66:
680:
1343:
128:
25:
886:
3552:
642:
Another method based on the diffusion model is the hex-path algorithm, developed by R. Andrew Russel for underground chemical odor localization with a buried probe controlled by a robotic manipulator. The probe moves at a certain depth along the edges of a closely packed hexagonal grid. At each state
617:
is the odor source concentration. This is the simplest dynamic equation in odor detection modeling, ignoring external wind or other interruptions. Under the diffusion-dominated propagation model, different algorithms were developed by simply tracking chemical concentration gradients to locate an odor
391:
Odor localization methods are often classified according to odor dispersal modes in a range of environmental conditions. These modes can generally be divided into two categories: diffusion-dominated fluid flow and turbulence-dominated fluid flow. These have different algorithms for odor localization,
400:
Tracking and localization methods for diffusion-dominated fluid flow – which is mostly used in underground odor localization – must be designed so that olfaction machinery can operate in environments in which fluid motion is dominated by viscosity. This means that diffusion leads to the dispersal of
267:
There are three basic detection techniques using conductive-polymer odor sensors (polypyrrole), tin-oxide gas sensors, and quartz-crystal micro-balance sensors. They generally comprise (1) an array of sensors of some type, (2) the electronics to interrogate those sensors and produce digital signals,
1355:
A simple algorithm that can be used for location estimation is the triangulation method (Figure 2). Consider the odor detection equation above, the position of the odor source can be estimated by organizing sensor distances on one side of the equation and ignoring the noise. The source position can
3833:
In 2007, a strategy called infotaxis was proposed in which a mental model is created utilizing previously collected information about where a smell's source is likely to be. The robot moves in a direction that maximizes information. Infotaxis is designed for tracking in turbulent environments. It
378:
The earliest instrument for specific odor detection was a mechanical nose developed in 1961 by Robert
Wighton Moncrieff. The first electronic nose was created by W. F. Wilkens and J. D. Hartman in 1964. Larcome and Halsall discussed the use of robots for odor sensing in the nuclear industry in the
633:
algorithm. In this process, the odor sensor simply compares concentration information from different locations. The robot moves along repeated straight lines in random directions. When the current state odor information is improved compared to the previous reading, the robot will continue on the
634:
current path. However, when the current state condition is worse than the previous one, the robot will backtrack then move in another random direction. This method is simple and efficient, however, the length of the path is highly variable and missteps increase with proximity to the source.
275:
Conventional electronic noses are not analytical instruments in the classical sense and very few claim to be able to quantify an odor. These instruments are first 'trained' with the target odor and then used to 'recognize' smells so that future samples can be identified as 'good' or 'bad'.
708:
382:
Mechanical odor localization can be executed via the following three steps, (1) search for the presence of a volatile chemical (2) search for the position of the source with an array of odor sensors and certain algorithms, and (3) identify the tracked odor source (odor recognition).
3322:
2222:
296:
Odor localization is a combination of quantitative chemical odor analysis and path-searching algorithms, and environmental conditions play a vital role in localization quality. Different methods are being researched for various purposes and in different real-world conditions.
1907:
3110:
3714:
305:
Odor localization is the technique and process of locating a volatile chemical source in an environment containing one or several odors. It is vitally important for all living beings for both finding sustenance and avoiding danger. Unlike the other basic human
287:
Electronic noses are able to discriminate between odors and volatiles from a wide range of sources. The list below shows just some of the typical applications for electronic nose technology – many are backed by research studies and published technical papers.
310:, the sense of smell is entirely chemical-based. However, in comparison with the other dimensions of perception, detection of odor faces additional problems due to the complex dynamic equations of odor and unpredictable external disturbances such as wind.
3824:
1098:
379:
early 1980s, and research on odor localization was started in the early 1990s. Odor localization is now a fast-growing field. Various sensors have been developed and a variety of algorithms have been proposed for diverse environments and conditions.
2050:
The main difference between the LSM algorithm and the direct triangulation method is the noise. In LSM, noise is considered, and the odor source location is estimated by minimizing the squared error. The nonlinear least square problem is given by:
522:
Assuming the chemical odor flow only disperses in one direction with a uniform cross-section profile, the relationship of odor concentration at a certain distance and certain time point between odor source concentrations is modeled as
490:
3293:
585:
881:{\displaystyle {\frac {\partial C}{\partial t}}=D_{x}{\frac {\partial ^{2}C}{\partial x^{2}}}+D_{y}{\frac {\partial ^{2}C}{\partial y^{2}}}+\alpha {\frac {\partial C}{\partial x}}+\beta {\frac {\partial C}{\partial x}}}
283:
arrays has proposed solutions to differentiate between artificial and biological olfaction related to dimensionality. This biologically-inspired approach involves creating unique algorithms for information processing.
2989:
2404:
1745:
1615:
1485:
3547:{\displaystyle L(\theta )\sim {\frac {1}{2}}\sum _{i=1}^{N}{\|Z_{i}-\gamma _{i}{\frac {c}{d_{i}^{2}}}\|}={\frac {1}{2}}\sum _{i=1}^{N}{({\frac {Ri-\mu _{i}}{\sigma _{i}}}-\gamma _{i}{\frac {c}{d_{i}^{2}}})^{2}}}
2056:
2046:
649:, there are two paths (left and right) for choosing, and the robot will take the path that leads to higher concentration of the odor based on the previous two junction states odor concentration information
691:
In turbulence-dominated fluid flow, localization methods are designed to deal with background fluid (wind or water) flow as turbulence interruption. Most of the algorithms under this category are based on
271:
The entire system is a means of converting complex sensor responses into a qualitative profile of the volatile (or complex mixture of chemical volatiles) that make up a smell, in the form of an output.
1759:
2288:
233:, and the successful design of a pattern analysis system for machine olfaction requires a careful consideration of the various issues involved in processing multivariate data: signal-preprocessing,
2995:
3581:
3995:
Stassen, I.; Bueken, B.; Reinsch, H.; Oudenhoven, J. F. M.; Wouters, D.; Hajek, J.; Van
Speybroeck, V.; Stock, N.; Vereecken, P. M.; Van Schaijk, R.; De Vos, D.; Ameloot, R. (2016).
3723:
960:
direction. Additionally assuming that the environment is uniform and the plume source is constant, the equation for odor detection in each robot sensor at each detection time point
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1337:
975:
198:
are produced by unique sets of (potentially numerous) odorant compounds. The technology, though still in the early stages of development, promises many applications, such as:
190:. An emerging application in modern engineering, it involves the use of robots or other automated systems to analyze air-borne chemicals. Such an apparatus is often called an
3152:
1295:
1174:
1238:
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T. C. Pearce, S. S. Schiffman, H. T. Nagle, J. W. Gardner (editors), Handbook of
Machine Olfaction: Electronic Nose Technology, Wiley-VCH, Weinheim, 2002. In PDF at:
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2707:
952:
1936:
1201:
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615:
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or e-nose. The development of machine olfaction is complicated by the fact that e-nose devices to date have responded to a limited number of chemicals, whereas
418:
249:, and validation. Another challenge in current research on machine olfaction is the need to predict or estimate the sensor response to aroma mixtures. Some
229:
instruments capable of detecting, identifying, and measuring volatile compounds. However, a critical element in the development of these instruments is
3161:
529:
1754:
The least square method (LSM) is a slightly complicated algorithm for odor localization. The LSM version of the odor tracking model is given by:
4126:
Vembu, Shankar; Vergara, Alexander; Muezzinoglu, Mehmet K.; Huerta, Ramón (2012). "On time series features and kernels for machine olfaction".
2899:
2329:
1621:
1491:
1361:
140:
3835:
2217:{\displaystyle J=\sum _{i=1}^{N}({{\frac {C}{\sqrt {(x_{i}-{\widehat {x_{s}}})^{2}(y_{i}-{\widehat {y_{s}}})^{2}}}}-{\overline {z_{l}}})}}
4250:
Robotics in nuclear engineering: computer-assisted teleoperation in hazardous environments with particular reference to radiation fields
1943:
253:
problems in machine olfaction such as odor classification and odor localization can be solved by using time series kernel methods.
1902:{\displaystyle R_{i},_{t}=\gamma _{i}{\frac {C}{\|{\rho _{k}-r_{i}}\|^{2}}}+\omega _{i}=\gamma _{i}{\frac {C}{d^{2}}}+\omega _{i}}
2229:
366:
4538:
3940:"Diagnosing viral and bacterial respiratory infections in acute COPD exacerbations by an electronic nose: a pilot study"
4390:
4091:
Phaisangittisagul, Ekachai; Nagle, H. Troy (2011). "Predicting odor mixture's responses on machine olfaction sensors".
3105:{\displaystyle {\frac {R_{i}-\mu _{i}}{\sigma _{i}}}\sim N({\frac {\gamma _{i}}{\sigma _{i}}}{\frac {C}{d_{i}^{2}}},1)}
38:
3709:{\displaystyle I(\theta )=\sum _{i=1}^{N}{({\frac {Ri-\mu _{i}}{\sigma _{i}}}-\gamma _{i}{\frac {c}{d_{i}^{2}}})^{2}}}
170:
109:
87:
52:
80:
4372:
3819:{\displaystyle {\frac {\partial {I(\theta )}}{\partial (x)}}=0,{\frac {\partial {I(\theta )}}{\partial (y)}}=0}
145:
4426:
2414:
1093:{\displaystyle R_{i}=\gamma _{i}\sum _{k=1}^{K}{\frac {C_{k}}{\|{\rho _{k}-r_{k}}\|^{\alpha }}}+\omega _{i}}
2293:
1300:
700:
3114:
With these matrices, the plume-based odor detection model can be expressed with the following equation:
242:
4532:
667:
algorithm, the dodecahedron algorithm, the probe moves in a path that corresponds to a closely packed
4264:
Kowadlo, Gideon; Russell, R. Andrew (2008-08-01). "Robot Odor
Localization: A Taxonomy and Survey".
408:
The diffusion of chemical vapor through soil without external pressure gradient is often modeled by
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359:
219:
74:
3119:
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1216:
693:
684:
91:
44:
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Gardner, Julian W.; Bartlett, Philip N. (1994-03-01). "A brief history of electronic noses".
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1914:
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409:
485:{\displaystyle {\frac {\partial C}{\partial t}}=D{\frac {\partial ^{2}C}{\partial d^{2}}}}
8:
250:
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4222:
4139:
4104:
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Then the MLE can be applied to the modeling and form the probability density function
1339:. Under plume modeling, different algorithms can be used to localize the odor source.
4573:
4511:
4454:
4355:
4329:
4312:
Russell, R. Andrew (2004-01-01). "Robotic location of underground chemical sources".
4281:
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4038:
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238:
215:
4585:
4474:"Searching for a source without gradients: how good is infotaxis and how to beat it"
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4565:
4503:
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Proceedings of the Royal
Society A: Mathematical, Physical and Engineering Sciences
4446:
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246:
230:
4293:
3856: – Material with changing electrical resistance according to its surroundings
2417:(MLE). In this odor localization method, several matrices are defined as follows:
1938:
is the
Euclidean distance between the sensor node and the plume source, given by:
326:
322:
280:
262:
203:
199:
191:
4056:
Gutierrez-Osuna, R. (2002). "Pattern analysis for machine olfaction: A review".
3288:{\displaystyle f(Z,\theta )=2\pi ^{-(N/2)}e^{-{\frac {1}{2}}(Z-GDC)^{T}(Z-GDC)}}
1342:
580:{\displaystyle {\frac {C}{C_{s}}}=\operatorname {erfc} {\frac {d}{\sqrt {4Dt}}}}
4163:
Sensor-based machine olfaction with neuromorphic models of the olfactory system
3997:"Towards metal–organic framework based field effect chemical sensors: UiO-66-NH
3873: – Using the presence or absence of molecules to digitally encode messages
347:
211:
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4147:
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3921:
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4515:
4458:
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330:
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Odor localization technology shows promise in many applications, including:
4577:
4507:
4042:
4024:
3981:
3938:
Geffen, Wouter H. van; Bruins, Marcel; Kerstjens, Huib A. M. (2016-01-01).
3876:
668:
226:
4425:
Reddy, Gautam; Murthy, Venkatesh N.; Vergassola, Massimo (10 March 2022).
3718:
and the accurate position of the odor source can be estimated by solving:
3317:
is the estimated odor source position, and the log likelihood function is
4473:
679:
2984:{\displaystyle \zeta _{i}=(\omega _{i}-\mu _{i})/\sigma _{i}\sim N(0,1)}
2399:{\displaystyle {\overline {z_{l}}}={\frac {1}{M}}\sum _{i=1}^{M}{z_{i}}}
1740:{\displaystyle (x_{3}-x_{s})^{2}+(y_{3}-y_{s})^{2}=R_{3}/(\gamma _{3}C)}
1610:{\displaystyle (x_{2}-x_{s})^{2}+(y_{2}-y_{s})^{2}=R_{2}/(\gamma _{2}C)}
1480:{\displaystyle (x_{1}-x_{s})^{2}+(y_{1}-y_{s})^{2}=R_{1}/(\gamma _{1}C)}
401:
odor flow, and the concentration of odor decreases from the source as a
4170:
4016:
4569:
671:, so that at each state point there are three possible path choices.
207:
187:
703:. The simplified boundary condition of the Gaussian-based model is:
4490:
4185:
2324:
is the average of multiple measurements at the sensors, given by:
336:
locating the source of dangerous substances (e.g.: explosives and
2041:{\displaystyle d_{i}={\sqrt {(x_{i}-x-s)^{2}+(y_{i}+y_{s})^{2}}}}
699:
Plume dynamics are based on
Gaussian models, which are based on
637:
4542:
4533:
Electronic Nose
Technologies from Scensive Technologies Ltd, UK
3994:
4125:
307:
225:
One type of proposed machine olfaction technology is via gas
4427:"Olfactory Sensing and Navigation in Turbulent Environments"
3879: – Instrument used to detect and measure odor dilution
195:
279:
Research into alternative pattern recognition methods for
4186:"Review on: Odor Localization Robot Aspect and Obstacles"
3862: – The study of smelling things through a computer
2283:{\displaystyle ({\widehat {x_{s}}},{\widehat {y_{s}}})}
4543:
Network on artificial
Olfactory Sensing (NOSE) Archive
4090:
2408:
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978:
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596:
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421:
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and (3) data processing and user interface software.
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with a stationary target in a two-dimensional grid.
4356:"Chemical Source Location and the RoboMole Project"
3818:
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4548:Lundström, Ingemar (2000). "Picture the smell".
373:
4307:
4305:
4303:
4208:
4055:
3933:
3931:
3556:The maximum likelihood parameter estimation of
4266:The International Journal of Robotics Research
4263:
3890:
4472:Loisy, Aurore; Eloy, Christophe (June 2022).
638:Hex-path algorithm and dodecahedron algorithm
4300:
3928:
3836:partially observable Markov decision process
3421:
3373:
1831:
1802:
1749:
1356:be estimated using the following equations:
1065:
1036:
343:discovering underground resources or hazards
53:Learn how and when to remove these messages
2413:Another method based on plume modeling is
1350:
137:needs attention from an expert in Robotics
4547:
4489:
4471:
4431:Annual Review of Condensed Matter Physics
4402:
4388:
4382:
4032:
3963:
171:Learn how and when to remove this message
110:Learn how and when to remove this message
4451:10.1146/annurev-conmatphys-031720-032754
4246:
1341:
678:
507:is distance in the diffusion direction,
73:This article includes a list of general
4311:
3850: – Arrangement of chemical sensors
386:
4595:
3900:"Special issue on machine olfaction".
346:detecting prohibited materials (e.g.:
148:may be able to help recruit an expert.
4465:
4418:
4183:
4161:Raman, Baranidharan (December 2005).
4160:
2290:is the estimated source location and
367:chronic obstructive pulmonary disease
365:early diagnosis of diseases (e.g. in
621:
291:
214:, explosives and other dangerous or
121:
59:
18:
2409:Maximum likelihood estimation (MLE)
2317:{\displaystyle {\overline {z_{l}}}}
1332:{\displaystyle N(\mu ,\sigma ^{2})}
1297:is background noise that satisfies
954:is the linear wind velocity in the
928:is the linear wind velocity in the
186:is the automated simulation of the
13:
4373:"Survey: Odor Source Localization"
3795:
3776:
3749:
3730:
869:
861:
843:
835:
810:
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763:
749:
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715:
466:
452:
433:
425:
79:it lacks sufficient corresponding
14:
4619:
4526:
4211:Sensors and Actuators B: Chemical
4165:(PhD). Texas A&M University.
4128:Sensors and Actuators B: Chemical
4093:Sensors and Actuators B: Chemical
34:This article has multiple issues.
4389:Mackenzie, Dana (6 March 2023).
3576:can be calculated by minimizing
1270:is plume attenuation parameter,
629:A simple tracking method is the
126:
64:
23:
16:Simulation of the sense of smell
4391:"How animals follow their nose"
4365:
4348:
4257:
4240:
675:Turbulence-dominated fluid flow
42:or discuss these issues on the
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1988:
1962:
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1346:Figure 2. Triangulation method
1326:
1307:
513:is chemical concentration and
396:Diffusion-dominated fluid flow
313:
1:
3965:10.1088/1752-7155/10/3/036001
3883:
2415:maximum likelihood estimation
374:History and problem statement
300:
4231:10.1016/0925-4005(94)87085-3
3828:
3147:{\displaystyle Z=GDC+\zeta }
2345:
2309:
2205:
256:
7:
4556:(6797). Springer: 682–683.
4247:Larcombe, M. H. E. (1984).
3841:
1290:{\displaystyle \omega _{i}}
1169:{\displaystyle \gamma _{i}}
663:. In the 3D version of the
501:is the diffusion constant,
353:searching for survivors of
10:
4624:
4001:for nerve agent detection"
3944:Journal of Breath Research
3834:has been implemented as a
908:are diffusion constants;
696:modeling (Figure 1).
260:
4404:10.1146/knowable-030623-4
4326:10.1017/S026357470300540X
4184:Moshayedi, Ata Jahangir.
4148:10.1016/j.snb.2012.06.070
4113:10.1016/j.snb.2010.12.049
3922:10.1109/JSEN.2011.2167171
1750:Least square method (LSM)
1233:{\displaystyle \rho _{k}}
218:, disaster response, and
4278:10.1177/0278364908095118
4078:10.1109/jsen.2002.800688
3866:Fido explosives detector
3860:Digital scent technology
360:environmental monitoring
329:(e.g. taints, bacterial
220:environmental monitoring
4236:(subscription required)
3871:Molecular communication
3569:{\displaystyle \theta }
3310:{\displaystyle \theta }
2888:{\displaystyle \zeta =}
1351:Triangulation algorithm
1263:{\displaystyle \alpha }
921:{\displaystyle \alpha }
701:Navier–Stokes equations
94:more precise citations.
4508:10.1098/rspa.2022.0118
3820:
3710:
3620:
3570:
3548:
3458:
3371:
3311:
3289:
3148:
3106:
2985:
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2814:
2703:
2702:{\displaystyle G=diag}
2574:
2400:
2383:
2318:
2284:
2218:
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2042:
1932:
1903:
1741:
1611:
1481:
1347:
1333:
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1234:
1197:
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1123:
1094:
1022:
948:
947:{\displaystyle \beta }
922:
882:
688:
611:
581:
486:
3848:Chemical sensor array
3821:
3711:
3600:
3571:
3549:
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3312:
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2815:
2704:
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2401:
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2319:
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2219:
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1933:
1931:{\displaystyle d_{i}}
1904:
1742:
1612:
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1345:
1334:
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1265:
1235:
1198:
1196:{\displaystyle C_{k}}
1171:
1124:
1122:{\displaystyle R_{i}}
1095:
1002:
949:
923:
883:
682:
612:
610:{\displaystyle C_{s}}
582:
487:
403:Gaussian distribution
4058:IEEE Sensors Journal
3902:IEEE Sensors Journal
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3301:
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419:
387:Localization methods
146:WikiProject Robotics
4562:2000Natur.406..682L
4500:2022RSPSA.47820118L
4443:2022ARCMP..13..191R
4223:1994SeAcB..18..210G
4140:2012SeAcB.174..535V
4105:2011SeAcB.155..473P
4070:2002ISenJ...2..189G
3956:2016JBR....10c6001V
3914:2011ISenJ..11.3486.
3692:
3530:
3418:
3090:
2804:
2770:
2745:
1240:is the location of
251:pattern recognition
4484:(2262): 20220118.
4397:. Annual Reviews.
4017:10.1039/C6SC00987E
3908:(12): 3486. 2011.
3816:
3706:
3678:
3566:
3544:
3516:
3404:
3307:
3285:
3144:
3102:
3076:
2981:
2885:
2813:{\displaystyle D=}
2810:
2790:
2756:
2731:
2699:
2573:{\displaystyle Z=}
2570:
2396:
2314:
2280:
2214:
2038:
1928:
1899:
1737:
1607:
1477:
1348:
1329:
1287:
1260:
1230:
1213:source intensity,
1193:
1166:
1119:
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944:
918:
878:
689:
607:
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235:feature extraction
216:illegal substances
212:detection of drugs
4395:Knowable Magazine
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410:Fick's second law
392:discussed below.
355:natural disasters
292:Odor localization
239:feature selection
184:Machine olfaction
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4217:(1–3): 210–211.
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4190:www.academia.edu
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338:chemical warfare
231:pattern analysis
206:, detection and
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90:this article by
81:inline citations
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4608:Robotic sensing
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327:food processing
323:quality control
316:
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281:chemical sensor
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263:Electronic nose
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204:food processing
200:quality control
192:electronic nose
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86:Please help to
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4527:External links
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210:in medicine,
209:
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135:This article
133:
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111:
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71:
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4408:. Retrieved
4394:
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4350:
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4259:
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4193:. Retrieved
4189:
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4086:
4061:
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3901:
3877:Olfactometer
3832:
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295:
286:
278:
274:
270:
266:
227:sensor array
224:
183:
182:
167:
154:January 2019
151:
143:for details.
136:
106:
100:January 2019
97:
78:
50:
43:
37:
36:Please help
33:
4171:1969.1/4984
4134:: 535–546.
669:dodecahedra
314:Application
139:. See the
92:introducing
4597:Categories
4491:2112.10861
4195:2015-11-12
3884:References
1139:sample of
683:Figure 1.
301:Motivation
247:clustering
75:references
39:improve it
4603:Olfaction
4516:1364-5021
4459:1947-5454
4334:1469-8668
4286:0278-3649
4005:Chem. Sci
3974:1752-7163
3829:Infotaxis
3796:∂
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3777:∂
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3333:θ
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830:α
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797:∂
764:∂
750:∂
724:∂
716:∂
643:junction
625:algorithm
557:
519:is time.
467:∂
453:∂
434:∂
426:∂
257:Detection
208:diagnosis
141:talk page
45:talk page
4586:16957778
4578:10963577
4410:13 March
4342:40463021
4314:Robotica
4043:30034722
3982:27310311
3842:See also
1149:sensor,
687:modeling
665:hex-path
618:source.
331:spoilage
4558:Bibcode
4496:Bibcode
4439:Bibcode
4219:Bibcode
4136:Bibcode
4101:Bibcode
4066:Bibcode
4034:6024240
3952:Bibcode
3910:Bibcode
1911:where
1129:is the
631:E. coli
623:E. coli
340:agents)
88:improve
4584:
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4550:Nature
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4294:348058
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3297:where
2226:where
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590:where
495:where
308:senses
77:, but
4582:S2CID
4486:arXiv
4376:(PDF)
4359:(PDF)
4338:S2CID
4290:S2CID
694:plume
685:plume
196:odors
4574:PMID
4512:ISSN
4455:ISSN
4412:2023
4330:ISSN
4282:ISSN
4039:PMID
3978:PMID
3970:ISSN
899:and
554:erfc
4566:doi
4554:406
4504:doi
4482:478
4447:doi
4399:doi
4322:doi
4274:doi
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4167:hdl
4144:doi
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325:in
202:in
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3765:=
3759:)
3756:x
3753:(
3744:)
3738:(
3735:I
3701:2
3697:)
3689:2
3684:i
3680:d
3676:c
3669:i
3654:i
3643:i
3632:i
3629:R
3623:(
3617:N
3612:1
3609:=
3606:i
3598:=
3595:)
3589:(
3586:I
3539:2
3535:)
3527:2
3522:i
3518:d
3514:c
3507:i
3492:i
3481:i
3470:i
3467:R
3461:(
3455:N
3450:1
3447:=
3444:i
3434:2
3431:1
3426:=
3415:2
3410:i
3406:d
3402:c
3395:i
3382:i
3378:Z
3368:N
3363:1
3360:=
3357:i
3347:2
3344:1
3336:)
3330:(
3327:L
3281:)
3278:C
3275:D
3272:G
3266:Z
3263:(
3258:T
3254:)
3250:C
3247:D
3244:G
3238:Z
3235:(
3230:2
3227:1
3218:e
3212:)
3209:2
3205:/
3201:N
3198:(
3187:2
3184:=
3181:)
3175:,
3172:Z
3169:(
3166:f
3139:+
3136:C
3133:D
3130:G
3127:=
3124:Z
3100:)
3097:1
3094:,
3087:2
3082:i
3078:d
3074:C
3065:i
3055:i
3045:(
3042:N
3032:i
3021:i
3008:i
3004:R
2979:)
2976:1
2973:,
2970:0
2967:(
2964:N
2956:i
2947:/
2943:)
2938:i
2925:i
2917:(
2914:=
2909:i
2883:]
2878:N
2870:.
2867:.
2864:.
2861:,
2856:2
2848:,
2843:1
2835:[
2832:=
2808:]
2801:2
2796:N
2792:d
2788:1
2783:.
2780:.
2777:.
2774:,
2767:2
2762:2
2758:d
2754:1
2749:,
2742:2
2737:1
2733:d
2729:1
2724:[
2721:=
2718:D
2697:]
2690:N
2680:N
2670:.
2667:.
2664:.
2661:,
2654:2
2644:2
2634:,
2627:1
2617:1
2607:[
2604:g
2601:a
2598:i
2595:d
2592:=
2589:G
2568:]
2561:N
2550:N
2537:N
2533:R
2526:.
2523:.
2520:.
2517:,
2510:2
2499:2
2486:2
2482:R
2475:,
2468:1
2457:1
2444:1
2440:R
2433:[
2430:=
2427:Z
2391:i
2387:z
2380:M
2375:1
2372:=
2369:i
2359:M
2356:1
2351:=
2341:l
2337:z
2305:l
2301:z
2278:)
2267:s
2263:y
2256:,
2245:s
2241:x
2234:(
2211:)
2201:l
2197:z
2183:2
2179:)
2167:s
2163:y
2151:i
2147:y
2143:(
2138:2
2134:)
2122:s
2118:x
2106:i
2102:x
2098:(
2094:C
2088:(
2083:N
2078:1
2075:=
2072:i
2064:=
2061:J
2032:2
2028:)
2022:s
2018:y
2014:+
2009:i
2005:y
2001:(
1998:+
1993:2
1989:)
1985:s
1979:x
1971:i
1967:x
1963:(
1958:=
1953:i
1949:d
1924:i
1920:d
1895:i
1887:+
1880:2
1876:d
1872:C
1865:i
1857:=
1852:i
1844:+
1836:2
1825:i
1821:r
1812:k
1799:C
1792:i
1784:=
1779:t
1775:,
1769:i
1765:R
1735:)
1732:C
1727:3
1719:(
1715:/
1709:3
1705:R
1701:=
1696:2
1692:)
1686:s
1682:y
1673:3
1669:y
1665:(
1662:+
1657:2
1653:)
1647:s
1643:x
1634:3
1630:x
1626:(
1605:)
1602:C
1597:2
1589:(
1585:/
1579:2
1575:R
1571:=
1566:2
1562:)
1556:s
1552:y
1543:2
1539:y
1535:(
1532:+
1527:2
1523:)
1517:s
1513:x
1504:2
1500:x
1496:(
1475:)
1472:C
1467:1
1459:(
1455:/
1449:1
1445:R
1441:=
1436:2
1432:)
1426:s
1422:y
1413:1
1409:y
1405:(
1402:+
1397:2
1393:)
1387:s
1383:x
1374:1
1370:x
1366:(
1327:)
1322:2
1314:,
1308:(
1305:N
1283:i
1245:−
1243:k
1226:k
1208:−
1206:k
1189:k
1185:C
1162:i
1144:−
1142:i
1134:−
1132:t
1115:i
1111:R
1086:i
1078:+
1059:k
1055:r
1046:k
1031:k
1027:C
1019:K
1014:1
1011:=
1008:k
998:i
990:=
985:i
981:R
965:−
963:t
957:y
931:x
904:y
902:D
895:x
893:D
873:x
865:C
853:+
847:x
839:C
827:+
819:2
815:y
806:C
801:2
788:y
784:D
780:+
772:2
768:x
759:C
754:2
741:x
737:D
733:=
727:t
719:C
659:n
652:n
646:n
603:s
599:C
572:t
569:D
566:4
562:d
551:=
544:s
540:C
536:C
516:t
510:C
504:d
498:D
475:2
471:d
462:C
457:2
446:D
443:=
437:t
429:C
369:)
350:)
333:)
174:)
168:(
156:)
152:(
113:)
107:(
102:)
98:(
84:.
55:)
51:(
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