second draft finish - false images

tex/chapters/conclusion.tex

@@ -1,13 +1,13 @@
 \section{Conclusion}
 
 In this work we presented an approach for mixing two different localisation schemes using an IMMPF and a non-trivial Markov switching process, which is easy to adapt to many existing systems.
-By mixing two particle sets based upon the Kullback-Leibler divergence and a Wi-Fi quality factor, we were able to satisfy the need of diversity and focus to recover from sample impoverishment in context of indoor localisation. 
+By mixing two particle sets based upon the Kullback-Leibler divergence and a \docWIFI{} quality factor, we were able to satisfy the need of diversity and focus to recover from sample impoverishment in context of indoor localisation. 
-It was shown, that the here presented approach is able to improve the robustness, while keeping the error low.
+It was shown, that the here presented approach is able to improve the robustness, without increasing the error.
-However, in some rare situations given bad Wi-Fi readings we were not able to increase the results as usual. 
+However, in some rare situations given bad \docWIFI{} readings we were not able to increase the results. 
-This requires further investigations regarding the Wi-Fi quality factor. 
+This requires further investigations regarding the \docWIFI{} quality factor. 
 
 Finally, the possibility of combining different localisation models enables many new approaches and techniques. 
 By incorporating completely different modes, not only transitions, the robustness and accuracy can be further increased.
-This would additionally allow an on-the-fly switching between sensor models, e.g. different signal strength methods.
+This would additionally allow for on-the-fly switching between sensor models, e.g. different signal strength prediction methods.
 Such a modular solution could be able to fit any environment and thus form a highly flexible and adjustable localisation system. 
 However, adjusting the Markov switching process to any number of modes is no easy task and therefore requires intensive future work.

tex/chapters/experiments.tex

@@ -1,14 +1,7 @@
 \section{Experiments}
 
 % allgemeine infos über pfade und gebäude. wo 
-% bild: mit pfaden drauf und eventl. wifi qualität in jeweiligen bereichen? (kann frank das)
+
-	\begin{figure}
-		\centering
-		\input{gfx/eval/paths.tex}
-		\caption{The three paths that were part of the experiments. Starting positions are marked with black circles. The red squares illustrate the \docWIFI{} quality in this sector. The intensity of red indicates a low coverage and thus a bad quality for localisation.}
-		\label{fig:paths}
-	\end{figure}
-%
 %Gebäude
 All upcoming experiments were carried out on four floors (0 to 3) of a \SI{77}{m} x \SI{55}{m} sized faculty building. 
 It includes several staircases and elevators and has a ceiling height of about \SI{3}{m}. 
@@ -18,6 +11,14 @@ To get an idea about the \docWIFI{} quality, we interpolated the \docWIFI{} qual
 In fig. \ref{fig:paths} the resulting colourized floorplan is illustrated.
 Here, the intensity of red indicates a low signal strength and thus a bad quality for localising a pedestrian within this area using \docWIFI{}.
 
+% bild: mit pfaden drauf und eventl. wifi qualität in jeweiligen bereichen? (kann frank das)
+	\begin{figure}
+		\centering
+		\input{gfx/eval/paths.tex}
+		\caption{The three paths that were part of the experiments. Starting positions are marked with black circles. The red squares illustrate the \docWIFI{} quality in this sector. The intensity of red indicates a low coverage and thus a bad quality for localisation.}
+		\label{fig:paths}
+	\end{figure}
+%
 %Pfade
 We arranged three distinct walks (see also fig. \ref{fig:paths}).
 The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only. 
@@ -45,32 +46,43 @@ Finally, the pedestrian's most likely position (state) was then estimated using
 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 \cite{Fetzer2016OMC}.
+The approximation error is then calculated by comparing the interpolated ground truth position with
+the current estimation \cite{Fetzer2016OMC}.
+
+The here presented walks were selected because they fail in some way using a restrictive transition model and thus are well suited to represent the benefits and drawbacks of the IMMPF approach.
+In this context, it should be noted that the localisation system used for the experiments is very basic and can be seen as a slimmed version of our previous works \cite{Fetzer2016OMC, Ebner-16}. 
+Optimizing the \docWIFI{} parameters and adding additional methods will improve the localisation results significantly. 
+
+To avoid misunderstandings in the upcoming discussions, the used terminologies for the different filter schemes are summarized as follows: 
+graph-based and simple filter are standard independently running particle filters (PF) using the graph-based and simple transition as described at the end of section \ref{sec:rse}. 
+In contrast, dominant and support filter are indeed the same filters, but used as modes within the IMMPF procedure as described in section \ref{sec:immpf}. 
+To allow a detailed discussion of the results shown by images, we separated the paths in different segments (seg.) of interest.
 
 %error at the beginning always very high. about 44 meters. therefore the median is better value oder 75 quantil.
 
 % zeigen das es stucken verhindert (eventl. hier eine andere aufnahme die mitten drinnen stecken bleibt)
 % bild: stucken im raum + nicht mehr stucken im raum + kld mit anzeigen
-	\begin{figure}
+	\begin{figure}[b]
 		\centering
 		\input{gfx/eval/path3.tex}
 		\input{gfx/eval/path3-kld.tex}
-		\caption{Exemplary results on path 3 for the common particle filter using the graph-based (red) or simple transition model (blue) and our IMMPF approach (green). The Kullback-Leibler divergence $D_{\text{KL}}$ between the standalone filters (purple) proves itself as a good indicator, if one filter gets stuck or loses track.}
+		\caption{Exemplary results on path 3 for the graph-based filter (red), the simple filter (blue) and our IMMPF approach (green). The Kullback-Leibler divergence $D_{\text{KL}}$ between the graph-based and the simple filter (purple) proves itself as a good indicator, if one filter gets stuck or loses track.}
 		\label{fig:path3}
 	\end{figure}
 	%
-At first, we discuss the results of path 3, starting at the left-hand side of the building. 
+First, we discuss the results of path 3, starting at the left-hand side of the building. 
-Exemplary estimation results, using the modes standalone and combined within the IMMPF, can be seen in fig. \ref{fig:path3}.
+Exemplary estimation results for the IMMPF, the graph-based and the simple particle filter, can be seen in fig. \ref{fig:path3}. 
 As mentioned above, every run of a walk starts with a uniform distribution as prior.
-Due to a low Wi-Fi coverage at the starting point, the pedestrian's position is falsely estimated into a room instead of the corridor.   
+Due to a low \docWIFI{} coverage at the starting point in seg. 1, the pedestrian's position is falsely estimated into a room instead of the corridor.   
 All three filters are able to overcome this false detection. 
-However, the common particle filter (red) gets then indissoluble captured within a room, because of its restrictive behaviour and the aftereffects of the initial Wi-Fi readings. 
+However, the graph-based filter (red) gets then indissoluble captured within a room, because of its restrictive behaviour and the aftereffects of the initial \docWIFI{} readings (cf. fig. \ref{fig:path3} seg. 2). 
-It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{75} = \SI{3884}{\centimeter}$ and got captured in \SI{100}{\percent} of all runs.
+It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{75} = \SI{3884}{\centimeter}$ and got stuck in \SI{100}{\percent} of all runs.
-As expected and discussed earlier, the simple transition (blue) is less prone to bad observations and provides not so accurate, but very robust results of $\tilde{x}_{75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$.
+As expected and discussed earlier, the simple filter (blue) is less prone to bad observations and provides not accurate, but very robust results of $\tilde{x}_{75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$.
-Looking at $D_{\text{KL}}$ over time confirms our assumption made in section \ref{sec:immpf}. 
+Looking at $D_{\text{KL}}$ over time confirms our assumption made in section \ref{sec:divergence}. 
-The graph-based filter (red) gets stuck and is not able to recover, starting on from this point, the Kullback-Leibler divergence $D_{\text{KL}}$ (purple) further increases due to the growing distance between both filters (blue and red).
+The graph-based filter (red) gets stuck and is not able to recover. 
+Starting on from this point, the Kullback-Leibler divergence $D_{\text{KL}}$ (purple) further increases due to the growing distance between both filters (blue and red) starting at seg. 2 until the end of seg. 4.
 It is clearly visible, that this divergence between both filters is a very good indicator to observe, if a filter gets stuck or loses track.
-Following, the IMMPF (green) results in a very natural and straight path estimation and a low $D_{\text{KL}}$ between modes and no sticking.
+Following, the IMMPF (green) results in a very natural and straight path estimation and a low $D_{\text{KL}}$ between modes.
 The benefits of mixing both filtering schemes within the scenario of path 3 are thus obvious.
 The IMMPF filters with an error of $\tilde{x}_{75} = \SI{667}{\centimeter}$ and $\bar{\sigma} = \SI{558}{\centimeter}$.
 
@@ -80,24 +92,24 @@ The IMMPF filters with an error of $\tilde{x}_{75} = \SI{667}{\centimeter}$ and
 		\centering
 		\input{gfx/eval/path2.tex}
 		\input{gfx/eval/path2-wifi-quality.tex}
-		\caption{Comparison of the estimation results on path 2 with (green) and without (red) the Wi-Fi quality factor in the Markov transition matrix. The low Wi-Fi quality and thus high errors between the \SI{80}{th} and \SI{130}{th} second are caused by the high attenuation and low signal coverage inside the zig-zag stairwell on the building's backside.}
+		\caption{Comparison of the estimation results on path 2 with (green) and without (red) the \docWIFI{} quality factor in the Markov transition matrix. The low \docWIFI{} quality and thus high errors between the \SI{80}{th} and \SI{130}{th} second are caused by the high attenuation and low signal coverage inside the zig-zag stairwell on the building's backside.}
 		\label{fig:path2}
 	\end{figure}
 	%
 Next, we investigate the performance of our approach by considering the scenario in path 2. 
-Here, the overall Wi-Fi quality is rather low, especially in the zig-zag stairwell on the buildings back and the small entrance area at floor 1 (cf. fig. \ref{fig:paths}). 
+Here, the overall \docWIFI{} quality is rather low, especially in the zig-zag stairwell on the buildings back and the small entrance area at floor 1 (cf. fig. \ref{fig:paths} and fig. \ref{fig:path2} seg. 3). 
-Path 2 starts in the second floor, walking town the centred stairs into the first floor, then making a right turn and walking the stairs down to zero floor, from there we walk back to second floor using the zig-zag stairwell and after finally crossing a room we are back at the start. 
+Path 2 starts in the second floor, walking down the centred stairs into the first floor, then making a right turn and walking the stairs down to zeroth floor, from there we walk back to second floor using the zig-zag stairwell and after finally crossing a room we are back at the start. 
-This is a very challenging scenario, at first the estimation got stuck on the first floor in a room's corner and after that the Wi-Fi is highly attenuated.
+This is a very challenging scenario, at first the estimation got stuck on the first floor in a room's corner for \SI{20}{\second} (see fig. \ref{fig:path2} seg. 2) and after that the \docWIFI{} is highly attenuated at the beginning and end of seg. 3.
-Looking at fig. \ref{fig:path2}, one can observe the impact of the Wi-Fi quality factor within the Markov transition matrix. 
+Looking at fig. \ref{fig:path2}, one can observe the impact of the \docWIFI{} quality factor within the Markov transition matrix. 
-Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between the \SI{80}{th} and \SI{130}{th} second. 
+Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between \SIrange{80}{130}{\second} in seg. 3. 
-As described before, the bad Wi-Fi readings are causing $D_{\text{KL}}$ to grow.
+As described earlier, the bad \docWIFI{} readings are causing $D_{\text{KL}}$ to grow.
 It follows that the accurate dominant filter draws new particles from the uncertain support and therefore worsen the position estimation.
-In this scenario it is cold comfort that the system is able to recover thanks to its high diversity during situations with uncertain measurements.
+Given this outcome, it is not very satisfying that the system is able to recover thanks to its high diversity during situations with uncertain measurements.
-Only by adding the Wi-Fi quality factor the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{75} = \SI{953}{\centimeter}$ with $\bar{\sigma} = \SI{543}{\centimeter}$.
+By adding the \docWIFI{} quality factor, the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{75} = \SI{953}{\centimeter}$ with $\bar{\sigma} = \SI{543}{\centimeter}$.
 However, this is far from perfect and in some cases ($\sim \SI{9}{\percent}$) the quality factor was not able to prevent the estimation to drift in the courtyard. 
-This solely happened when particles were sampled directly onto the courtyard while changing from first to zero floor. 
+This solely happened when particles were sampled directly onto the courtyard while changing from first to zeroth floor (cf. fig. \ref{fig:path2} seg. 3). 
 Those particles then received a high weight due to the attenuated measurements, causing a weight degeneracy.
-Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor or optimizing the access-points parameters can resolve this problem \cite{}.
+Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor or optimizing the access-point's parameters can resolve this problem \cite{Ebner-17}.
 
 % zeigen das immpf nicht viel schlechter als normaler pf (ohne stucken) ist. 
 % bild: er schafft es nicht die treppe rauf + er schafft es immpf + er schafft es normal filter
@@ -111,13 +123,26 @@ Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor
 	%
 An exemplary result for path 1 is illustrated in fig. \ref{fig:path1}. 
 The path starts on the first floor and finishes on the third after walking two straight stairs. 
-Using the graph-based particle filter for localisation, we were able to obtain a very accurate path (blue) in \SI{80}{\percent} of the runs providing $\tilde{x}_{75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$. 
+Using the graph-based filter for localisation, we were able to obtain a very accurate path (blue) in \SI{80}{\percent} of the runs providing $\tilde{x}_{75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$. 
-Due to a lack of particles near the stairs, the other \SI{20}{\percent} failed to detect the first floor change (red). 
+Due to a lack of particles near the stairs, the other \SI{20}{\percent} of the estimations given by the graph-based filter failed to detect the first floor change (red). 
 Using our approach (green), we were able detect all floor changes and thus never lost track. 
-It performs with $\tilde{x}_{75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$. 
+Fig. \ref{fig:path1} shows an example, where the dominant filter also failed to change floors within seg. 2. 
-Those very similar estimation results confirm the efficiency of the mixing and how it is able to keep the accuracy while providing a higher robustness against failures.
+By looking at seg. 2 of the error plot, we can observe a more or less constant error of \SIrange{5}{6}{\meter}, which then drops rapidly at the beginning of seg. 3. 
+This reduction of the error is caused by the growing importance of the mixing stage, where more and more particles from the support filter are incorporated into the dominant filter.
+Going on in seg. 3, the \docWIFI{} measurements suffer from an attenuation directly after leaving the stairs, what leads to a high error using the graph-based filter (blue and red). 
+In contrast, the IMMPF is able to compensate the false detection due to an decreasing \docWIFI{} quality and thus a highly focused posterior provided by the dominant filter. 
+The IMMPF then performs with $\tilde{x}_{75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$. 
+Those very similar estimation results between IMMPF (green) and the graph-based filter (blue) confirm the efficiency of the mixing and how it is able to keep the accuracy while providing a higher robustness against failures.
+
+%allgemeines abschließendes blabla?
+To summarize, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area.
+The above deployed experiments have shown, that the Markov switching process, as presented in sec. \ref{sec:immpf}, enables a reasonable mixing between two particle filters with different transition schemes.
+Therefore, the quality and success of the results depend highly on the parameters used within the Markov matrix $\Pi_t$. 
+Those values are very sensitive and should be chosen carefully in regard to the specific system and use case.
+The experiments have further shown, that faulty \docWIFI{} measurements can lead to significant errors in a very short time.
+That has to do with the fact that \docWIFI{} is the only absolute information source within the state evaluation and thus plays a significant part in the mixing stage of \eqref{equ:immpMode2}.
+Adding additional absolute sensors like bluetooth beacons or ultrasonics sensors, it is possible to reduce the \docWIFI{} component's significance towards other sensor models evaluating the pedestrian's possible whereabouts.
 
-\todo{mehr die ergebnisse von bild 5 diskutieren. an manchen stellen verlieren wir genauigkeit, an anderen wird es besser.}
 
 % gegenüberstellung aller pfade und werte in tabelle
 %	\begin{table}
@@ -142,14 +167,12 @@ Those very similar estimation results confirm the efficiency of the mixing and h
 %	\end{table}
 
 %An overview of all localisation results can be seen in table \ref{tbl:err}.
-The here presented walks were selected because they fail in some way using a restrictive transition model and thus are well suited to represent the benefits and drawbacks of the IMMPF approach.
-%So the results of table \ref{tbl:err} should not be seen as best case localization results, but more as proofing robustness while providing room for further improvements.
-In this context, it should be noted that the localisation system used for the experiments is very basic and can be seen as a slimmed version of our previous works \cite{Fetzer2016OMC, Ebner-16}. 
-Optimizing the Wi-Fi parameters and adding additional methods will improve the localisation results significantly. 
 
-Especially, the graph-based transition model allows many optimizations and performance boosts.
+%So the results of table \ref{tbl:err} should not be seen as best case localization results, but more as proofing robustness while providing room for further improvements.
-More importantly, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area. 
+
-All results were similar or more accurate then the ones provided by the standalone filters, even when the localisation did not suffer from any problems.
+%Especially, the graph-based transition model allows many optimizations and performance boosts.
+%More importantly, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area. 
+%All results were similar or more accurate then the ones provided by the standalone filters, even when the localisation did not suffer from any problems.
 
 %how the Markov transition matrix regulates the impact of the supporting filter in the right amount.
 

tex/chapters/method.tex

@@ -116,6 +116,7 @@ The mixing step requires that the independently running filtering processes are
 With the above, we are finally able to combine the two filters described in section \ref{sec:rse} and realize the considerations made in section \ref{sec:divergence}. 
 Within the IMMPF we utilize the restrictive graph-based filter as the \textit{dominant} one, providing the state estimation for the localisation. 
 Due to its robustness and good diversity the simple, more permissive filter, is then used as \textit{support} for possible sample impoverishment. 
+The names dominant and support are now applied as synonyms for the respective filters used as modes within the IMMPF.
 
 As a reminder, both filters (modes) are running in parallel for the entire estimation life cycle.
 If we recognize that the dominant filter diverges from the supporting filter and thus got stuck or lost track, particles from the supporting filter will be picked with a higher probability while mixing the new particle set for the dominant filter. 

tex/chapters/system.tex

@@ -134,6 +134,7 @@ Given the above, we are now able to implement two different localisation schemes
 The graph-based transition keeps the localisation error low by using a very realistic propagation model, while being prone to sample impoverishment. 
 On the other hand, the simple transition provides a high diversity with a robust, but uncertain position estimation. 
 Both are evaluating a state $\mStateVec_{t}$ using \eqref{eq:evalBayes}.
+In the upcoming, the filter using the graph-based transition is refereed to as \textit{graph-based filter} and the filter using the simple transition as \textit{simple filter}.
 
 % 
 %In the following, two very different transition models, each providing one of this abilities, are presented. 

tex/gfx/eval/path1-time.tex

@@ -128,7 +128,7 @@
       \put(4255,1234){\makebox(0,0)[r]{\strut{}\footnotesize{PF (bad)}}}%
     }%
     \gplbacktext
-    \put(0,0){\includegraphics{gfx/eval/path1-time}}%
+    \put(410,410){\includegraphics{gfx/eval/path1-time}}%
     \gplfronttext
   \end{picture}%
 \endgroup

tex/gfx/eval/path1.tex

@@ -86,11 +86,11 @@
       \csname LTb\endcsname%
       \put(4431,2388){\makebox(0,0)[r]{\strut{}\footnotesize{ground truth}}}%
       \csname LTb\endcsname%
-      \put(4431,2168){\makebox(0,0)[r]{\strut{}\footnotesize{PF (good)}}}%
+      \put(4431,2168){\makebox(0,0)[r]{\strut{}\footnotesize{graph-based PF (good)}}}%
       \csname LTb\endcsname%
       \put(4431,1948){\makebox(0,0)[r]{\strut{}\footnotesize{IMMPF}}}%
       \csname LTb\endcsname%
-      \put(4431,1728){\makebox(0,0)[r]{\strut{}\footnotesize{PF (bad)}}}%
+      \put(4431,1728){\makebox(0,0)[r]{\strut{}\footnotesize{graph-based PF (bad)}}}%
     }%
     \gplbacktext
     \put(0,0){\includegraphics{gfx/eval/path1}}%

tex/gfx/eval/path2-wifi-quality.tex

@@ -120,7 +120,7 @@
       \put(2720,-44){\makebox(0,0){\strut{}\footnotesize{time (seconds)}}}%
     }%
     \gplbacktext
-    \put(0,0){\includegraphics{gfx/eval/path2-wifi-quality}}%
+    \put(400,400){\includegraphics{gfx/eval/path2-wifi-quality}}%
     \gplfronttext
   \end{picture}%
 \endgroup

tex/gfx/eval/path3-kld.tex

@@ -123,10 +123,10 @@
       \csname LTb\endcsname%
       \put(1518,1448){\makebox(0,0)[r]{\strut{}\footnotesize{IMMPF}}}%
       \csname LTb\endcsname%
-      \put(1518,1228){\makebox(0,0)[r]{\strut{}\footnotesize{PF}}}%
+      \put(1518,1228){\makebox(0,0)[r]{\strut{}\footnotesize{PF's}}}%
     }%
     \gplbacktext
-    \put(0,0){\includegraphics{gfx/eval/path3-kld}}%
+    \put(400,400){\includegraphics{gfx/eval/path3-kld}}%
     \gplfronttext
   \end{picture}%
 \endgroup

tex/gfx/eval/path3.tex

@@ -86,17 +86,17 @@
       \csname LTb\endcsname%
       \put(4431,1012){\makebox(0,0)[r]{\strut{}\footnotesize{ground truth}}}%
       \csname LTb\endcsname%
-      \put(4431,792){\makebox(0,0)[r]{\strut{}\footnotesize{PF}}}%
+      \put(4431,792){\makebox(0,0)[r]{\strut{}\footnotesize{graph-based PF}}}%
       \csname LTb\endcsname%
-      \put(4431,572){\makebox(0,0)[r]{\strut{}\footnotesize{PF simple}}}%
+      \put(4431,572){\makebox(0,0)[r]{\strut{}\footnotesize{simple PF}}}%
       \csname LTb\endcsname%
       \put(4431,352){\makebox(0,0)[r]{\strut{}\footnotesize{IMMPF}}}%
       \csname LTb\endcsname%
       \put(4431,1012){\makebox(0,0)[r]{\strut{}\footnotesize{ground truth}}}%
       \csname LTb\endcsname%
-      \put(4431,792){\makebox(0,0)[r]{\strut{}\footnotesize{PF}}}%
+      \put(4431,792){\makebox(0,0)[r]{\strut{}\footnotesize{graph-based PF}}}%
       \csname LTb\endcsname%
-      \put(4431,572){\makebox(0,0)[r]{\strut{}\footnotesize{PF simple}}}%
+      \put(4431,572){\makebox(0,0)[r]{\strut{}\footnotesize{simple PF}}}%
       \csname LTb\endcsname%
       \put(4431,352){\makebox(0,0)[r]{\strut{}\footnotesize{IMMPF}}}%
     }%