added wi-fi part, path lengths, discussion to walk1

This commit is contained in:
toni
2018-07-03 14:45:28 +02:00
parent 8881557b99
commit e4c2078cd3
11 changed files with 17180 additions and 40 deletions

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@@ -1,3 +1,9 @@
\section{Conclusion}
KDE besser machen, nicht nur maximumg
simple impoverishment nur dann einschalten wenn wirklich gebraucht
wifi optimierung noch besser machen und wände mitnehmen also raytracing
Conclusion Conclusion

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@@ -22,9 +22,8 @@ However, similar to our previous, award-winning system, the setup is able to run
The experiments are separated into four sections:
At first, we discuss the performance of the novel transition model and compare it to a grid-based approach.
In section \ref{sec:exp:opti} we have a look at \docWIFI{} optimization and how the real \docAPshort{} positions differ from it.
Following, we conducted several test walks throughout the building to examine the estimation accuracy (in \SI{}{\meter}) of the localisation system and try to resolve sample impoverishment with the here presented methods.
Finally, the different estimation methods are compared in section \ref{sec:exp:est}.
Following, we conducted several test walks throughout the building to examine the estimation accuracy (in \SI{}{\meter}) of the localisation system and discuss the here presented solutions for sample impoverishment.
Finally, the respective estimation methods are discussed in section \ref{sec:eval:est}.
\subsection{Transition}
To make a statement about the performance of our novel transition model presented within section \ref {}, we chose a simple scenario, in which a tester walks up and down a staircase three times.
@@ -67,8 +66,10 @@ Other transmitters like smart TVs or smartphone hotspots are ignored as they mig
\end{figure}
%
The 4 chosen walking paths can be seen in fig. \ref{fig:floorplan}.
\todo{wie lang sind die walks meter und zeit?}
They were carried out be 4 different male testers using either a Samsung Note 2, Google Pixel One or Motorola Nexus 6 for recording the measurements.
Walk 0 is \SI{152}{\meter} long and took about \SI{2.30}{\minutes} to walk.
Walk 2 has a length of \SI{223}{\meter} and Walk 3 a length of \SI{231}{\meter}, both required about \SI{6}{\minutes} to walk.
Finally, walk 3 is \SI{310}{\meter} long and needs \SI{10}{\minutes} to walk.
All walks were carried out be 4 different male testers using either a Samsung Note 2, Google Pixel One or Motorola Nexus 6 for recording the measurements.
All in all, we recorded \SI{28}{} distinct measurement series, \SI{7}{} for each walk.
The picked walks intentionally contain erroneous situations, in which many of the above treated problems occur.
Thus we are able to discuss everything in detail.
@@ -145,8 +146,15 @@ Without a method to recover from impoverishment, the system lost track in \SI{10
By using the simple method, the overall error can be reduced and the impoverishment resolved. Nevertheless, unpredictable jumps of the estimation are causing the system to be highly uncertain in some situations, even if those jumps do not last to long.
Only the use of the $D_\text{KL}$ method is able to produce reasonable results.
As described in chapter \ref{}, we use a Wi-Fi model optimized for each floor instead of a single global one.
A good example why we do this, can be seen in fig. \ref{}, considering walk 3.
\begin{figure}[bt]
\centering
\includegraphics[width=0.9\textwidth]{gfx/wifiOptGlobalFloor/combined_dummy.png}
\caption{A small section of walk 3. Optimizing the system with a global Wi-Fi optimization scheme (blue) causes a big jump and thus high errors. This happens due to highly attenuated Wi-Fi signals and inappropriate Wi-Fi parameters. We compare this to a system optimized for each floor individually (red), resolving the situation a producing reasonable results.}
\label{fig:wifiopt}
\end{figure}
%
As described in chapter \ref{sec:wifi}, we use a Wi-Fi model optimized for each floor instead of a single global one.
A good example why we do this, can be seen in fig. \ref{fig:wifiopt}, considering a small section of walk 3.
Here, the system using the global Wi-Fi model makes a big jump into the right-hand corridor and requires \SI{5}{\second} to recover.
This happens through a combination of environmental occurrences, like the many different materials and thus attenuation factors, as well as the limitation of the here used Wi-Fi model, only considering ceilings and ignoring walls.
Following, \docAPshort{}'s on the same floor level, which are highly attenuated by \SI{2}{\meter} thick stone walls, are neglected and \docAPshort{}'s from the floor above, which are only separated by a thin wooden ceiling, have a greater influence within the state evaluation process.
@@ -156,48 +164,47 @@ In contrast, the model optimized for each floor only considers the respective \d
A major disadvantage of the method is the reduced number of visible \docAPshort{}'s and thus measurements within an area.
This could lead to an underrepresentation of \docAPshort{}'s for triangulation.
%walk 1
Looking at the results of table \ref{table:overall} again, it can be seen that the $D_\text{KL}$ method is able to improve the results in three of the four walks.
Those walks have in common, that they suffer in some way from sample impoverishment or other problems causing the system to stuck.
The only exception is walk 1.
It was set up to provide a challenging scenario, leading to as many multimodalities as possible.
We intentionally searched for situations in which there was a great chance that the particle set would separate, e.g. by providing multiple possible whereabouts through crossings or by blocking and thus separating a straight path with objects like movable walls.
Similar to the other walks, we added different pausing intervals of \SI{10}{\second} to \SI{60}{\second}.
This helps to analyse how the particles behave in such situations, especially in this multimodal setting.
\todo{fuer eins brauchen wir aber noch estimated path}
\todo{boxkde 0.2 point2(1,1);}
\todo{
BILD: Von einem Pfad der steckenbleibt und den beiden anderen verfahren mit fehler über die zeit.
BILD: WIFI-Fehler unten bei den Kellern.
BILD: Estimation Fehler
}
%To analyse the drawbacks and benefits of the here presented method to resolve sample impoverishment,
%The benefits of the here presented solution to resolve sample impoverishment can be seen in the example shown in fig. \ref{}.
%probleme mit impoverishment aufzeigen, wo bringt es was, was macht es kaputt etc pp
Besides uncertain measurements, one of the main sources for multimodalities are restrictive transition models, e.g. no walking through walls.
As shown in section \ref{sec:impo}, the $D_\text{KL}$ method compares the current posterior $p(\mStateVec_{t} \mid \mObsVec_{1:t})$ with the probability grid $\probGrid_{t, \text{wifi}}$ using the Kullback-Leibler divergence and a Wi-Fi quality factor.
Environmental restriction like walls are not considered while creating $\probGrid_{t, \text{wifi}}$, that is why the grid is not effected by a transition-based multimodal setting.
Given accurate Wi-Fi measurements, it is therefore very likely that $\probGrid_{t, \text{wifi}}$ represents a unimodal distribution, even if the particles got separated by an obstacle or wall.
This leads to a situation, in which posterior and grid differ.
As a result, the radius $r_\text{sub}$ increases and thus the diversity of particles.
We are able to confirm the above by examining the different scenarios integrated into walk 1.
For this, we compared the error development with the corresponding radius $r_\text{sub}$ over time.
In situations where the errors given by the $D_\text{KL}$ method and the simple method differ the most, $r_\text{sub}$ also increases the most.
Here, the radius grows to a maximum of $r_\text{sub} = $ \SI{666}{\meter}.
In contrast, a real sample impoverishment scenario, as seen in walk 0 (cf. fig. \ref{fig:errorOverTimeWalk0}), provides a maximum radius of \SI{777}{\meter}.
Nevertheless, such an slightly increased diversity is enough to influence the estimation error of the $D_\text{KL}$ in a negative way (cf. walk 1 in table \ref{table:overall}).
Ironically, this is again some type of sample impoverishment, caused by the aforementioned environmental restrictions not allowing particles inside walls or other out of reach areas.
%%estimation
\subsection{Estimation Methods}
\label{sec:exp:est}
\subsection{Estimation}
\label{sec:eval:est}
As discussed before, the single estimation methods only vary by a few centimetres in the overall localization error.
As mentioned before, the single estimation methods (cf. chapter \ref{sec:estimation}) only vary by a few centimetres in the overall localization error.
That means, they differ mainly in the representation of the estimated locations.
More easily spoken, in which way the estimated path is drawn and thus presented to the user.
Regarding the underlying particle set, different shapes of probability distributions need to be considered, especially those with multimodalities.
%
\begin{figure}
\centering
\input{gfx/walk.tex}
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of the walk. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides a high error compared to the ground truth (solid black), while the BoxKDE approach (orange) does not. }
\caption{Occurring bimodal distribution caused by uncertain measurements in the first \SI{13.4}{\second} of walk 1. After \SI{20.8}{\second}, the distribution gets unimodal. The weigted-average estimation (blue) provides a high error compared to the ground truth (solid black), while the KDE approach (orange) does not. }
\label{fig:realWorldMulti}
\end{figure}
%
The main advantage of a KDE-based estimation is that it provides the "correct" mode of a density, even under a multimodal setting (cf. section \ref{sec:estimation}).
That is why we again have a look at walk 1.
A situation in which the system highly benefits from this is illustrated in fig. \ref{fig:realWorldMulti}.
Here, a set of particles splits apart, due to uncertain measurements and multiple possible walking directions.
Indicated by the black dotted line, the resulting bimodal posterior reaches its maximum distance between the modes at \SI{13.4}{\second}.
@@ -223,15 +230,24 @@ Only with new measurements coming from the hallway or other parts of the buildin
\label{fig:realWorldTime}
\end{figure}
This lead to the conclusion, that a weighted average approach provides a more smooth representation of the estimated locations and thus a higher robustness.
This leads to the conclusion, that a weighted average approach provides a more smooth representation of the estimated locations and thus a higher robustness.
\todo{bild vom gesamten walk 2 und den unterschied zwischen weighted average estimation und kde estimation zeigen. wie sich das auf dne estimated path auswirkt. also der eine pfad springt viel und der andere ist halt smoother}
In contrast, a KDE-based approach for estimation is able to resolve multimodalities.
It does not always provide the lowest error, since it depends more on an accurate sensor model then a weighted average approach, but is very suitable as a good indicator about the real performance of a sensor fusion system.
At the end, in the here shown examples we only searched for a global maxima, even though this approach opens a wide range of other possibilities for finding a best estimate.
%wie in bulli paper.
\todo{boxkde 0.2 point2(1,1);}
\todo{
BILD: Von einem Pfad der steckenbleibt und den beiden anderen verfahren mit fehler über die zeit.
BILD: WIFI-Fehler unten bei den Kellern.
BILD: Estimation Fehler
}
%letzer absatz nochmal gesamtergebniss des gesamten systems
%was läuft noch schief? wo macht was probleme?

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@@ -45,3 +45,5 @@ The goal of this work is to propose a fast to deploy and low-cost localization s
Consequently, we believe that by utilizing our localization approach to such a challenging scenario, it is possible to prove those characteristics.
Finally, it should be mentioned that the here presented work is an highly updated version of the winner of the smartphone-based competition at IPIN 2016 \cite{Ebner-15}.
\todo{Dankesagung Moehring oder einfach mit als Autor?}

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31.7207 35.5418 1.8
31.7207 35.5418 1.8
31.9779 35.5418 1.8
31.7207 36.3722 1.8
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31.4635 38.0331 1.8
30.9492 38.3099 1.8
31.4635 38.5867 1.8
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28.8917 38.0331 1.8
28.3773 38.0331 1.8
27.6058 38.0331 1.8
26.8342 38.0331 1.8
26.3199 38.0331 1.8
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17.5756 38.8635 1.8
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19.1187 41.9084 1.6
20.919 38.8635 1.8
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19.1187 40.8011 1.7
19.3759 42.462 1.5
19.3759 43.0156 1.2
19.3759 43.2924 1
19.3759 43.5692 1
19.3759 43.846 1.2
19.6331 44.1228 1.3
18.6044 39.4171 1.5
18.8615 38.8635 1.4
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538636 4.00663
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540151 4.54021
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588170 2.35226
588620 4.09437
589164 4.85194
589741 5.40974
590507 6.22289
590979 6.47376
==========================================================
Average of all statistical data:
Median: 3.01603
Average: 3.93866
Standard Deviation: 3.67323
75 Quantil: 4.84232
1 935 3.37744
2 2418 2.61961
3 3031 2.8039
4 3582 3.2869
5 4132 2.14532
6 4689 1.05611
7 5263 0.58046
8 5773 0.370401
9 6229 0.62646
10 6734 0.817983
11 7353 1.01709
12 7903 1.28711
13 8471 1.54028
14 8969 1.6342
15 9522 1.39373
16 10087 1.33773
17 10655 1.50997
18 11194 1.16285
19 11679 2.16394
20 12358 2.60174
21 13000 3.11666
22 13689 2.32636
23 14143 2.70312
24 14790 2.66065
25 15333 1.53309
26 15970 1.50754
27 16711 1.61012
28 17504 2.29428
29 18138 2.74911
30 19481 2.86313
31 24685 4.11052
32 37648 1.4347
33 38383 2.24361
34 41551 2.52692
35 41982 2.6566
36 42590 2.47945
37 43264 2.22912
38 43876 2.50013
39 44401 2.45235
40 45076 2.17915
41 45531 2.25418
42 46108 3.09171
43 46774 4.09682
44 47183 3.30524
45 47741 4.55706
46 48412 5.2523
47 48901 6.16501
48 49541 6.75941
49 50001 7.67147
50 50533 8.36573
51 51164 9.37429
52 51702 10.3562
53 52231 11.0995
54 52662 1.6854
55 53288 1.60292
56 53824 4.2151
57 54355 4.19943
58 54891 4.0094
59 55403 4.35427
60 55927 4.3963
61 56465 4.21048
62 57002 4.2834
63 57527 4.11684
64 58078 4.17491
65 58579 4.29926
66 59037 4.22323
67 59637 3.98302
68 60191 3.81222
69 60724 3.9262
70 61252 3.53561
71 61787 3.90652
72 62319 3.77148
73 62834 3.62479
74 63392 1.68196
75 63908 1.82908
76 64475 1.67586
77 65003 1.98296
78 65527 1.81834
79 66048 1.19329
80 66574 1.3621
81 67148 3.45714
82 67681 3.54997
83 68228 3.60173
84 68774 1.18557
85 69301 2.49635
86 69848 3.98945
87 70438 2.9178
88 70886 3.10215
89 71517 2.0563
90 72099 2.20594
91 72763 2.99841
92 73207 3.37907
93 73872 3.1873
94 74489 3.74747
95 74925 3.19097
96 75444 3.53698
97 76194 2.33997
98 76676 2.50524
99 77430 0.674557
100 78061 0.926307
101 78678 1.39113
102 79210 2.17158
103 79761 2.87975
104 80673 4.71984
105 81152 4.84588
106 81706 5.1945
107 82487 5.17218
108 84503 5.94523
109 86435 5.83251
110 94515 5.47969
111 99174 5.66734
112 104624 5.42577
113 106108 4.85752
114 106559 4.9516
115 107164 4.64832
116 107565 4.20716
117 107989 4.00093
118 108395 3.97179
119 109007 3.75982
120 117762 4.0989
121 118440 4.43577
122 119245 5.91086
123 120801 6.12286
124 121682 5.0563
125 122163 4.7835
126 123192 4.49181
127 123875 4.4678
128 124526 4.70427
129 125059 4.34286
130 125683 4.06191
131 126337 4.24209
132 127045 2.91357
133 127742 2.54645
134 128403 3.39918
135 129015 2.67484
136 129630 1.44267
137 130322 3.64314
138 130935 0.418453
139 131464 1.83847
140 132348 1.97509
141 132999 1.66605
142 133867 2.16901
143 145180 6.12667
144 145695 6.25568
145 146241 6.90961
146 146834 7.14284
147 147413 4.68936
148 147975 4.03704
149 148599 3.57933
150 149194 2.99894
151 149722 2.28483
152 150325 1.94899
153 150837 1.83251
154 151521 1.82361
155 152157 3.19797
156 152682 4.38713
157 153393 5.34337
158 154009 5.91562
159 154597 1.87462
160 155153 1.32054
161 155706 1.42105
162 156202 1.20127
163 156740 1.20359
164 157276 1.3875
165 157818 1.28155
166 158328 1.64889
167 158875 1.84871
168 159402 1.57753
169 159961 1.49124
170 160392 1.48364
171 161000 1.49956
172 161508 1.08241
173 162053 0.966131
174 162550 0.979702
175 163101 0.936242
176 163638 1.28483
177 164161 1.16228
178 164699 1.17361
179 165242 1.20167
180 165764 1.15047
181 166276 1.20173
182 166800 1.2692
183 167354 1.33019
184 167913 1.39659
185 168450 1.49157
186 168940 1.64341
187 169521 1.49138
188 170006 1.4366
189 170608 1.27558
190 171040 0.962273
191 171724 0.692571
192 172204 0.864591
193 172918 1.67122
194 173606 1.87187
195 174094 1.90436
196 174601 1.87725
197 175362 1.80108
198 175992 2.12382
199 176793 3.34148
200 177320 4.15614
201 177903 5.779
202 178487 6.90071
203 179100 16.6367
204 179686 17.9988
205 180228 19.0183
206 180769 20.3154
207 181267 21.5709
208 181820 22.6235
209 182346 23.8925
210 182890 24.9369
211 183416 26.2207
212 183953 27.5055
213 184477 28.5307
214 185035 18.0599
215 185507 18.0088
216 186052 17.7752
217 186459 12.5239
218 186862 12.4247
219 187290 13.649
220 187932 13.2769
221 188458 13.5576
222 188960 13.9942
223 189619 14.5641
224 190154 2.82469
225 190659 2.28575
226 191329 2.25123
227 191968 2.89728
228 192456 2.75161
229 193431 4.38768
230 194275 3.08249
231 194900 2.49504
232 195457 1.77399
233 196027 0.943718
234 196586 1.07829
235 197415 0.868193
236 198229 1.19014
237 199744 1.59255
238 211572 1.66971
239 212271 2.26537
240 213372 1.70178
241 214204 2.40096
242 214673 1.90749
243 215320 2.51392
244 215853 2.0941
245 216487 2.5162
246 217057 2.85232
247 217648 0.368407
248 218302 0.638629
249 219005 0.211782
250 219645 0.601473
251 220262 1.84329
252 220949 2.81096
253 221590 1.58951
254 222299 1.94832
255 223528 2.2831
256 226245 1.9418
257 227200 2.47363
258 228494 2.81574
259 231978 3.29574
260 254675 3.63846
261 255692 3.88887
262 256318 3.97407
263 256977 3.8745
264 257727 2.72657
265 258405 2.8348
266 258978 3.03754
267 259535 3.04425
268 260174 2.30463
269 260740 2.35017
270 261537 2.70864
271 262311 3.2729
272 262857 3.11005
273 263394 3.17134
274 263896 2.93781
275 264410 2.98015
276 265081 3.39465
277 265832 2.98281
278 266890 2.44491
279 267484 1.38727
280 268110 1.71597
281 268640 1.91167
282 269282 2.30776
283 269838 0.881876
284 270462 0.85099
285 270942 0.542407
286 271449 2.12807
287 272017 2.97195
288 272612 4.01269
289 273188 4.30898
290 273769 4.93209
291 274215 5.4251
292 274811 6.08301
293 275361 6.7184
294 275943 7.35254
295 276454 7.75007
296 277049 8.21661
297 277616 8.50352
298 278070 8.86684
299 278657 10.1116
300 279268 11.2449
301 279844 11.8097
302 280395 3.40603
303 280923 3.40999
304 281501 9.67447
305 282027 9.70039
306 282500 9.75042
307 283030 9.88636
308 283496 10.118
309 284127 5.80337
310 284866 5.44227
311 285703 6.22799
312 286381 6.94154
313 286955 3.6595
314 287645 4.05119
315 288206 4.44256
316 288740 4.39579
317 289248 4.6618
318 289742 4.71275
319 290312 4.60131
320 290859 4.49006
321 291374 3.40203
322 291907 3.35053
323 292409 3.16612
324 292924 2.99722
325 293440 2.8304
326 293985 2.69617
327 294496 2.52604
328 295050 2.40303
329 295561 2.23582
330 296107 1.73385
331 296600 1.92616
332 297155 3.76115
333 297649 4.22549
334 298212 4.54657
335 298727 4.99395
336 299279 4.58439
337 299758 4.16811
338 300332 3.20033
339 300841 3.64442
340 301365 4.07302
341 301867 4.25783
342 302418 4.65564
343 302933 4.55072
344 303483 4.12666
345 304003 4.8446
346 304553 4.42764
347 305086 3.76
348 305628 4.0541
349 306134 3.62207
350 306680 2.60432
351 307219 1.96087
352 307755 1.6031
353 308330 1.27464
354 308826 1.87658
355 309492 2.19546
356 310072 1.54423
357 310676 1.39882
358 311245 0.559307
359 311772 1.61612
360 312372 5.19361
361 312834 5.9971
362 313574 6.40546
363 314103 6.00193
364 314630 6.08009
365 315340 5.99202
366 315816 3.40138
367 316563 2.77676
368 317114 1.4071
369 317554 1.07428
370 318057 1.72413
371 318488 1.3186
372 319013 1.72294
373 319485 2.16361
374 320037 4.87163
375 320442 2.16487
376 320939 2.30383
377 321376 1.26059
378 321996 1.62682
379 322401 1.96903
380 322974 2.11611
381 323487 2.19708
382 324135 1.83713
383 324645 1.63688
384 325203 1.52235
385 325609 1.13014
386 326592 0.700748
387 327125 0.61833
388 327533 0.714656
389 328125 0.725565
390 328532 0.918122
391 329135 1.03341
392 329597 1.00469
393 330152 1.13876
394 330693 0.929793
395 331226 1.12541
396 331746 1.48749
397 332279 1.59415
398 333316 2.51933
399 333993 3.58162
400 334641 3.16127
401 335390 3.52825
402 336005 3.92916
403 336556 4.34355
404 337160 4.18986
405 337652 3.92201
406 338235 2.82938
407 338703 1.15198
408 339296 1.27909
409 339769 1.34902
410 340396 2.19192
411 340848 2.92176
412 341512 3.37413
413 342007 3.60166
414 342651 3.01603
415 343436 2.54328
416 346315 6.29999
417 355491 6.08454
418 358621 5.62644
419 359024 5.92691
420 359638 5.71533
421 360467 6.39731
422 361731 6.11918
423 362162 6.42041
424 362897 6.16278
425 363567 6.59255
426 370406 6.97294
427 370898 8.19197
428 371458 8.44664
429 377243 10.0601
430 385546 10.3745
431 386379 10.4264
432 387026 11.5256
433 387617 12.0603
434 388339 11.5779
435 388910 11.0564
436 389514 9.37637
437 390123 8.64402
438 390893 7.00032
439 391426 6.12555
440 392108 5.72493
441 392623 5.64236
442 393156 5.73407
443 393710 5.92037
444 394295 5.87529
445 395035 5.80018
446 395869 6.05348
447 400999 6.22828
448 407010 6.34751
449 413239 6.32135
450 414557 6.54895
451 414961 6.61714
452 419245 1.19769
453 419653 1.15677
454 432403 1.90482
455 433115 2.12789
456 433594 2.51371
457 434529 2.65273
458 453071 2.66546
459 454660 2.6733
460 455202 3.10323
461 457329 4.35248
462 458017 6.22071
463 458744 6.30311
464 459370 7.42614
465 460005 7.83169
466 460589 7.88146
467 461168 7.43589
468 461746 7.31201
469 462355 6.65256
470 463043 6.21706
471 463646 5.8753
472 464276 5.5965
473 464920 5.25049
474 465536 4.84232
475 467010 4.13549
476 468821 3.29305
477 473583 3.08313
478 477613 2.30365
479 478155 2.12581
480 478860 2.06295
481 479597 1.95113
482 480291 2.20084
483 480930 1.96611
484 481593 2.22346
485 482203 2.65603
486 482772 0.592951
487 483256 0.632287
488 483951 1.32025
489 484611 1.99564
490 485083 2.14254
491 485651 0.889592
492 486254 0.682908
493 486717 1.09681
494 487259 0.956944
495 487759 0.976142
496 488419 1.2675
497 488866 1.22831
498 489408 1.2286
499 489966 1.37219
500 490518 1.36722
501 491070 0.614271
502 491602 0.478187
503 492158 0.536677
504 492717 0.606935
505 493308 0.72082
506 493881 2.75997
507 494758 4.4352
508 495409 5.56522
509 496095 6.42176
510 496562 5.35027
511 497123 6.9226
512 497695 7.19932
513 498391 6.51872
514 498950 4.58106
515 499406 3.95878
516 499985 2.90859
517 500595 2.65154
518 501288 1.55207
519 501878 0.784693
520 502421 0.442216
521 503081 0.179889
522 503788 1.18849
523 504683 0.125869
524 505243 0.540522
525 505894 0.914394
526 506481 1.54922
527 507112 2.17044
528 507695 2.09127
529 508318 1.76214
530 508946 1.6904
531 509719 2.02231
532 510391 1.67206
533 510841 1.64483
534 511571 2.1857
535 512320 2.29042
536 517390 3.60523
537 517824 3.60121
538 518689 4.31895
539 519197 4.79663
540 519815 5.04184
541 520361 4.4201
542 521037 3.85627
543 521493 3.77049
544 522060 3.22866
545 522610 2.73802
546 523209 2.78317
547 523925 2.56069
548 524598 4.07212
549 525007 5.32468
550 525412 5.39162
551 525886 5.37099
552 526323 5.45073
553 526812 5.32705
554 527284 3.04357
555 527748 3.3756
556 528169 3.50419
557 528632 3.37528
558 529087 3.25943
559 529536 5.25575
560 529995 5.57332
561 530445 5.66924
562 530981 5.94327
563 531457 6.10783
564 531959 6.19944
565 532435 6.41394
566 532932 5.5441
567 533417 5.22206
568 533856 5.25279
569 534478 5.17672
570 535110 3.33099
571 535761 3.07419
572 536377 3.00231
573 536989 3.51306
574 537479 3.55209
575 538015 3.80816
576 538636 4.00663
577 539155 4.41198
578 539624 4.83721
579 540151 4.54021
580 540680 4.26323
581 541234 3.70005
582 541783 3.79527
583 542367 3.96757
584 543037 2.82428
585 543526 2.11558
586 544154 1.19056
587 544719 0.703653
588 545198 1.0259
589 545767 1.09324
590 546361 1.1107
591 547060 1.17678
592 547615 1.0408
593 548197 1.11706
594 548742 1.18584
595 549299 1.25451
596 549904 1.33307
597 550441 1.48604
598 551025 1.51802
599 551592 1.72262
600 552173 1.84531
601 552768 1.67372
602 553378 2.02956
603 554566 2.27793
604 555418 2.46328
605 559729 2.97764
606 560425 3.50184
607 560909 3.78778
608 561636 3.75109
609 568996 3.5449
610 569840 3.3171
611 574135 2.55146
612 581798 1.44888
613 582220 1.72336
614 585202 1.40231
615 585884 1.13109
616 586457 1.89076
617 587100 2.27793
618 587563 1.9665
619 588170 2.35226
620 588620 4.09437
621 589164 4.85194
622 589741 5.40974
623 590507 6.22289
624 590979 6.47376
625 ==========================================================
626 Average of all statistical data:
627 Median: 3.01603
628 Average: 3.93866
629 Standard Deviation: 3.67323
630 75 Quantil: 4.84232

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197423 3.53579
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211605 4.8236
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215863 9.57839
216496 9.94323
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419249 7.88751
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==========================================================
Average of all statistical data:
Median: 2.62305
Average: 4.2586
Standard Deviation: 3.98062
75 Quantil: 5.79015
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2 3041 0.961315
3 3590 1.67789
4 4143 1.16452
5 4694 1.54299
6 5268 2.06934
7 5773 2.30173
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11 7907 2.55427
12 8475 2.76569
13 8973 2.49902
14 9523 2.40722
15 10095 2.65859
16 10663 2.63747
17 11201 2.94528
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19 12368 3.21608
20 13008 3.24365
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22 14143 4.54674
23 14795 4.501
24 15445 3.85643
25 15974 4.57246
26 16717 2.10704
27 17504 2.13861
28 18143 3.95023
29 19500 3.94104
30 24706 7.62465
31 37670 3.59044
32 41986 3.94598
33 42595 3.43345
34 43269 5.00966
35 43884 3.0943
36 44401 2.36738
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38 45531 1.33262
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52 53296 2.08307
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54 54359 2.23401
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56 55407 2.35406
57 55931 2.28559
58 56469 1.98842
59 57002 1.87373
60 57531 1.77462
61 58078 1.93816
62 58587 1.37693
63 59126 1.16453
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65 60199 1.03902
66 60736 1.11181
67 61260 1.21169
68 61793 1.30902
69 62319 1.42194
70 62834 1.29673
71 63392 1.38074
72 63908 1.52
73 64475 1.20676
74 65003 1.4348
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78 67148 1.63868
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121 127751 1.18261
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123 129137 1.26169
124 129630 0.645919
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126 130943 1.04158
127 131468 1.09626
128 132365 1.46639
129 133881 1.10457
130 145190 4.92926
131 145716 4.63325
132 146267 4.98671
133 146839 5.01883
134 147430 4.81272
135 148055 2.6764
136 148604 2.30853
137 149199 1.91002
138 149727 1.3647
139 150332 1.46931
140 150851 1.54403
141 151530 1.80449
142 152162 0.602381
143 152686 0.613139
144 153403 1.19207
145 154011 1.50893
146 154602 1.08279
147 155158 1.36368
148 155706 1.19998
149 156207 0.682676
150 156747 1.6601
151 157276 1.77043
152 157818 1.8749
153 158347 1.7729
154 158875 1.47151
155 159405 1.00696
156 159965 1.13335
157 160507 1.1851
158 161025 1.00012
159 161512 1.18386
160 162057 1.28396
161 162554 0.910122
162 163105 0.813935
163 163647 0.725723
164 164166 1.22464
165 164703 1.39721
166 165245 1.6561
167 165769 2.18186
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169 166809 2.59625
170 167359 2.10863
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172 168455 0.809694
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179 172204 0.678601
180 172918 0.835065
181 173606 1.28329
182 174102 0.950558
183 174609 0.54339
184 175362 0.504686
185 175992 0.989147
186 176798 0.779365
187 177326 0.420637
188 177911 1.59442
189 178487 1.57756
190 179109 1.6988
191 179694 1.85246
192 180236 1.85327
193 180774 1.85703
194 181277 1.50723
195 181825 1.69701
196 182346 1.91902
197 182897 2.12617
198 183416 2.01376
199 183960 5.68342
200 184477 5.68761
201 185041 5.13791
202 185510 4.68086
203 186056 4.14888
204 186459 4.06291
205 186862 3.1106
206 187290 3.27016
207 187937 2.68192
208 188458 1.4567
209 188963 1.9092
210 189623 2.38154
211 190167 1.60452
212 190665 1.08135
213 191343 1.66708
214 191971 2.34041
215 192456 2.60762
216 193439 2.93631
217 194275 4.35779
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220 196035 4.80087
221 196590 3.70838
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223 198235 3.62272
224 211605 4.8236
225 213412 5.22759
226 214209 5.0676
227 215325 9.2098
228 215863 9.57839
229 216496 9.94323
230 217065 9.88609
231 217656 2.00758
232 218307 0.905007
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235 220415 0.990355
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238 222317 1.205
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242 256340 3.97235
243 256982 3.40304
244 257742 3.50338
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246 258982 2.85229
247 259541 3.18707
248 260194 2.79981
249 260747 3.05196
250 261545 2.63541
251 262329 3.28585
252 262862 3.65476
253 263399 3.31366
254 263909 3.25055
255 264416 3.42033
256 265095 1.92116
257 265839 2.84171
258 266912 2.11525
259 267484 1.61136
260 268115 1.39038
261 268657 0.993702
262 269295 1.40688
263 269845 1.16704
264 270467 1.63497
265 270956 1.4906
266 271462 1.51028
267 272022 2.62305
268 272620 2.96958
269 273193 2.67619
270 273769 4.21225
271 274223 4.63943
272 274816 4.68063
273 275371 6.22773
274 275947 7.27467
275 276462 7.24162
276 277062 7.80441
277 277616 9.434
278 278079 9.82845
279 278674 10.6976
280 279273 10.6574
281 279849 11.1818
282 280399 11.7046
283 280928 8.65264
284 281505 2.51716
285 282029 2.69264
286 282505 2.91761
287 283030 2.51156
288 283496 2.27445
289 284135 1.33925
290 284905 1.50233
291 285708 1.57259
292 286381 2.31014
293 286959 2.03479
294 287649 2.25229
295 288213 2.52279
296 288753 2.45922
297 289248 2.50946
298 289742 2.56023
299 290317 2.59985
300 290867 2.47682
301 291378 1.79389
302 291911 1.65
303 292414 1.70874
304 292937 1.42951
305 293443 1.61624
306 293989 1.48514
307 294500 0.585846
308 295055 0.455205
309 295565 0.861499
310 296112 0.765383
311 296605 0.455065
312 297162 0.610709
313 297653 0.184103
314 298219 0.281158
315 298729 0.888634
316 299283 0.787971
317 299768 1.19005
318 300338 0.488492
319 300845 0.88292
320 301374 1.164
321 301871 0.780495
322 302422 1.09092
323 302937 0.804457
324 303488 0.934444
325 304008 1.00435
326 304558 0.926466
327 305091 1.05436
328 305652 0.890037
329 306138 1.0206
330 306682 0.682184
331 307227 0.815448
332 307768 1.09813
333 308338 1.62301
334 308826 1.40825
335 309504 2.00219
336 310072 0.565492
337 310682 0.47027
338 311259 0.353614
339 311778 0.0787535
340 312411 5.22445
341 312842 6.0735
342 314111 7.17424
343 314767 7.26271
344 315349 6.72959
345 315816 6.23895
346 316563 5.37447
347 317128 1.03861
348 317563 1.1696
349 318065 1.5829
350 318498 1.97222
351 319016 2.45705
352 319492 5.294
353 320046 6.44505
354 320451 2.42023
355 320961 2.32881
356 321389 2.61391
357 322006 3.60897
358 322411 4.55551
359 322983 4.79951
360 323500 4.33895
361 324143 3.95687
362 324650 3.06339
363 325218 1.98075
364 325622 1.66933
365 326599 2.59178
366 327147 3.56173
367 327555 5.79015
368 328131 6.94007
369 328532 7.85222
370 329143 9.0611
371 329610 10.1813
372 330183 11.2712
373 330698 12.2684
374 331230 13.4973
375 331750 14.6105
376 332368 15.7985
377 333329 15.9852
378 333993 16.0742
379 334646 13.2851
380 335398 13.5851
381 336011 13.8316
382 336569 13.8871
383 337168 14.0481
384 337659 14.2355
385 338243 14.3363
386 338793 14.546
387 339308 14.8158
388 339769 14.8182
389 340404 14.7309
390 340848 14.7008
391 341518 14.7825
392 342017 14.8479
393 342665 14.922
394 343453 15.0644
395 346315 14.8055
396 355507 14.8467
397 358982 14.7286
398 359656 14.5946
399 362184 14.5894
400 362915 14.7997
401 371463 15.4469
402 385603 16.2857
403 386379 16.0399
404 387034 16.5711
405 387617 16.996
406 388352 17.0209
407 388921 17.2568
408 389514 17.748
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410 390893 5.79475
411 391427 6.49895
412 392116 6.65378
413 392623 8.28732
414 393156 8.87924
415 393716 10.1171
416 394295 8.68055
417 395040 9.84972
418 407040 10.668
419 413248 9.53184
420 419249 7.88751
421 419656 7.65055
422 432554 8.40441
423 453107 9.7778
424 457347 8.97023
425 458038 9.2487
426 459379 8.7753
427 460005 8.80387
428 460589 8.00831
429 461272 7.77215
430 461750 6.75686
431 462359 6.7927
432 463184 6.18462
433 463650 5.80955
434 464285 5.7455
435 465046 5.89504
436 477627 4.8242
437 478161 4.53392
438 478871 4.36869
439 479597 4.82152
440 480291 4.26508
441 480934 3.36191
442 481603 3.04222
443 482220 1.87135
444 483287 1.64425
445 483959 1.33122
446 484612 2.5118
447 485093 1.73696
448 485735 0.632515
449 486255 1.27077
450 486717 3.28788
451 487259 3.77343
452 487764 3.75548
453 488423 3.56621
454 488873 4.10184
455 489413 4.03901
456 489983 4.22128
457 490630 4.03929
458 491074 3.81144
459 491607 3.75982
460 492162 3.75826
461 492721 14.8972
462 493409 13.1629
463 493885 11.7739
464 494763 11.1992
465 495414 11.1316
466 496098 10.0165
467 496576 9.27619
468 497259 8.91764
469 497709 9.57476
470 498391 8.15295
471 498950 7.65385
472 499406 7.03603
473 499988 6.53812
474 500595 6.02482
475 501301 5.68478
476 501975 5.68052
477 502421 5.2306
478 503081 5.57101
479 503812 5.99706
480 504689 6.18679
481 505243 6.63462
482 505899 7.19081
483 506489 7.95001
484 507119 8.5195
485 507705 9.84844
486 508322 10.578
487 508946 11.5455
488 509726 11.5589
489 511580 10.8646
490 517838 7.73628
491 519202 6.80744
492 519824 6.71395
493 520371 6.64485
494 521039 5.10198
495 521502 4.9332
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497 522614 5.42461
498 523212 6.23737
499 523932 6.21022
500 524610 7.02927
501 525020 7.47532
502 525425 8.12362
503 525891 6.67237
504 526333 7.06939
505 526812 6.70685
506 527292 6.97072
507 527748 7.19584
508 528169 7.26873
509 528632 3.64766
510 529092 1.10612
511 529546 1.21371
512 529999 1.19866
513 530445 2.07784
514 530985 2.05019
515 531462 1.55402
516 531969 1.33781
517 532439 1.15789
518 532936 1.26473
519 533422 0.979284
520 533856 1.14777
521 534478 1.27268
522 535110 1.52161
523 535761 1.78096
524 536377 2.71338
525 537017 2.9151
526 537479 2.8227
527 538020 4.96541
528 538645 5.5891
529 539161 4.65842
530 539645 5.58029
531 540165 6.93976
532 540686 6.86248
533 541234 3.09955
534 541783 4.35721
535 542367 4.09857
536 543046 3.54351
537 543608 3.84445
538 544163 3.97808
539 544727 4.97707
540 545203 6.20857
541 545767 6.72879
542 546361 6.78487
543 547069 0.671932
544 547621 5.82008
545 548197 5.42823
546 548743 1.93752
547 549307 2.06086
548 549904 1.3945
549 550442 2.1108
550 551033 2.03564
551 551598 1.3256
552 552177 1.51403
553 552781 1.65053
554 553378 2.17683
555 554836 2.25527
556 559738 2.73829
557 560922 2.74273
558 561658 2.77552
559 574171 3.88248
560 582190 4.43344
561 586049 3.86081
562 586466 2.90364
563 587109 0.559653
564 587563 0.550365
565 588175 1.02689
566 588629 1.40344
567 589287 8.90757
568 589746 12.1738
569 590524 12.8458
570 590992 13.2814
571 ==========================================================
572 Average of all statistical data:
573 Median: 2.62305
574 Average: 4.2586
575 Standard Deviation: 3.98062
576 75 Quantil: 5.79015

View File

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47.4089 5.64677 2
46.8945 5.92357 1.9
45.8658 5.64677 1.9
45.8658 5.92357 1.9
45.3514 5.92357 1.8
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33.0066 21.9783 1.8
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17.8328 39.4171 1.8
17.8328 39.4171 1.8
17.8328 39.4171 1.8
17.5756 38.8635 1.8
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17.5756 38.8635 1.8
19.1187 41.9084 1.6
20.919 38.8635 1.8
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18.8615 39.4171 1.8
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18.3472 39.4171 1.8
19.1187 40.8011 1.7
19.3759 42.462 1.5
19.3759 43.0156 1.2
19.3759 43.2924 1
19.3759 43.5692 1
19.3759 43.846 1.2
19.6331 44.1228 1.3
18.6044 39.4171 1.5
18.8615 38.8635 1.4
18.09 38.8635 1.4
18.09 39.1403 1.5
22.7193 45.7837 0.7
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25.8055 45.23 0.1
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26.577 44.6764 0.1
27.6058 44.6764 0.1
28.1201 44.6764 0.1
26.8342 44.6764 0.1
26.577 44.6764 0.1
25.8055 44.9532 0.1
25.5483 44.9532 0.1
24.7768 44.6764 0.1
24.0052 44.6764 0.1
23.748 45.23 0.1
22.7193 45.5068 0.1
22.4621 45.7837 0.1
21.6906 45.5068 0.1
21.6906 45.7837 0.1
21.6906 45.7837 0.1
20.6618 45.5068 0.1
e
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