158 lines
22 KiB
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158 lines
22 KiB
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\newlabel{fig:wifiOptFuncTXPEXP}{{1a}{7}{Modifying \docTXP {} \mTXP {} and \docEXP {} \mPLE {} [known position $\mPosAPVec {}$, fixed \mWAF {}] denotes a convex function. \relax }{subfigure.1.1}{}}
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\newlabel{sub@fig:wifiOptFuncTXPEXP}{{a}{7}{Modifying \docTXP {} \mTXP {} and \docEXP {} \mPLE {} [known position $\mPosAPVec {}$, fixed \mWAF {}] denotes a convex function. \relax }{subfigure.1.1}{}}
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\newlabel{fig:referenceMeasurements}{{2a}{10}{The size of each square denotes the number of permanently installed \docAPshort {}s that were visible while scanning, and ranges between 2 and 22 with an average of 9. \relax }{subfigure.2.1}{}}
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\newlabel{sub@fig:referenceMeasurements}{{a}{10}{The size of each square denotes the number of permanently installed \docAPshort {}s that were visible while scanning, and ranges between 2 and 22 with an average of 9. \relax }{subfigure.2.1}{}}
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\newlabel{fig:modelBBoxes}{{2b}{10}{Each distinct floor-color denotes a region (6 indoors, 1 outdoors) for {\em \optPerRegion {}}. Often more than one bounding box is needed to describe the region's shape. \relax }{subfigure.2.2}{}}
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\newlabel{sub@fig:modelBBoxes}{{b}{10}{Each distinct floor-color denotes a region (6 indoors, 1 outdoors) for {\em \optPerRegion {}}. Often more than one bounding box is needed to describe the region's shape. \relax }{subfigure.2.2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \leavevmode {\color {red} Locations of the 121 reference measurements (left) and bounding-boxes used for {\em model per region{}} (right). Indoor-areas are denoted using a grey fill-color per floor, outdoor-areas are green. } \relax }}{10}{figure.2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces \leavevmode {\color {red} Measurable signal strengths of a testing AP{} (black dot). While the signal diminishes slowly along the corridor (wide, black rectangle) the building's metallized windows (dashed, grey lines) between the indoor-region (grey) and the outdoor-region (green) attenuate the signal by over \ensuremath {30}\text {\tmspace +\thinmuskip {.1667em}dB} (small, black rectangle). } \relax }}{10}{figure.3}}
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\newlabel{fig:wifiIndoorOutdoor}{{3}{10}{\changed { Measurable signal strengths of a testing \docAPshort {} (black dot). While the signal diminishes slowly along the corridor (wide, black rectangle) the building's metallized windows (dashed, grey lines) between the indoor-region (grey) and the outdoor-region (green) attenuate the signal by over \SI {30}{\decibel } (small, black rectangle). } \relax }{figure.3}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Cumulative error distribution for all optimization strategies. The error results from the (absolute) difference between model predictions and real-world values for each reference measurement. The higher the number of variable parameters, the better the model resembles real-world conditions. \relax }}{11}{figure.4}}
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\newlabel{fig:wifiModelError}{{4}{11}{Cumulative error distribution for all optimization strategies. The error results from the (absolute) difference between model predictions and real-world values for each reference measurement. The higher the number of variable parameters, the better the model resembles real-world conditions. \relax }{figure.4}{}}
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\newlabel{fig:wifiModelErrorMaxA}{{5a}{11}{\em \noOptEmpiric {}\relax }{subfigure.5.1}{}}
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\newlabel{sub@fig:wifiModelErrorMaxA}{{a}{11}{\em \noOptEmpiric {}\relax }{subfigure.5.1}{}}
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\newlabel{fig:wifiModelErrorMaxB}{{5b}{11}{\em \optParamsPosEachAP {}\relax }{subfigure.5.2}{}}
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\newlabel{sub@fig:wifiModelErrorMaxB}{{b}{11}{\em \optParamsPosEachAP {}\relax }{subfigure.5.2}{}}
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\newlabel{fig:wifiModelErrorMaxC}{{5c}{11}{\em \optPerRegion {}\relax }{subfigure.5.3}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces \leavevmode {\color {red}At every of the 121 reference measurements more than one AP{} is visible, and for for every visible AP{} there is a difference between model estimated and real-world signal strength. The three figures depict the highest among those errors around the location of each reference measurement. While optimization is able to reduce the average error, local maxima remain due to overadaption. }\relax }}{11}{figure.5}}
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\newlabel{fig:wifiModelErrorMax}{{5}{11}{\changed {At every of the 121 reference measurements more than one \docAPshort {} is visible, and for for every visible \docAPshort {} there is a difference between model estimated and real-world signal strength. The three figures depict the highest among those errors around the location of each reference measurement. While optimization is able to reduce the average error, local maxima remain due to overadaption. }\relax }{figure.5}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Impact of reducing the number of reference measurements for optimizing {\em model per region{}}. The cumulative error distribution is determined by comparing its signal strength prediction against all 121 measurements. While using only \ensuremath {50}\text {\tmspace +\thinmuskip {.1667em}\%} of the 121 scans has barely an impact on the error, 30 measurements (\ensuremath {25}\text {\tmspace +\thinmuskip {.1667em}\%}) are clearly insufficient. \relax }}{12}{figure.6}}
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\newlabel{fig:wifiNumFingerprints}{{6}{12}{Impact of reducing the number of reference measurements for optimizing {\em \optPerRegion {}}. The cumulative error distribution is determined by comparing its signal strength prediction against all 121 measurements. While using only \SI {50}{\percent } of the 121 scans has barely an impact on the error, 30 measurements (\SI {25}{\percent }) are clearly insufficient. \relax }{figure.6}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Wi\hbox {-}Fi{} location estimation error}{12}{subsection.5.2}}
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Overview of all conducted paths, each starting at the denoted rectangle. Outdoor areas are marked in green. The length of the paths is as follows: path 1: \ensuremath {207}\text {\tmspace +\thinmuskip {.1667em}m}, path 2: \ensuremath {138}\text {\tmspace +\thinmuskip {.1667em}m}, path 3: \ensuremath {86}\text {\tmspace +\thinmuskip {.1667em}m}, path 4: \ensuremath {140}\text {\tmspace +\thinmuskip {.1667em}m}, and path 5: \ensuremath {97}\text {\tmspace +\thinmuskip {.1667em}m}. \relax }}{13}{figure.7}}
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\newlabel{fig:allWalks}{{7}{13}{Overview of all conducted paths, each starting at the denoted rectangle. Outdoor areas are marked in green. The length of the paths is as follows: path 1: \SI {207}{\meter }, path 2: \SI {138}{\meter }, path 3: \SI {86}{\meter }, path 4: \SI {140}{\meter }, and path 5: \SI {97}{\meter }. \relax }{figure.7}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces \leavevmode {\color {red}Cumulative error distribution for the error between a location estimation using eq.\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces \ref {eq:bestWiFiPos}\unskip \@@italiccorr )}} (only Wi\hbox {-}Fi{}) and the corresponding ground truth depending on the signal strength prediction model, using each of the 3756 Wi\hbox {-}Fi{} measurements within the 13 walks. All models suffer from several (extremely) high errors that relate to bad Wi\hbox {-}Fi{} coverage e.g. within outdoor areas (see Fig.\nobreakspace {}\ref {fig:wifiIndoorOutdoor}). This negatively affects the resulting average and 75th percentile. The strategies {\em optimization 1{}} and {\em optimization 2{}} sometimes suffered from overadaption, indicated by increased error values for the 25th percentile. }\relax }}{13}{figure.8}}
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\newlabel{fig:modelPerformance}{{8}{13}{\changed {Cumulative error distribution for the error between a location estimation using \refeq {eq:bestWiFiPos} (only \docWIFI {}) and the corresponding ground truth depending on the signal strength prediction model, using each of the 3756 \docWIFI {} measurements within the 13 walks. All models suffer from several (extremely) high errors that relate to bad \docWIFI {} coverage e.g. within outdoor areas (see \reffig {fig:wifiIndoorOutdoor}). This negatively affects the resulting average and 75th percentile. The strategies {\em \optParamsAllAP {}} and {\em \optParamsEachAP {}} sometimes suffered from overadaption, indicated by increased error values for the 25th percentile. }\relax }{figure.8}{}}
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\citation{PotentialRisks}
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\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Wi\hbox {-}Fi{}-only location probability for three distinct scans where higher color intensities denote a higher likelihood for eq.\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces \ref {eq:bestWiFiPos}\unskip \@@italiccorr )}}. The first scan (left, green) depicts a best-case scenario, where the region around the ground truth (black rectangle) is highly probable. Often, other locations are just as likely as the ground truth (2nd scan, blue), or the location with the highest probability is far from the actual ground truth (3rd scan, right, red). \relax }}{14}{figure.9}}
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\newlabel{fig:wifiMultimodality}{{9}{14}{\docWIFI {}-only location probability for three distinct scans where higher color intensities denote a higher likelihood for \refeq {eq:bestWiFiPos}. The first scan (left, green) depicts a best-case scenario, where the region around the ground truth (black rectangle) is highly probable. Often, other locations are just as likely as the ground truth (2nd scan, blue), or the location with the highest probability is far from the actual ground truth (3rd scan, right, red). \relax }{figure.9}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Filtered location estimation error}{15}{subsection.5.3}}
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\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Cumulative error distribution for each model when used within the final localization system from eq.\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces \ref {eq:recursiveDensity}\unskip \@@italiccorr )}}. \leavevmode {\color {red}The error between ground truth and estimation is calculated for each filter update, every \ensuremath {500}\text {\tmspace +\thinmuskip {.1667em}ms}.} Especially {\em optimization 1{}} suffered from overadaption and thus provided worse results. Compared to just using Wi\hbox {-}Fi{} (Fig.\nobreakspace {}\ref {fig:modelPerformance}) the error difference between the models now is much more distinct. Starting from {\em optimization 2{}} the system rarely gets stuck and provides a viable accuracy. \relax }}{16}{figure.10}}
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\newlabel{fig:overallSystemError}{{10}{16}{Cumulative error distribution for each model when used within the final localization system from \refeq {eq:recursiveDensity}. \changed {The error between ground truth and estimation is calculated for each filter update, every \SI {500}{\milli \second }.} Especially {\em \optParamsAllAP {}} suffered from overadaption and thus provided worse results. Compared to just using \docWIFI {} (\reffig {fig:modelPerformance}) the error difference between the models now is much more distinct. Starting from {\em \optParamsEachAP {}} the system rarely gets stuck and provides a viable accuracy. \relax }{figure.10}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion and Future Work}{16}{section.6}}
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\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces Detailed analysis of the Wi\hbox {-}Fi{} error for {\em empiric params{}} (unoptimized) and {\em model per floor{}} using {\em path 1} (see Fig.\nobreakspace {}\ref {fig:allWalks}). While optimization reduces the error indoors, the error outdoors is increased (bold line). A particle filter (PF, eq.\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces \ref {eq:recursiveDensity}\unskip \@@italiccorr )}}) on top of the optimized model takes \ensuremath {5}\text {\tmspace +\thinmuskip {.1667em}s} to initialize the starting-position (rectangles), fixes the outdoor-issue and improves indoor situations. A filter on top of {\em empiric params{}} got stuck right before entering the 2nd building. Both, the filtered and unfiltered version of {\em empiric params{}} are dragged into the 2nd floor in the middle of the walk. \leavevmode {\color {red}As the particle filter starts uniformly distributed along the whole area, the initial estimations determine the pedestrian's position to be in the center of the area (average position among all particles). The black and green walks thus start in empty space above the ground. After a few filter updates (see first seconds of the error plot) the estimation represents the pedestrian's actual position within the building. } \relax }}{17}{figure.11}}
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\newlabel{fig:final}{{11}{17}{Detailed analysis of the \docWIFI {} error for {\em \noOptEmpiric {}} (unoptimized) and {\em \optPerFloor {}} using {\em path 1} (see \reffig {fig:allWalks}). While optimization reduces the error indoors, the error outdoors is increased (bold line). A particle filter (PF, \refeq {eq:recursiveDensity}) on top of the optimized model takes \SI {5}{\second } to initialize the starting-position (rectangles), fixes the outdoor-issue and improves indoor situations. A filter on top of {\em \noOptEmpiric {}} got stuck right before entering the 2nd building. Both, the filtered and unfiltered version of {\em \noOptEmpiric {}} are dragged into the 2nd floor in the middle of the walk. \changed {As the particle filter starts uniformly distributed along the whole area, the initial estimations determine the pedestrian's position to be in the center of the area (average position among all particles). The black and green walks thus start in empty space above the ground. After a few filter updates (see first seconds of the error plot) the estimation represents the pedestrian's actual position within the building. } \relax }{figure.11}{}}
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\citation{Fetzer-17}
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\bibdata{egbib}
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\bibcite{Koeping14}{{1}{2014}{{K{\"o}ping \em {et~al.}}}{{K{\"o}ping, Grzegorzek, and Deinzer}}}
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\bibcite{radar}{{2}{2000}{{Bahl and Padmanabhan}}{{}}}
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\bibcite{horus}{{3}{2005}{{Youssef and Agrawala}}{{}}}
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\bibcite{ProbabilisticWlan}{{4}{2002}{{Roos \em {et~al.}}}{{Roos, Myllym\"{a}ki, Tirri, Misikangas, and Siev\"{a}nen}}}
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\bibcite{secureAndRobust}{{5}{2011}{{Meng \em {et~al.}}}{{Meng, Xiao, Ni, and Xie}}}
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\bibcite{robotFingerprinting}{{6}{2011}{{Palaniappan \em {et~al.}}}{{Palaniappan, Mirowski, Ho, Steck, Whiting, and MacDonald}}}
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\bibcite{ANewPathLossPrediction}{{7}{1994}{{Polydorou and Capsalis}}{{}}}
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\bibcite{PredictingRFCoverage}{{8}{1996}{{Rajkumar \em {et~al.}}}{{Rajkumar, Naylor, Feisullin, and Rogers}}}
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\bibcite{empiricalPathLossModel}{{9}{2006}{{Erceg \em {et~al.}}}{{Erceg, Greenstein, Tjandra, Parkoff, Gupta, Kulic, Julius, and Bianchi}}}
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\bibcite{WithoutThePain}{{10}{2010}{{Chintalapudi \em {et~al.}}}{{Chintalapudi, Padmanabha~Iyer, and Padmanabhan}}}
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\bibcite{crowdinside}{{11}{2012}{{Alzantot and Youssef}}{{}}}
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\bibcite{rssModelOpt1}{{12}{2006}{{Li}}{{}}}
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\bibcite{autoRssModel}{{13}{2009}{{Mazuelas \em {et~al.}}}{{Mazuelas, Bahillo, Lorenzo, Fernandez, Lago, Garcia, Blas, and Abril}}}
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\bibcite{indoorKalman}{{14}{2015}{{Chen \em {et~al.}}}{{Chen, Zou, Jiang, Zhu, Soh, and Xie}}}
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\bibcite{indoorKalman2}{{15}{2016}{{Li \em {et~al.}}}{{Li, Wang, Liu, Zhang, and Li}}}
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\bibcite{TimeDifferenceOfArrival1}{{16}{2008}{{Khanzada \em {et~al.}}}{{Khanzada, Ali, and Omar}}}
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\bibcite{TOAAOA}{{17}{2007}{{Deligiannis \em {et~al.}}}{{Deligiannis, Louvros, and Kotsopoulos}}}
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\bibcite{particleFilter}{{18}{1964}{{Ho and Lee}}{{}}}
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\bibcite{robotics}{{19}{2005}{{Thrun \em {et~al.}}}{{Thrun, Burgard, and Fox}}}
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\bibcite{Ebner2016OPN}{{20}{2016}{{Ebner \em {et~al.}}}{{Ebner, Fetzer, Grzegorzek, and Deinzer}}}
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\bibcite{Fetzer2016OMC}{{21}{2016}{{Fetzer \em {et~al.}}}{{Fetzer, Ebner, K{\"o}ping, Grzegorzek, and Deinzer}}}
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\bibcite{Koeping14-PSA}{{22}{2014}{{K\"{o}ping \em {et~al.}}}{{K\"{o}ping, Grzegorzek, and Deinzer}}}
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\bibcite{IntroductionToRadio}{{23}{1971}{{Friis}}{{}}}
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\bibcite{WirelessCommunications}{{24}{2002}{{Rappaport}}{{}}}
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\bibcite{PathLossPredictionModelsForIndoor}{{25}{1992}{{Seidel and Rappaport}}{{}}}
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\bibcite{competition2016}{{26}{2017}{{Torres-Sospedra \em {et~al.}}}{{Torres-Sospedra, Jim{\'e}nez, Knauth, Moreira, Beer, Fetzer, Ta, Montoliu, Seco, Mendoza-Silva, Belmonte, Koukofikis, Nicolau, Costa, Meneses, Ebner, Deinzer, Vaufreydaz, Dao, and Castelli}}}
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\bibcite{ElectromagneticPropagation}{{27}{2000}{{Richalot \em {et~al.}}}{{Richalot, Bonilla, Wong, Fouad-Hanna, Baudrand, and Wiart}}}
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\bibcite{Ebner-15}{{28}{2015}{{Ebner \em {et~al.}}}{{Ebner, Fetzer, K{\"o}ping, Grzegorzek, and Deinzer}}}
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\bibcite{gradientDescent}{{29}{2013}{{Mofarreh-Bonab and Ghorashi}}{{}}}
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\bibcite{downhillSimplex1}{{30}{1962}{{Powell}}{{}}}
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\bibcite{downhillSimplex2}{{31}{1965}{{Nelder and Mead}}{{}}}
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\bibcite{goldberg89}{{32}{1989}{{Goldberg}}{{}}}
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\bibcite{Kirkpatrick83optimizationby}{{33}{1983}{{Kirkpatrick \em {et~al.}}}{{Kirkpatrick, Gelatt, and Vecchi}}}
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\bibcite{Fetzer-17}{{34}{2017, accepted}{{Fetzer \em {et~al.}}}{{Fetzer, Ebner, Deinzer, and Grzegorzek}}}
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\bibcite{PotentialRisks}{{35}{2012}{{Jung \em {et~al.}}}{{Jung, Bell, Petrenko, and Sizo}}}
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