ contain the measurements of all nearby \docAP{}s (\docAPshort{})
-	and \docIBeacon{}s, respectively. $\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number
-	of steps detected for the pedestrian. $\mObsPressure$ is the relative barometric pressure with respect to a fixed reference. 
-	Finally, $\mObsActivity$ contains the activity, currently estimated for the pedestrian, which is one of: unknown, standing, walking or
-	walking stairs. 
-	%For further information on how to incorporate such highly different sensor types,
-	%one should refer to the process of probabilistic sensor fusion \cite{Khaleghi2013}.
-	By assuming statistical independence of all sensors, the probability density of the state evaluation is given by 
+covering all relevant sensor measurements. 
+Here, $\mRssiVec_\text{wifi}$ and $\mRssiVec_\text{ib}$ contain the measurements of all nearby \docAP{}s (\docAPshort{}) and \docIBeacon{}s, respectively. 
+$\mObsHeading$ and $\mObsSteps$ describe the relative angular change and the number of steps detected for the pedestrian. 
+$\mObsPressure$ is the relative barometric pressure with respect to a fixed reference. 
+Finally, $x$ contains the activity, currently estimated for the pedestrian, which is one of: unknown, standing, walking or walking stairs. 
+
+The probability density of the state evaluation is given by 
 	%
 	\begin{equation}
 		%\begin{split}
@@ -54,23 +44,16 @@
 			p(\vec{o}_t \mid \vec{q}_t)_\text{baro} 
 			\,p(\vec{o}_t \mid \vec{q}_t)_\text{ib}
 			\,p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}
-			\enspace.
+			\enspace
 		%\end{split}
 		\label{eq:evalBayes}
 	\end{equation}
 	%
-	Here, every single component refers to a probabilistic sensor model. 
-	The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$,
-	whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for
-	\docIBeacon{}s and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. 
-
-	%It is well known that finding analytic solutions for densities is very difficult and only possible in rare cases.
-	%Therefore, numerical solutions like Gaussian filters or the broad class of Monte Carlo methods are deployed \cite{sarkka2013bayesian}. 
-	Since we assume indoor localisation to be a time-sequential, non-linear and non-Gaussian process,
-	a particle filter is chosen as approximation of the posterior distribution. 
-	\commentByFrank{smoothing?}
-	%Within this work the state transition $p(\mStateVec_{t} \mid \mStateVec_{t-1}, \mObsVec_{t-1})$ is used as proposal distribution,
-	%also known as CONDENSATION algorithm \cite{Isard98:CCD}.
+and therefore similar to \cite{Ebner-16}.
+Here, we assume a statistical independence of all sensors and every single component refers to a probabilistic sensor model. 
+The barometer information is evaluated using $p(\vec{o}_t \mid \vec{q}_t)_\text{baro}$, whereby absolute position information is given by $p(\vec{o}_t \mid \vec{q}_t)_\text{ib}$ for \docIBeacon{}s and by $p(\vec{o}_t \mid \vec{q}_t)_\text{wifi}$ for \docWIFI{}. 
+
+



--- a/tex/egbib.bib
+++ b/tex/egbib.bib
@@ -975,16 +975,6 @@ ISSN={0162-8828},}
 year={2006},
 }

-@misc{VAP2,
- title={IEEE P802.11 Wireless LANs - Virtual Access Points},
- author={Aboba, Bernard},
- year={2003},
- REMurl={http://aboba.drizzlehosting.com/IEEE/11-03-154r1-I-Virtual-Access-Points.doc},
- note={\url{http://aboba.drizzlehosting.com/IEEE/11-03-154r1-I-Virtual-Access-Points.doc}},
- note={zuletzt abgerufen am 28.11.2013},
- pages={13},
-}
-
 % reference points to reset errors, automatic floorplan generation, backend-phase
@inproceedings{crowdinside,
 author = {Alzantot, Moustafa and Youssef, Moustafa},
@@ -2082,16 +2072,15 @@ year = {2014}
@incollection{Platzer:2008,
 	year={2008},
 	isbn={978-3-540-78639-9},
-	booktitle={Bildverarbeitung für die Medizin 2008},
+	booktitle={Bildverarbeitung f\"ur die Medizin 2008},
 	series={Informatik Aktuell},
-	editor={Tolxdorff, Thomas and Braun, Jürgen and Deserno, ThomasM. and Horsch, Alexander and Handels, Heinz and Meinzer, Hans-Peter},
+	editor={Tolxdorff, Thomas and Braun, J\"urgen and Deserno, Thomas M. and Horsch, Alexander and Handels, Heinz and Meinzer, Hans-Peter},
 	doi={10.1007/978-3-540-78640-5_58},
-	title={3D Blood Flow Reconstruction from 2D Angiograms},
-	url={http://dx.doi.org/10.1007/978-3-540-78640-5_58},
+	title={{3D Blood Flow Reconstruction from 2D Angiograms}},
 	publisher={Springer Berlin Heidelberg},
 	author={Platzer, Esther-S. and Deinzer, Frank and Paulus, Dietrich and Denzler, Joachim},
-	pages={288-292},
-	language={English}
+	pages={288--292},
+	language={English},
 }

@article{haugh2004monte,
@@ -2273,12 +2262,12 @@ IGNOREmonth={Apr},
 } 

@incollection{isard1998smoothing,
-  title={A Smoothing Filter for Condensation},
+  title={{A Smoothing Filter for Condensation}},
  author={Isard, Michael and Blake, Andrew},
  booktitle={Computer Vision—ECCV'98},
  pages={767--781},
  year={1998},
-  publisher={Springer}
+  publisher={Springer},
 }

@inproceedings{klaas2006fast,
@@ -2717,5 +2706,21 @@ volume = {13},
 year = {1967}
 }

+@article{Perez2004,
+author = {P{\'{e}}rez, Patrick and Vermaak, Jaco and Blake, Andrew},
+doi = {10.1109/JPROC.2003.823147},
+isbn = {0018-9219},
+issn = {00189219},
+journal = {Proceedings of the IEEE},
+keywords = {Color,Data fusion,Motion,Particle filters,Sound,Visual tracking},
+IGNOREmonth = {mar},
+number = {3},
+pages = {495--513},
+shorttitle = {Proceedings of the IEEE},
+title = {{Data Fusion for Visual Tracking with Particles}},
+url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1271403},
+volume = {92},
+year = {2004}
+}