diff --git a/tex/bare_conf.dvi b/tex/bare_conf.dvi index d932d85..3d2a035 100644 Binary files a/tex/bare_conf.dvi and b/tex/bare_conf.dvi differ diff --git a/tex/bare_conf.tex b/tex/bare_conf.tex index 970a58f..9b527f8 100644 --- a/tex/bare_conf.tex +++ b/tex/bare_conf.tex @@ -82,6 +82,9 @@ \usepackage{algorithm} \usepackage{algpseudocode} +\usepackage{caption} +\usepackage{subcaption} + % replacement for the SI package \newcommand{\SI}[2]{\ensuremath{#1}\text{\,#2}} @@ -117,7 +120,7 @@ % gfx include folder -\graphicspath{ {gfx/baro/},{gfx/graph/},{gfx/paths/},{gfx/eval/},{gfx/},{gfx/grid/},{gfx/activity/},{gfx/eval/interval_path4_comp/},{gfx/eval/interval_path3_bad/},{gfx/particles/}, {gfx/eval/lag_path4_error/}} +\graphicspath{ {gfx/baro/},{gfx/graph/},{gfx/paths/},{gfx/eval/},{gfx/},{gfx/grid/},{gfx/activity/},{gfx/eval/interval_path4_comp/},{gfx/eval/interval_path3_bad/},{gfx/particles/}, {gfx/eval/lag_path4_error/}, {gfx/eval/interval_path3_good/}} % correct bad hyphenation here diff --git a/tex/chapters/experiments.tex b/tex/chapters/experiments.tex index 82c2dbb..a004a5b 100644 --- a/tex/chapters/experiments.tex +++ b/tex/chapters/experiments.tex @@ -42,7 +42,7 @@ Additionally, we used five \docIBeacon{}s for slight enhancements in some areas. The empirically chosen values for \docWIFI{} were $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}, \mWAF_{\text{wifi}} = \SI{8}{\dB}$, and $\mPLE_{\text{ib}} = \SI{1.5}{}$ for the \docIBeacon{}s, respectively. The system was tested by omitting any time-consuming calibration processes for those values. We therefore expect the localisation process to perform generally worse compared to standard fingerprinting methods \cite{Ville09}. -However, incorporating prior knowledge and smoothing will often compensate for those poorly chosen system parameters. +However, smoothing will often compensate for those poorly chosen system parameters. For the filtering we used $\sigma_\text{wifi} = \sigma_\text{ib} = 8.0$ as uncertainties, both growing with each measurement's age. While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically (see \ref{sec:eval}). @@ -63,7 +63,7 @@ By adding the activity recognition to the system of \cite{Ebner-16}, we are able The approximation error decreases by an average of \SI{XX}{\centimeter} for all 4 paths on 10 MC runs. Due to this additional knowledge, the state transition samples mostly depending upon the current activity and therefore limits the possibility of false floor changes. Fig. \ref{fig:activityRecognition} shows the recognized activities for path 4 using the Nexus 6. -Despite a short misdetection caused by faulty pressure readings, the recognition can be considered to be very robust and accurate. +Despite a short misdetection in seg. 2, caused by faulty pressure readings, the recognition can be considered to be very robust and accurate. %Fixed Interval Smoothing At first, both FBS and BS are compared in context of fixed-interval smoothing. @@ -75,35 +75,43 @@ Thus, we calculate only the positional error between estimation and ground truth \caption{particles. green = avg50, black = avg. gnuplot zickt bei der legende} \label{fig:particles} \end{figure} -In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position. -As illustrated in fig. \ref{fig:particles}, the estimated position (black dot) for filtering and FBS is identical although the weights are highly different. -To address this problem, we are calculating the average state using the \SI{50}{\percent} best weighted particles (green dot). -For evaluating the FBS this estimation method was applied to filtering and smoothing likewise. -We deployed 10 MC runs using \SI{2500}{} particles for approximation. -%The resulting positional error between estimated and ground truth along path 4 can be seen in fig. \ref{}. -Now, the positional average error along all 4 paths could be improved from \SI{2.49}{\meter} to \SI{2.2}{\meter} for the Galaxy and from \SI{1.76}{\meter} to \SI{1.54}{\meter} for the Nexus. -%Similar outcomes can be observed by adding a resampling step at the end of every smoothing iteration. +In contrast to BS, the FBS is not able to improve the results using the weighted arithmetic mean for estimating the current position. +Fig. \ref{fig:particles} illustrates the filtered and smoothed particle set at a certain time step on path 4. +It can be seen that the estimated position (black dot) for filtering and FBS is identical although the particle weights are highly different. +To address this problem, we are extending the FBS by adding a resampling step. +Here, particles with large weights are likely to be drawn multiple times. +This focuses the computational resources of the FBS into regions with high probability mass and finally improves the estimation. +Since smoothing operates on known states, the danger of sample impoverishment is negligible. -However, BS still outperforms the FBS with an average error of \SI{1.74}{\meter} for the Galaxy and \SI{1.41}{\meter} for the Nexus on all 4 paths using the same number of particles and $500$ sample realisations. -A visual example comparing both smoothing methods on path 4 is illustrated in fig. \ref{fig:intcomp}. + +We deployed 10 MC runs using \SI{2500}{} particles for approximation and a multinomial resampling step to every smoothing interval of the FBS. +Now, the positional average error along all 4 paths using the Nexus and the Galaxy could be improved from \SI{2.08}{\meter} to \SI{1.37}{\meter}. +Using the same number of particles and $500$ sample realisations the BS performs with an average error of \SI{2.21}{\meter} for filtering and \SI{1.51}{\meter} for smoothing. +The difference between both filtering steps is of course based upon the randomized behaviour of the respective probabilistic models. +It is interesting to note, that the positional error is very similar for both used smartphones, although the approximation error varies greatly as we will see later. + +A visual example of the smoothing outcome for path 3 is illustrated in fig. \ref{fig:int_path3_a}. The estimation of BS looks way more realistic and adapts better to the ground truth path. -However, in this particular example the FBS starts at an earlier position (cf. fig. \ref{fig:intcomp} seg. 2), better handling the initial uniform distribution. -Another advantage of BS over FBS, is the ability to still improve the filtering results even while reducing the number of particles radical. -For example \SI{50}{} particles and \SI{25}{} sample realisations are providing reliable estimations similar to above experiments, though the risk of losing track is higher. -\begin{figure} - \input{gfx/eval/interval_path4_comp/path4_interval} - \caption{Comparison between FBS (red) and BS (blue) on path 4 (black). Both were approximated using $2500$ particles and \SI{500}{} sample realisations for BS. The measurements were recorded using the Nexus 6. } - \label{fig:intcomp} -\todo{Filter mit rein} -\end{figure} +%However, in this particular example the FBS starts at an earlier position (cf. fig. \ref{fig:intcomp} seg. 2), better handling the initial uniform distribution. +%Another advantage of BS over FBS, is the ability to still improve the filtering results even while reducing the number of particles radical. +%For example \SI{50}{} particles and \SI{25}{} sample realisations are providing reliable estimations similar to above experiments, though the risk of losing track is higher. \begin{figure} - \input{gfx/eval/interval_path3_bad/path3_interval} - \caption{A situation where BS smoothing (blue) was not able to improve the filtering results (green). Two main factors are causing this: an initial position within a detached room and inaccurate pressure readings given by the Galaxy S5.} - \label{fig:intervalbad} + \begin{subfigure}{0.175\textwidth} + \input{gfx/eval/interval_path3_good/path3_interval_good} + \caption{} + \label{fig:int_path3_a} + \end{subfigure} + \begin{subfigure}{0.175\textwidth} + \input{gfx/eval/interval_path3_bad/path3_interval} + \caption{} + \label{fig:int_path3_b} + \end{subfigure} + \caption{a) Exemplary comparison between BS (blue) and filtering (green) using 2500 particles and 500 sample realisations. b) A situation where BS smoothing was not able to improve the filtering results. Two main factors are causing this: an initial position within a detached room and inaccurate pressure readings given by the Galaxy S5.} +\label{fig:int_path3_comp} \end{figure} Despite the very good outcomes provided by both interval smoother, there are some rare situations in which smoothing does not improve the filtered estimation or even improves the visual path. -For example fig. \ref{fig:intervalbad} depicts such a situation for path 3 using BS and measurements provided by the Galaxy S5. +For example fig. \ref{fig:int_path3_b} depicts such a situation for path 3 using BS and measurements provided by the Galaxy S5. Here, the estimation was not able to change floors correctly due to faulty pressure readings. Additionally, the initial position was located within a detached room. This shows that the smoothing results are of course highly depend upon the filtering performance. @@ -142,7 +150,7 @@ It is obvious that a lag of \SI{30}{} time steps has access to much more future Considering an update interval of \SI{500}{\milli\second}, a lag of \SI{30}{} would however mean that the smoother is \SI{15}{\second} behind the filter. Nevertheless, there are practical applications like accurately verifying hit checkpoints or continuously optimizing a recurring segment of the path. - +%verlgeich noch zwischen bs und fbs. bs weniger partikel und somit schneller. ändern der estimations kann aber auch ein möglichkeit sein. diff --git a/tex/gfx/eval/interval_path3_bad/path3_interval.eps b/tex/gfx/eval/interval_path3_bad/path3_interval.eps index 25cd5f1..1748ea4 100644 --- a/tex/gfx/eval/interval_path3_bad/path3_interval.eps +++ b/tex/gfx/eval/interval_path3_bad/path3_interval.eps @@ -1,9 +1,9 @@ %!PS-Adobe-2.0 EPSF-2.0 %%Title: path3_interval.tex %%Creator: gnuplot 5.0 patchlevel 1 -%%CreationDate: Thu May 5 16:46:53 2016 +%%CreationDate: Mon May 9 13:49:37 2016 %%DocumentFonts: -%%BoundingBox: 50 50 294 150 +%%BoundingBox: 50 50 222 150 %%EndComments %%BeginProlog /gnudict 256 dict def @@ -43,7 +43,7 @@ gnudict begin /vpt vpt_ def /doclip { ClipToBoundingBox { - newpath 50 50 moveto 294 50 lineto 294 150 lineto 50 150 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\setlength{\fboxsep}{1pt}% -\begin{picture}(4896.00,2014.00)% +\begin{picture}(3456.00,2014.00)% \gplgaddtomacro\gplbacktext{% }% \gplgaddtomacro\gplfronttext{% \csname LTb\endcsname% - \put(4453,1802){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% + \put(2578,393){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% \csname LTb\endcsname% - \put(4453,1582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% + \put(2578,173){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% \csname LTb\endcsname% - \put(4453,1802){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% + \put(2578,393){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% \csname LTb\endcsname% - \put(4453,1582){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% + \put(2578,173){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% }% \gplbacktext \put(0,0){\includegraphics{path3_interval}}% diff --git a/tex/gfx/eval/interval_path3_bad/vis.gp b/tex/gfx/eval/interval_path3_bad/vis.gp index 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a/tex/gfx/eval/interval_path3_good/BS/est_smooth_bergwerk_path3_nexus_simple_interval4.dat b/tex/gfx/eval/interval_path3_good/BS/est_smooth_bergwerk_path3_nexus_simple_interval4.dat new file mode 100644 index 0000000..2275b8c --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/BS/est_smooth_bergwerk_path3_nexus_simple_interval4.dat @@ -0,0 +1,153 @@ +994.088 2766.68 1060 +1012.57 2799.17 1060 +1039.51 2829.99 1060 +1066.98 2846.21 1060 +1102.31 2845.48 1060 +1105.97 2841.27 1060 +1112.37 2852.12 1060 +1124.49 2852.25 1060 +1124.33 2856.93 1060 +1147.6 2859.54 1060 +1164.64 2878.51 1060 +1158.08 2863.58 1060 +1191.39 2854.65 1060 +1282.15 2919.6 1060 +1294.78 2905.74 1060 +1330.37 2910.2 1060 +1384.19 2926.73 1060 +1443.83 2956.71 1060 +1494.98 2949.88 1060 +1516.7 2988.93 1060 +1494.95 2969.9 1060 +1586.22 2950.11 1060 +1606.01 2984.25 1060 +1710.13 3065.44 1060 +1677.44 3094.26 1060 +1668.23 3137.24 1060 +1701.75 3088.1 1059.99 +1713.32 3098.6 1059.95 +1687.52 3153.76 1060 +1686.16 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100644 index 0000000..58c62f8 --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/BS/path_bergwerk_path3_nexus_simple_interval4.dat @@ -0,0 +1,15 @@ +210 2880 1060 +210 2880 1060 +1140 2880 1060 +1340 3180 1060 +1340 3680 890 +1340 4050 720 +1141.08 4050 720 +1141.08 3170 720 +1340 3170 720 +1340 3680 550 +1340 4070 380 +1140 4070 380 +1110 3030 380 +1160.04 1290 380 +e diff --git a/tex/gfx/eval/interval_path3_good/BS/plot_bergwerk_path3_nexus_simple_interval4.gp b/tex/gfx/eval/interval_path3_good/BS/plot_bergwerk_path3_nexus_simple_interval4.gp new file mode 100644 index 0000000..1f7dbbe --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/BS/plot_bergwerk_path3_nexus_simple_interval4.gp @@ -0,0 +1,16 @@ +set terminal eps size 3.4,2 +set output 'bergwerk_path3_nexus_simple_interval4.eps' +set termoption dashlength 0.5 +set ticslevel 0 +set view equal xy +set zrange [0:2200] +set multiplot layout 1,1 scale 2.7,2.7 offset 0,0.23 +set view 72,33 +unset border +unset xtics +unset ytics +unset ztics +splot \ +'floors.dat' skip 21 notitle with lines lc rgb '#777777', \ +'path_bergwerk_path3_nexus_simple_interval4.dat' skip 21 notitle with lines lw 2.5 dashtype 2 lc rgb '#007700', \ +'est_norm_bergwerk_path3_nexus_simple_interval4.dat' skip 21 notitle with lines lw 2.5 lc rgb '#000099', 'est_smooth_bergwerk_path3_nexus_simple_interval4.dat' skip 21 notitle with lines lw 2.5 lc rgb '#000000' \ No newline at end of file diff --git a/tex/gfx/eval/interval_path3_good/BS/plot_dist_err_bergwerk_path3_nexus_simple_interval4.gp b/tex/gfx/eval/interval_path3_good/BS/plot_dist_err_bergwerk_path3_nexus_simple_interval4.gp new file mode 100644 index 0000000..33f0b90 --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/BS/plot_dist_err_bergwerk_path3_nexus_simple_interval4.gp @@ -0,0 +1,3 @@ +plot \ +'err_dist_norm_bergwerk_path3_nexus_simple_interval4.dat' with lines, \ +'err_dist_smooth_bergwerk_path3_nexus_simple_interval4.dat' with lines \ No newline at end of file diff --git a/tex/gfx/eval/interval_path3_good/BS/plot_err_bergwerk_path3_nexus_simple_interval4.gp b/tex/gfx/eval/interval_path3_good/BS/plot_err_bergwerk_path3_nexus_simple_interval4.gp new file mode 100644 index 0000000..ad86d2a --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/BS/plot_err_bergwerk_path3_nexus_simple_interval4.gp @@ -0,0 +1,3 @@ +plot \ +'err_norm_bergwerk_path3_nexus_simple_interval4.dat' with lines, \ +'err_smooth_bergwerk_path3_nexus_simple_interval4.dat' with lines \ No newline at end of file diff --git a/tex/gfx/eval/interval_path3_good/BS/unsmoothed_bergwerk_path3_nexus_simple_interval4.stats b/tex/gfx/eval/interval_path3_good/BS/unsmoothed_bergwerk_path3_nexus_simple_interval4.stats new file mode 100644 index 0000000..e69de29 diff --git a/tex/gfx/eval/interval_path3_good/floors.dat b/tex/gfx/eval/interval_path3_good/floors.dat new file mode 100644 index 0000000..3b0c9aa --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/floors.dat @@ -0,0 +1,2297 @@ +1090 5140 0 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gnuplot or load the package + color.sty in LaTeX.}% + \renewcommand\color[2][]{}% + }% + \providecommand\includegraphics[2][]{% + \GenericError{(gnuplot) \space\space\space\@spaces}{% + Package graphicx or graphics not loaded% + }{See the gnuplot documentation for explanation.% + }{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}% + \renewcommand\includegraphics[2][]{}% + }% + \providecommand\rotatebox[2]{#2}% + \@ifundefined{ifGPcolor}{% + \newif\ifGPcolor + \GPcolorfalse + }{}% + \@ifundefined{ifGPblacktext}{% + \newif\ifGPblacktext + \GPblacktexttrue + }{}% + % define a \g@addto@macro without @ in the name: + \let\gplgaddtomacro\g@addto@macro + % define empty templates for all commands taking text: + \gdef\gplbacktext{}% + \gdef\gplfronttext{}% + \makeatother + \ifGPblacktext + % no textcolor at all + \def\colorrgb#1{}% + \def\colorgray#1{}% + \else + % gray or color? + \ifGPcolor + \def\colorrgb#1{\color[rgb]{#1}}% + \def\colorgray#1{\color[gray]{#1}}% + 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\expandafter\def\csname LT0\endcsname{\color{black}}% + \expandafter\def\csname LT1\endcsname{\color{black}}% + \expandafter\def\csname LT2\endcsname{\color{black}}% + \expandafter\def\csname LT3\endcsname{\color{black}}% + \expandafter\def\csname LT4\endcsname{\color{black}}% + \expandafter\def\csname LT5\endcsname{\color{black}}% + \expandafter\def\csname LT6\endcsname{\color{black}}% + \expandafter\def\csname LT7\endcsname{\color{black}}% + \expandafter\def\csname LT8\endcsname{\color{black}}% + \fi + \fi + \setlength{\unitlength}{0.0500bp}% + \ifx\gptboxheight\undefined% + \newlength{\gptboxheight}% + \newlength{\gptboxwidth}% + \newsavebox{\gptboxtext}% + \fi% + \setlength{\fboxrule}{0.5pt}% + \setlength{\fboxsep}{1pt}% +\begin{picture}(3456.00,2014.00)% + \gplgaddtomacro\gplbacktext{% + }% + \gplgaddtomacro\gplfronttext{% + \csname LTb\endcsname% + \put(2112,4147){\makebox(0,0)[r]{\strut{}\footnotesize{filtered}}}% + \csname LTb\endcsname% + \put(2112,3927){\makebox(0,0)[r]{\strut{}\footnotesize{smoothed (BS)}}}% + }% + \gplbacktext + \put(0,0){\includegraphics{path3_interval_good}}% + \gplfronttext + \end{picture}% +\endgroup diff --git a/tex/gfx/eval/interval_path3_good/startpoints_moved.dat b/tex/gfx/eval/interval_path3_good/startpoints_moved.dat new file mode 100644 index 0000000..1dec0c6 --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/startpoints_moved.dat @@ -0,0 +1,4 @@ +1210 470 1060 +1060.18 4520 0 +180 2970 1060 +1070 470 1060 diff --git a/tex/gfx/eval/interval_path3_good/vis.gp b/tex/gfx/eval/interval_path3_good/vis.gp new file mode 100644 index 0000000..3b3f108 --- /dev/null +++ b/tex/gfx/eval/interval_path3_good/vis.gp @@ -0,0 +1,21 @@ +set terminal epslatex size 2.4,1.4 +set output "path3_interval_good.tex" +set termoption dashlength 0.5 +set ticslevel 0 +set view equal xy +set zrange [0:2200] +set xrange[0:2500] +set yrange[0:5000] +set multiplot layout 1,1 scale 3.1,3.1 offset -0.05,0.26 +set view 78,33 +unset border +unset xtics +unset ytics +unset ztics + + +splot \ + 'floors.dat' notitle with lines lc rgb '#999999', \ + 'path3.dat' notitle with lines lw 1.0 dashtype 2 lc rgb '#000000', \ + 'BS/est_norm_bergwerk_path3_nexus_simple_interval4.dat' skip 21 title "\\footnotesize{filtered}" with lines lw 1.0 lc rgb '#00FF00', \ + 'BS/est_smooth_bergwerk_path3_nexus_simple_interval4.dat' skip 21 title "\\footnotesize{smoothed (BS)}" with lines lw 1.0 lc rgb '#0000FF'