diff --git a/tex/chapters/relatedwork.tex b/tex/chapters/relatedwork.tex index 07a643c..15b3284 100644 --- 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 ... diff --git a/tex/chapters/system.tex b/tex/chapters/system.tex index 9d0b113..865d2e4 100644 --- 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{}. + + diff --git a/tex/egbib.bib b/tex/egbib.bib index aaaf1bd..7f9f2eb 100644 --- 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} +}