Linguistic checking

tex/chapters/abstract.tex

@@ -1,8 +1,8 @@
 \begin{abstract}
-Indoor localisation continuous to be a topic of growing importance. 
+Indoor localisation continues to be a topic of growing importance. 
 Despite the advances made, several profound problems are still present. 
 For example, estimating an accurate position from a multimodal distribution or recovering from the influence of faulty measurements.
-Within this work, we solve such problems with help of Monte Carlo smoothing methods, namely forward-backward smoother and backward simulation.
+Within this work, we solve such problems with the help of Monte Carlo smoothing methods, namely forward-backward smoother and backward simulation.
 In contrast to normal filtering procedures like particle filtering, smoothing methods are able to incorporate future measurements instead of just using current and past data.
 This enables many possibilities for further improving the position estimation. 
 Both smoothing techniques are deployed as fixed-lag and fixed-interval smoother and a novel approach for incorporating them easily within a conventional localisation system is presented.

tex/chapters/experiments.tex

@@ -14,21 +14,21 @@ The experiments were carried out on all four floors of the faculty building.
 Each floor is about \SI{77}{\meter} x \SI{55}{\meter} in size, with a ceiling height of about \SI{3.0}{\meter}.
 To resemble real-world conditions, the evaluation took place during an in-house exhibition. 
 Thus, many places were crowded and Wi-Fi signals attenuated.
-As can be seen in fig. \ref{fig:paths} we arranged 4 distinct walks, covering different distances, critical sections and uncertain decisions leading to multimodalities. 
+As can be seen in fig. \ref{fig:paths}, we arranged 4 distinct walks, covering different distances, critical sections and uncertain decisions leading to multimodalities. 
 The ground truth is measured by recording a timestamp at marked spots on the walking route.
 When passing a marker, the pedestrian clicked a button on the smartphone application. 
 Between two consecutive points, a constant movement speed is assumed.
 Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for error measurements.
 The approximation error is then calculated by comparing the interpolated ground truth position with the current estimation.
 Especially in the context of smoothing, it is also very interesting to exclude the temporal delay from the error calculations and measure only the positional difference between estimated and ground truth path. 
-This gives a statement about the extent to which the smoothed path superficially improves compared to the filtered one. 
+This provides a statement about the extent to which the smoothed path superficially improves compared to the filtered one. 
 
 All walks start with a uniform distribution (random position and heading) as prior for $\mStateVec_0$. 
-To allow the system to stabilize its initial state, the first few estimations are omitted from error calculations.
-Even though, the error during the following few seconds is expected to be much higher than the error when starting with a well known initial position and heading.
+To allow the system to stabilise its initial state, the first few estimations are omitted from error calculations.
+Even though the error during the following few seconds is expected to be much higher than the error when starting with a well known initial position and heading.
 
 The measurements were recorded using a Motorola Nexus 6 and a Samsung Galaxy S5.
-As the Galaxy's \docWIFI{} can not be limited to the \SI{2.4}{\giga\hertz} band only, its scans take much longer than those of the Nexus: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}.
+As the Galaxy's \docWIFI{} cannot be limited to the \SI{2.4}{\giga\hertz} band only, its scans take much longer than those of the Nexus: \SI{3500}{\milli\second} vs. \SI{600}{\milli\second}.
 Additionally, the Galaxy's barometer sensor provides far more inaccurate and less frequent readings than the Nexus does. 
 This results in a better localisation using the Nexus smartphone.	
 The computation for both filtering and smoothing was done offline using the aforementioned \mbox{CONDENSATION} algorithm and multinomal (cumulative) resampling. 
@@ -67,7 +67,7 @@ Despite a short misdetection in seg. 2, caused by faulty pressure readings, the
 
 %Fixed Interval Smoothing
 At first, both FBS and BS are compared in context of fixed-interval smoothing.
-As a reminder, fixed-interval smoother are using all observations until time $T$ and therefore run offline, after the filtering procedure is finished.
+As a reminder, fixed-interval smoother are using all observations until time $T$ therefore run offline, after the filtering procedure is finished.
 Thus, we calculate only the positional error between estimation and ground truth, since timely information are negligible. 
 %
 \begin{figure}

tex/chapters/filtering.tex

@@ -43,7 +43,7 @@
 			measuring the signal-strengths of nearby transmitters. The positions of detected \docAP{}s  (\docAPshort{}) and \docIBeacon{}s
 			are known beforehand. Using the wall-attenuation-factor signal strength prediction model \cite{Ebner-15}, we are able to 
 			compare each measurement with a corresponding estimation. To infer this estimation, the prediction model
-			uses the 3D distance $d$ and the number of floors $\Delta f$ between transmitter and the state-in-question $\mStateVec$:
+			uses the 3D distance $d$ and the number of floors $\Delta f$ between the transmitter and the state-in-question $\mStateVec$:
 			%	
 			\begin{equation}
 				P_r(d, \Delta f) = \mTXP - 10 \mPLE \log_{10}{\frac{\mMdlDist}{\mMdlDist_0}} + \Delta{f} \mWAF \enspace ,
@@ -54,8 +54,7 @@
 			$\mMdlDist_0$ (usually \SI{1}{\meter}), a path-loss exponent $\mPLE$ describing the transmitter's environment and the attenuation
 			per floor $\mWAF$.
 			To reduce the system's setup time, we use the same three values for all \docAP{}s at the cost of accuracy.
-			All parameters are chosen empirically. Further details on how to determine this parameters exactly,
-			can be found in \cite{PathLossPredictionModelsForIndoor}.
+			All parameters are chosen empirically. Further details on how to determine these parameters exactly	can be found in \cite{PathLossPredictionModelsForIndoor}.
 			
 			The same holds for the \docIBeacon{} component, except $\mTXP$,
 			which is broadcasted by each beacon. However, as \docIBeacon{}s cover only a small area, $\mPLE$ is usually much smaller compared
@@ -84,7 +83,7 @@
 		While sampling, to-be-walked edges are not chosen uniformly, but depending on a probability $p(\mEdgeAB)$.
 		The latter depends on several constraints and recent sensor-readings from the smartphone. Using those readings
 		directly within the transition step provides a more robust posterior distribution. Adding them to the evaluation
-		instead, would lead to sample impoverishment due to the used MC methods \cite{Isard98:CCD}.
+		instead would lead to sample impoverishment due to the used MC methods \cite{Isard98:CCD}.
 		
 		%\commentByFrank{ist das verstaendlich oder schon zu kurz?}
 				

tex/chapters/introduction.tex

@@ -30,27 +30,27 @@ Here, a set of weighted random samples is used to solve the state estimation pro
 
 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 movement (walking speed) within the transition model \cite{Ebner-15, Nurminen2014, Hilsenbeck2014}. 
+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.
-Like mentioned before, PDR suffers from an accumulating bias,
-the signal of \docWIFI{} gets attenuated by walls
+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}. 
-That 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. 
+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 estimate immensely. 
+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 can not completely prevent delays. 
+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. 
 %
@@ -67,7 +67,7 @@ For example, most mobile devices restrict the \docWIFI{} module to update only e
 %
 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 gets separated by a wall.
+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. 
@@ -80,14 +80,14 @@ However, standard filtering methods are not able to use any future information a
 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. 
+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.
-Namely, forward-backward smoothing \cite{doucet2000} and backward simulation \cite{Godsill04:MCS}.
+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. 
+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.
+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.
 
 

tex/chapters/relatedwork.tex

@@ -20,7 +20,7 @@ On the other hand, fixed-interval smoothing requires all observations until time
 %historie des smoothings und entwicklung der methoden.
 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 algorithm is often called the filter-smoother since it runs online and smoothing is provided while filtering.
 %\commentByFrank{das mit dem weighted paths irritiert mich etwas. war das original work auch fuer etwas, wo pfade im spiel waren? weils halt gar so gut passt. ned dass da begrifflichkeiten durcheinander kommen. beim lesen fehlt mir das beim 1. anlauf was damit gemeint ist}
 This approach uses the particle filter steps to update weighted paths $\{(W^i_t, \vec{X}_{1:t}^i)\}^N_{i=1}$, 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 to a monotonic decrease of distinct particles caused by resampling of each weighted path \cite{Doucet11:ATO}.
@@ -30,25 +30,25 @@ Algorithmic details will be shown in section \ref{sec:smoothing}.
 
 %wo werden diese eingesetzt, paar beispiele. offline, online 
 %\commentByFrank{wenn du meinst, 'bei indoor wirds NICHT verwendet' dann ist 'as' das falsche. wuerde auch 'got' statt 'gets' verwenden}
-In recent years, smoothing got attention mainly in other areas than indoor localisation. 
+In recent years, smoothing attracted attention mainly in areas other than 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. The authors of \cite{Hu2014} use a smoother to overcoming the problem of particle impoverishment while predicting the Remaining Useful Life (RUL) of equipment (e.g. a Lithium-ion battery).
+For example, in \cite{Platzer:2008} a particle smoother is used to reduce multimodalities in a blood flow simulation for human vessels. The authors of \cite{Hu2014} use a smoother to overcome the problem of particle impoverishment while predicting the Remaining Useful Life (RUL) of equipment (e.g. a Lithium-ion battery).
 
 %smoothing im bezug auf indoor
 Nevertheless, there are some promising approaches for indoor localisation systems as well. 
 For example \cite{Nurminen2014} deployed a fixed-interval forward-backward smoother to improve the position estimation for non-real-time applications. 
 They combined \docWIFI{}, step and turn detection, a simple line-of-sight model for floor plan restrictions and the barometric change within a particle filter. 
 The state transition samples a new state based on the heading change, altitude change and a fixed step length. 
-The experiments of \cite{Nurminen2014} clearly emphasize the benefits of smoothing techniques. The estimation error could be decreased significantly. 
+The experiments of \cite{Nurminen2014} clearly emphasise the benefits of smoothing techniques. The estimation error could be decreased significantly. 
 However, a fixed-lag smoother was discussed only in theory.
 
 In the work of \cite{Paul2009} both fixed-interval and fixed-lag smoothing were presented. 
 They implemented \docWIFI{}, binary infrared motion sensors, binary foot-switches and a potential field for floor plan restrictions. 
 Those sensors were incorporated using a sigma-point Kalman filter in combination with a forward-backward smoother.
-It was also proven by \cite{Paul2009}, that the fixed-lag smoother is slightly less accurate than the fixed-interval smoother, as one would expect from the theoretical foundation.
-Unfortunately, even a sigma-point Kalman filters is after all just a linearisation and therefore not as flexible and suited for the complex problem of indoor localisation as a non-linear estimator like a particle filter. 
+It was also proven by \cite{Paul2009} that the fixed-lag smoother is slightly less accurate than the fixed-interval smoother, as one would expect from the theoretical foundation.
+Unfortunately, even a sigma-point Kalman filter is after all just a linearisation and therefore not as flexible and suited for the complex problem of indoor localisation as a non-linear estimator like a particle filter. 
 %\commentByToni{Kann das jemand nochmal verifizieren? Das mit dem Kalman Filter. Danke.}
 %\commentByLukas{Ich wuerde den Satz ganz weglassen. Ansonsten musst du angeben, wo die eigentlichen Probleme liegen, also z.B. in welchen konkreten Situation das Kalman Filter nicht mehr funktioniert usw. So ist es jetzt erstmal nur eine Behauptung ohne jeglichen Hintergrund.}
 %\commentByToni{Ich bin mir nicht sicher ob das eine Behauptung ohne jeglichen Hintergrund ist. Meiner Meinung nach ist das ziemlich weitreichend bekannt. Finde den Satz persoenlich ganz gut, weil er uns deutlich von dieser Arbeit abgrenzt und das ist wichtig.}
@@ -61,9 +61,9 @@ Since humans with a specific destination in mind do not tend to change their dir
 %\commentByFrank{algorithmS?}
 %\commentByFrank{'is able to use', oder 'will use'? gehts um die eval (will use), oder generell um die theorie und moeglichkeiten (is able to)}
 %\commentByFrank{man koennte die reihenfolge vlt umstellen, erst die ganzen filtering sachen beschreiben, map, activity, ... und on top of that two smoothing algorithms both implemented as fixed-interval and fixed-lag?}
-The here presented approach will use two different smoothing algorithm, both implemented as fixed-interval and fixed-lag versions. 
-Further, our localisation system presented in \cite{Ebner-16} enables us to walk stairs and thus going into the third dimension.
-Therefore, a regularly tessellated graph is utilised to avoid walls, detecting doors and recognizing stairs. 
+The herein presented approach will use two different smoothing algorithms, both implemented as fixed-interval and fixed-lag versions. 
+Further, our localisation system presented in \cite{Ebner-16} enables us to walk stairs and thus go into the third dimension.
+Therefore, a regularly tessellated graph is utilised to avoid walls, detecting doors and recognising stairs. 
 Within this work, this is additionally supported by a simple classification that detects the activities unknown, standing, walking and walking stairs. 
 %Finally, we incorporate prior navigation knowledge by using syntactically calculated realistic human walking paths \cite{Ebner-16}. 
 %This method makes use of the given destination and thereby provides a more targeted movement. 

tex/chapters/smoothing.tex

@@ -17,7 +17,7 @@ p(\vec{q}_t \mid \vec{o}_{1:T}) \approx \sum^N_{i=1} W^i_{t \mid T} \delta_{\vec
 \end{equation}
 %\commentByFrank{support?}
 where $p(\vec{q}_t \mid \vec{o}_{1:T})$ has the same support as the filtering distribution $p(\vec{q}_t \mid \vec{o}_{1:t})$, but the weights are different. 
-This means, that the FBS maintains the original particle locations and just reweights the particles to obtain a smoothed density. 
+This means that the FBS maintains the original particle locations and just reweights the particles to obtain a smoothed density. 
 $\delta_{\vec{X}^i_{t}}$ denotes the Dirac delta function.
 The complete FBS can be seen in algorithm \ref{alg:forward-backwardSmoother} in pseudo-algorithmic form. 
 %\commentByFrank{forward step vlt etwas genauer erklaeren weil 1. mal benutzt? oder is das hinlaenglich bekannt? :P}
@@ -66,7 +66,7 @@ For smoothing applications with a high number of particles, it is often not nece
 This decision can, for example, be made due to a high sample impoverishment and/or highly accurate sensors.
 By choosing a good sub-set for representing the posterior distribution, it is theoretically possible to further improve the estimation. 
 
-Therefore, \cite{Godsill04:MCS} presented the backward simulation (BS). Where a number of independent sample realisations
+Therefore, \cite{Godsill04:MCS} presented the backward simulation (BS), where a number of independent sample realisations
 from the entire smoothing density are used to approximate the smoothing distribution. 
 %
 \begin{algorithm}[t]
@@ -91,7 +91,7 @@ from the entire smoothing density are used to approximate the smoothing distribu
 \end{algorithm}
 %
 This method can be seen in algorithm \ref{alg:backwardSimulation} in pseudo-algorithmic form.
-Again, a particle filter is performed at first and then the smoothing procedure gets applied.
+Again, a particle filter is performed at first and then the smoothing procedure is applied.
 %\commentByFrank{das klingt so, als waeren particle-filter und smoothing zwei komplett verschiedene sachen.}
 %\commentByToni{Sind sie doch auch irgendwo.}
 %\commentByFrank{was heisst 'drawn approximately'? nach welchen gesichtspunkte?}
@@ -109,7 +109,7 @@ Unlike the transition presented in section \ref{sec:transition}, it is not possi
 Here, $p(\vec{q}_{t+1} \mid \vec{q}_{t})$ needs to provide the probability of the \textit{known} future state $\vec{q}_{t+1}$ under the condition of its ancestor $\vec{q}_{t}$. 
 The smoothing transition model therefore calculates the probability of being in a state $\vec{q}_{t+1}$ in regard to previous states and the pedestrian's walking behaviour. 
 This means that a state $\vec{q}_t$ is more likely if it is a proper ancestor (realistic previous position) of a future state $\vec{q}_{t+1}$. 
-In the following a simple and inexpensive approach for receiving this information will be described.
+In the following, a simple and inexpensive approach for receiving this information will be described.
 
 By writing
 \begin{equation}
@@ -122,9 +122,9 @@ Of course, based on the graph structure, one could calculate the shortest path b
 However, this requires tremendous calculation time for negligible improvements. 
 Therefore this is not further discussed within this work. 
 The average step length $\mu_{\text{step}}$ is based on the pedestrian's walking speed and $\sigma_{\text{step}}^2$ denotes the step length's variance. 
-Both values are chosen depending on the activity $\mObsActivity$ recognized at time $t$. 
-For example $\mu_{\text{step}}$ gets smaller while a pedestrian is walking upstairs, than just walking straight.
-This requires to extend the smoothing transition by the current observation $\mObsVec_t$.
+Both values are chosen depending on the activity $\mObsActivity$ recognised at time $t$. 
+For example $\mu_{\text{step}}$ becomes smaller while a pedestrian is walking upstairs than just walking straight.
+This requires an extension of the smoothing transition by the current observation $\mObsVec_t$.
 Since $\mStateVec$ is hidden and the Markov property is satisfied, we are able to do so.
 
  
@@ -143,10 +143,10 @@ To further improve the results, especially in 3D environments, the vertical (non
 p(\vec{q}_{t+1} \mid \vec{q}_t, \mObsVec_t)_{\text{baro}} = \mathcal{N}(\Delta z \mid \mu_z, \sigma^2_{z}) \enspace .
 \label{eq:smoothingTransPressure}
 \end{equation}
-This assigns a low probability to false detected or misguided floor changes.
+This assigns a low probability to falsely detected or misguided floor changes.
 Similar to \refeq{eq:smoothingTransDistance} we set $\mu_z$ and $\sigma^2_{z}$ based on the activity recognised at time $t$.
 Therefore, $\mu_z$ is the expected change in $z$-direction between two time steps. 
-This means, if the pedestrian is walking alongside a corridor, we set $\mu_z = 0$. 
+This means that if the pedestrian is walking alongside a corridor, we set $\mu_z = 0$. 
 In contrast, $\mu_z$ is positive while walking downstairs or otherwise negative for moving upstairs. 
 The size of $\mu_z$ and also $\mu_{\text{step}}$ could be a predefined value or set dynamically based on the measured vertical and linear acceleration.
 
@@ -162,7 +162,7 @@ Looking at \refeq{eq:smoothingTransDistance} to \refeq{eq:smoothingTransPressure
 \enspace .
 \end{equation}
 %
-It is important to notice, that all particles at each time step $t$ of the forward filtering need to be saved. 
-Therefore, the memory requirement increases proportional to the processing time.
+It is important to notice that all particles at each time step $t$ of the forward filtering need to be saved. 
+Therefore, the memory requirement increases proportionally to the processing time.
 
 

tex/chapters/system.tex

@@ -37,8 +37,8 @@ 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, $\mObsActivity$ contains the activity, currently estimated for the pedestrian, which is one of:
-unknown, standing, walking, walking stairs up or walking stairs down.
+Finally, $\mObsActivity$ contains the activity currently estimated for the pedestrian, which is one of:
+unknown, standing, walking, walking up the stairs or walking down the stairs.
 
 The probability density of the state evaluation is given by 
 	%