Research Article Neural Virtual Sensors for Adaptive Magnetic...

Research ArticleNeural Virtual Sensors for Adaptive Magnetic Localization ofAutonomous Dataloggers

Dennis Groben Kittikhun Thongpull Abhaya Chandra Kammara and Andreas Koumlnig

Institute of Integrated Sensor Systems EIT TU Kaiserslautern Erwin-Schrodinger-Straszlige 12 67663 Kaiserslautern Germany

Correspondence should be addressed to Andreas Konig koenigeituni-klde

Received 12 June 2014 Revised 16 October 2014 Accepted 19 October 2014 Published 30 December 2014

Academic Editor Manwai Mak

Copyright copy 2014 Dennis Groben et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The surging advance in micro- and nanotechnologies allied with neural learning systems allows the realization of miniaturized yetextremely powerful multisensor systems and networks for wide application fields for example in measurement instrumentationautomation and smart environments Time and location context is particularly relevant to sensor swarms applied for distributedmeasurement in industrial environment such as for example fermentation tanks Common RF solutions face limits here whichcan be overcome by magnetic systems Previously we have developed the electronic system for an integrated data logger swarmwith magnetic localization and sensor node timebase synchronizationThe focus of this work is on an approach to improving bothlocalization accuracy and flexibility by the application of artificial neural networks applied as virtual sensors and classifiers in ahybrid dedicated learning system Including also data from an industrial brewery environment the best investigated neural virtualsensor approach has achieved an advance in localization accuracy of a factor of 4 compared to state-of-the-art numerical methodsand thus results in the order of less than 5 cm meeting industrial expectations on a feasible solution for the presented integratedlocalization system solution

1 Introduction

Sensor networks have established themselves in scientificindustrial and military applications Military reconnais-sance and surveillance for example employing distributedmicrophone or hydrophone arrays can be named hereIn the last decades numerous nonmilitary commercialapplications could be observed which incubated the cre-ation of more and more powerful and increasingly smartand networked data loggers The development was boostedby the soaring progress in microelectronics and MEMStechnology sensor technology communications and com-putational intelligence with a strong emphasis on artificalneural systems This advanced the integration of wirelessautonomous or even self-sufficient multisensor systems andsensor networks and opened due to miniaturization andcost-effectiveness new application fields from process con-trol and automation to Ambient-Intelligence for example[1] Internet-of-Things (IoT) Cyber-Physical-Systems (CPS)Cyber-Physical-Production Systems (CPPS) Industrie40and numerous biomedical tasks The key vision for this

development is the concept of Smart-Dust introduced forexample by the University of Berkeley [2 3] which for-mulates the idea to integrate in a cubic millimeter mul-tisensors processing communication energy supply andpotentially actuators to a Smart-Sensor corresponding net-works of numerous such units The ITRS roadmap [4]clearly points out the advantageous development of micro-electronics MEMS sensors and packaging technology forexample 3D integration technology in particular on theso-called More-than-Moore direction of development [5]for Systems-in-Package (SiP) solutions which allows theincrease of information processing in the named nodesthemselves More and more complex methods of computa-tional intelligence neural networks and learning systemsthus become amenable for the realization of distributedintelligent integrated sensory systems or sensory swarmsThough the Smart-Dust vision has not completely becomereality the named advance in micro- and nanotechnologiesalready allows with regard to sensory diversitybandwidthachievable measurement uncertainty and power dissipationminimization the realization of suitable sensor swarms for

Hindawi Publishing CorporationAdvances in Artificial Neural SystemsVolume 2014 Article ID 394038 17 pageshttpdxdoiorg1011552014394038

2 Advances in Artificial Neural Systems

distributed measurement in industrial applications in themeasurement and instrumentation field [6 7]

One important aspect in the practical application ofsensory networks or swarms with multisensory processparameter registration for example of temperature pressurehumidity conductivity or impedance spectrum is the log-ging of time and location context A synchronized timebasepotentially addional location sensors and apt signal process-ing are required for the task of context acquisition Evaluationof distributed swarm measurements will be of value onlyif time and location of the registration are available forswarm data visualization and analysis In many applicationscenarios including indoor outdoor or even maritine tasksthe radio signal itself and its attenuation (Received-Signal-Strength-Indicator (RSSI)) can serve as sensory source andbaseline for localization

However in industrially relevant scenarios of closedlarge-scale containers for example stainless-steel fermen-tation tanks in brewery industry shown in Figure 1 strongattenuation in the medium and reflections from containerwalls hamper communication itself and thus also localiza-tion

In our research an alternative localization system hasbeen conceived to locate the units of the sensor swarm basedon magnetic technology and inspired by existing trackingsystems and technology for example helmet tracking inmilitary applications or instrument or pill tracking inmedicalapplications The developed approach and system scales tothe required industrial tank sizes It employs integratedmagnetic sensors together with algorithms from compu-tational intelligence to robustly calculate the sensor nodelocalization from magnetic field emitting beacons In thispaper the basic electronic system and an extension by neuralnetworks as virtual sensors in a supervised approach forthe significant improvement of the localization quality andthe simplified adaptation to changed or new applicationscenarios are presented In Section 2 we will outline ourapproach system architecture and electronics scenariosdata acquisition and the synchronization approach with thecorresponding classification experiments In Section 3 virtualsensormethods and corresponding parameter settings will begiven In Section 4 before concluding our experiments andresults will be presented

2 Magnetic Localization System

Magnetic localization systems are in widespread use sincemore than two decades and related publication and patentactivity for example [8 9] can be observed Numerousconcepts and systems solutions can be found which achievea localization or a tracking of one or potentially severalobjects These systems can be conceived in two dual ways byeither employing an potentially integrated magnetic markerwhich is located by an external stationary sensor systemor sensor array or alternatively employing a plurality ofexternal stationary magnetic field generator units workingas beacons which are detected by magnetic sensors withinthe regarded mobile sensory nodes The first approachis commonly employed in medical tracking systems for

Figure 1 Fermentation tanks example of twenty meters height andsix meters diameter from brewery industry (Courtesy Warsteiner)

example in systems of Motilis [10] or Matesy [11] whichemploy permanent magnets as markers for example ina pill size arrangement moving through the human bodyTracking takes place at rather short distance Application to asensor swarm faces difficulties as the discerning of multiplemarkers that is sensor nodes in the swarm has not been sat-isfactorily solved so far Naturally instead of deploying per-manentmagnets in the sensory nodes also actively controlledmagnetic field generation by coil setups or spinning magnetsetups could have been considered However with regard tosize and power budget of autonomous miniaturized systemsThe second approach with active beacons and integratedmagnetic sensing in the swarm nodes thus is preferredin most applications for example in systems Polhemus[12] and Ascension [13] as well as medical applications ofinstrument or endoscopic task tracking Also this variant ismore fortunate for and compatible with the development ofSmart-Pills for example in the Vector-project [14] Basicallytwo beacon controlmethods can be distinguished employingAC-fields (eg systems of Polhemus [12]) or DC fields (egsystems of Ascension [13]) which in the latter casemeans thatthe beacons work in a timemultiplexing scheme that is eachbeacon emits a field at a defined time frame which allowsthe sensor and the the localization algorithms to uniquelyidentify the source However this feature also gives rise tothe synchrony of the beacon control and sensor swarm unitstime bases that is requiring an approach for maintainingsynchronization

AC-field generation additionally allows the use of fre-quencymultiplexing that is the simultaneous activity of sev-eral beacons at different frequencies However this requiresmore effort on the receiver side Also quasi-DC approachesare less vulnerable to the presence of magnetic materials andeddy-current induced fields

Advances in Artificial Neural Systems 3

Sensornode 1

Sensornode 2

Sensor

Gateway(IMST)

PC(MATLAB Localization

visualizationRT-coil control

Campaign parametersSensor data

Wirelessor UART

Sensor nodeAMR sensor T sensor p sensor

d1

d2

d3d4

d5

d6

Coil 1

Coil 2

Coil 3

Coil 4

Coil 5

Coil 6

15

15

151

1

105

05

050

0

0Y (m) X (m)

Z(m

)

Actual positionAMR sensor (NLM)

AMR sensor (triangulation)

node n

120583CDAQPython)

8

22

1

7

1

9 9 1010

6 6 55 4 4

3 88

77 2 9

6

510 4

3 3

1

Figure 2 The block diagram shows the implemented system and physical structure of the experimental setups

The various system solutions for example for indoorlocalization [15ndash18] or underground animal tracking [19] andso forth have employedmagnetic sensors from the spectrumof available principles for example SQUIDs miniaturizedcoils Hall elements for example [20] field plates ormagnetoresistive sensors with various operating principlessummarized as XMR sensors Compass sensors for examplefor the mobile phone market or automotive tasks haveincubated the conception of new sensory units for examplewith 9 axes including acceleration Gyros and magneticsensors in 3D arrangement [21 22] These rather novel chipson the market will support the compact implementations ofthe system and approach presented in this paper even betterFor reasons of sensitivity that is due to weak beacon fieldsor large distances between sensor and beacon Anisotrope-Magneto-Resistive (AMR) sensors are very attractive as theyfeature high sensitivity and offer favorite linearity propertiesand temperature range as well as small size and low-poweroperation

21 Pursued Magnetic Localization Approach In our re-search based on the outlined state-of-the-art and the partic-ular constraints of the regarded application domain a mag-netic localization system including synchronization capa-bility for a sensor swarm has been developed The systememploys the concept of quasi-DC field generation by sta-tionary field generating beacons realized by dedicated coilsand suitable computer controlled power electronics FurtherAMR sensors AFF755B [23] of Sensitec have been employedin 3 axial 3D arrangement which has been integrated byvarious packaging technologies [24] for example standardPCB or Active-Multi-Layer (AML) [25]

Figure 2 shows the block diagram of our magnetic local-ization system which has been implemented and employedin four different demonstrators

In our 3D-AMR magnetic sensor each AMR channelis connected to an AD 8290 instrumentation amplifierwhich provides a gain 119866 of 50 control of the bridge andpower-down of bridge and amplifier under control of themicrocontroller (atmel XMEGA256A3)Three such channelsserve for119883119884 and119885 registration and sampling takes place ina ternary scheme of the exciting magnetic field computingthe mean 119881

119898of positive and negative phase voltages 119881

119901

119894

and 119881119899

119894 in (1) Only the magnitude of the flux density 119861

119898is

required (see (2) and (3))

119881119894=

119881119901

119894minus 119881119899

119894

2 119894 = 119909 119910 119911 (1)

119881119898

= radic1198812119909+ 1198812119910+ 1198812119911 (2)

119861119898

= radic1198612119909+ 1198612119910+ 1198612119911=

119881119898

119878 sdot 119881119904sdot 119866

(3)

Here 119866 = 50 the bridge supply is 119881119878

= 33119881 and thesensitivity value 119878 is taken from the Sensitec datasheet withthe typical value of 117 which advocates the calibration of119878 for each sensor instance In our work we will comprisethis step by neural network learning In (4) Bio-Savarts-Law is employed to establish a relationship between theflux density values 119861

119898obtained from measurement and the

aspired distances 119889 by resolving for the distance 119889 in (5)

119861119898

=1205830

2sdot

119899 sdot 119868 sdot 1198772

(1198772 + 1198892)32

(4)

119889 = radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (5)

Here 1205830is the permeability in vacuum 119899 is the number of

windings of the coils 119868 is the DC current driving the coil


Table 1 Technical details of conceived demonstrators

ISEdemonstrator

Brewerydemonstrator

HMIdemonstrator

Dimensions [cm] D210 times H180 D220 times H300 D12 times H60Number of coils 6 12 6Coil diameter [cm] 125 32 12Number of windings 100 180 120Coil current in [A] 5 3 3Coil placement Cylindrical Cylindrical SphericalNumber of coil rings 2 3 2

and 119877 is the coil radius As this simple model only worksfine if the sensor is located on the principle coil axis and thesensor instance sensitivity is known the estimated distancescan be out of scale which is fixed in a first processing step bya heuristic global correction or scaling factor 120572 added in (6)The computation of 120572 is explained in Section 232(e)

119889 = 120572 sdot radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (6)

Thus RSSI equivalent distance values are obtained for thecase of the magnetic localization system and can be treatedwith the standard methods given in Section 23

22 Demonstrator and Integration Issues In order to validateand optimize the localization system under changing envi-ronmental condition and different scale three experimentalsetups or demonstrators were conceived

The first demonstrator is located in our ISE (integratedsensory systems) lab Six coils are placed in a cylindricalfashion similar to the shape of a steel tank The six coils areseparated into two rings of three coils each on two levelsrotated by an angle of 60

∘ An 119909-119910-movable sledge withattached scales serves for ground truth position acquisitionRelevant technical data is surveyed in Table 1 In the follow-ing this setup is referred to as ISE demonstrator

The brewery demonstrator (see Figure 3) is a real brew-ery container in smaller scale It was temporary set up atTechnikumWarstein to validate the localization system in theindustrial environment where parasitic magnetic fields of forexample large pumps or other heavy machinery might causeproblems The dimensions are bigger than those of the ISEdemonstrator so in total 12 coils separated into 3 rings of 4coils each were installed The coils itself were also larger indiameter The coil positions were appropriately determinedas a mandatory baseline for localization Relevant techni-cal details are summarized in Table 1 A suiting referencesystem for ground truth sensor position determination wasestablished inside the tank which for obvious reasons wasnot filled with liquid in these experiments Also acquiringa larger number of points than the registered 30 locationswithout proper climbing support was not easy especiallywithin the limited duration of availability of the experimentalsetup for this work

coils

Figure 3 The coils of the brewery demonstrator are separated intothree rings of four coils each

Here a lower limit for the achievable localization erroris in particular given by the uncertainty of the actual sensorcenter determination

Additionally the obtained data matches well with dataacquired from the target industrial process The reason forthis is that the experimental tank was placed in close prox-imity to the production environment including fermentationtanks so it can be rightfully assumed that it was subject tothe same sources of influence like pumps heaters coolersand so forth Due to the random nature of the switchingactivity of these devices with regard to the coil switching ofour localization scheme as well as enforced confidentialityon process details a comprehensive investigation is verydifficult But due to our ternary switching of the coil fieldsand ensuing differential processing in the sensory nodes allsources of influence quasiconstant in each coilrsquos time slot willbe significantly suppressed or even canceled out

The last demonstrator is a small down-scaled andmobileversion of our localization system and was specially designedand build for the presentation at Hannover Messe Industrie(HMI) 2013 Figure 4 shows the demonstrator at our boothwith the electronics on the table and a monitor showing aMATLAB GUI in the background The tank is modeled bya tube of acrylic glass Also the holding construction of thesix coils is made of this material See Table 1 for comparisonto the other demonstratorsThis mobile demonstrator will becalled HMI demonstrator in the following

The coil placement similar to the general problem ofanchor node placement in wireless sensor networks [26 27]was an important consideration in our work While a sym-metrical distribution of the coils is not essential equidistantplacement of the coils helps in making sure that in everypossible sensor position in the tank there is a minimum ofthree coils that generate fields of sufficient strength for properlocalization Also significant asymmetrical positioning of thecoils will aggravate the angle problem discussed in Section 21and will proportionally degrade the localization accuracyWe


Figure 4 The HMI demonstrator features spherically placed coilsto minimize the off-axis error of the coils The actual AMR-sensormodule in the current integration state of the prototype is wired tothe sensor development board located outside the acrylic glass tube

investigated 3 different topologies parallel planes cylindricaland ellipsoidal placement of coils The HMI demonstratorhas a very unfortunate aspect ratio and scale which couldbe partly compensated by the most promising ellipsoidal coilarrangement

The overall goal of the described research is the achieve-ment of a compact 3D integrated data logger for a sensorswarm in distributedmeasurements In the first developmentstep standard printed-circuit board (PCB) version of 3D-AMR-sensor (see Figure 5 (left)) [28] and the completedatalogger (see eg Figure 4) have been conceived The 3D-AMR-sensor has already seen implementation in various3D integration technologies [24] Figure 5 (right) shows theexample of the Active-Multilayer-Technology (AML) firstversion with a first-cut design size of 16mmtimes17mmtimes5mmThe bulky connectors visible in Figure 5 are required onlyfor the modular development systems and of course will beobsolete for the integrated target system Further substantialsize reduction by 3D layout optimization can be expectedAML technology is one favorable option to encapsulate andintegrate the complete aspired data logger

23 Standard Localization Algorithms

231 Standard Algorithms in Wireless Sensor Systems Inthe majority of wireless sensor systems RF-communicationsignals serve as the information source for the localizationapproaches The RSSI again is the most common indicatorto estimate the distance between a sender and receiver pairin the network for example a stationary beacon and a sensornode Based on four or more distance estimates quite similarto data visualization approaches triangulation multilatera-tion [29ndash31] or multidimensional scaling (MDS) methodsin particular the nonlinear Sammonrsquos mapping (NLM) [32]are employed in standard approaches for sensor location

Figure 5 Regarded 3D-AMR-sensor implementations standardPCB with AFF755B (left) and AML technology node with AFF756(right)

or coordinates estimation Sammonrsquos iterative mapping iscomputationally demanding and requires a postprocessingstep denoted as conformal mapping to compute the actualabsolute coordinates from the relative information Furtheremployed gradient descent technique might not converge tothe best solution The computationally fortunate multilatera-tion which is based on least squares optimization or Moore-Penrose pseudoinverse or the standard NLM both work finefor the magnetic system pursued here and the localizationresults of these unsupervised state-of-the art methods will becompared to those of the newly proposed ones

232 Enhanced Algorithms for Wireless Sensor Systems Theissues of high computational complexity 119874(119873

2

) potentiallocal optimum solution and required post processing forabsolute coordinate obtainment motivated the recent devel-opment of an advanced approach In the particular scenariofaced here mobile sensors individually have to estimate theirposition with regard to stationary beacons of known numberand position This can be tackled well with the NLM recall(NLMR) variant [33] reducing the computational complexityto 119874(119873) and immediately returns absolute coordinates Thisapproach along with advanced optimization methods forachievement of better solution quality has been introducedin [34] and will also serve in the variations briefly outlinedbelow for a self-contained presentation for comparison andextension of the newly proposed localization methods

(a) NLMRThe NLMR for localization as introduced in [34]has the following simplified cost function 119864

119894(119898) with 119898 as

step or iteration variable

119864119894(119898) =

1

119888

119870

sum

119895=1

(119889119883119894119895

minus 119889119884119894119895

(119898))2

119889119883119894119895

(7)

where

119889119883119894119895

= radic

119898

sum

119902=1

(V119903119894119902

minus V119905119895119902)2

119888 =

119870

sum

119895=1

119889119883119894119895

(8)

where 119889119883119894119895

is the distance between the currently mappedrecall datum and the 119870 previously mapped training datasamples in the high dimensional space The distances inthe new space can be found using standard or advancedoptimization methods


(b) Gradient Descent The gradient descent technique forNLMR is from [33 34] The equations are

119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)

where 119910119894119902(119898 + 1) is the new position MF is the magic factor

which reduces with time 119910119894119902(119898) is the current position and

119864119894(119898) is the cost function at the current position MF is

initialized to 1 We keep reducing the MF by 10 everytimewe find a better fitness

(c) NLMR-Simulated Annealing We use the basic simulatedannealing [34] where we start with a relatively high temper-ature (119879

0= 1) which is reduced (119879119909 = 119879

(119909minus1)lowast 08) over the

number of cycles and reduce the chances of choosing a badsolution as the temperature decreases (accept any solutionif 119901(0 1) lt 119905

119909) The new solutions are found by a Markov

chain shown in (9) with a random MF between minus1198900and 1198900

where 119890 (energy factor) reduces over timeThe algorithm runsfor 1000 iterations to get the best solutions The number ofiterations required was found heuristically

(d) NLMR Particle Swarm Optimization Standard particleswarm optimization described in [35] is used with 119862

1=

1198622= 2 and without inertia Having no inertia helped in faster

convergence of the algorithm 300 particles were used with150 generations to find the best results in the experiments

(e) Correction Factor 120572 A scale error in distance estimationbecame obvious from measurements that is introduced bythe model (see (3) to (5)) This reduces the accuracy ofthe algorithms Multilateration is mostly robust to this scaleerror because it uses only the differences in distance andnot absolute distance while the other methods require acorrection The correction factor 120572 shown in (6) can befound by determining the ratio of the model estimatedand actual distances We investigated suitable 120572-settings bycomputing this ratio for all samples of each data set andfound that there was only asymp1 variation in the result Soin the simplest case just taking one representative sample tocompute the correction factor already significantly improvesthe results More sophisticated search strategies to find thecorrection factor for example using unsupervised hyper-heuristics will be considered for future work

24 Data Acquisition The data sets acquired from the threedescribed demonstrators for the ensuing experiments havebeen collected by either a wired standard or a wirelessproprietary measurement system The wired one is a DataTranslation DT9816 data acquisition board (DAQ) whichis controlled by MATLAB The 3D-AMR-sensor module isdirectly wired to the DAQ and the amplified sensor voltagesare measured by analog input ports with 16-bit ADCs andare immediately available in MATLAB for signal processing

Table 2 Representative data sets acquired from the demonstratorsof Table 1 for the experiments

ISEL1 2data set

BREWdata set

HMI dataset

Demonstrator ISE Brewery HMISensor nodeSensor type

Std PCBAFF755B

Std PCBAFF755B

AMLAFF756

DAQ system DT9816 DT9816 XMEGA256A3

ADC resolution 16 bit 16 bit 12 bit

Coil control DT9816 XMEGA256A3

XMEGA256A3

Number ofsamplesplateau 10000 10000 128

Number of positions 169 30 44Number of repetitions 0 min 10 3Total number of trials 169 325 132

and localization computation The wireless system (see alsoFigure 2) corresponds to the target architecture of the finaldata logger which in the first step has been implemented as amodular development PCB system This development board(see Figure 4) features process sensors and a radio modulefor host PC via a gateway communication for examplefor configuration and measured process data transfer Forconversion of the 3D-AMR-sensor voltages the 12-bit ADCof the 120583C atmel XMEGA 256A3 is used in time-multiplexTable 2 gives an overview of the three representative data setschosen as the baseline for the following investigations TheISEL data in particular serves with a 13 times 13 equidistantspatial sampling with a a 10 cm pitch in a plane for theelucidation of the spatial localization error distribution ISELwas recorded two times with two different sensor instanceswhich will be denoted as ISEL

1and ISEL

2in the following

Figure 7 shows rawdata from the ISELdata setsThenoiselevel is quite substantial in comparison to the actual signalHigh frequent noise is alleviated bymultiple sampling of eachDC plateau for example 10000 times and computing theplateaumeanThis approach has been chosen instead of a lowpass filter because the edges of the magnetic DC plateaus alsoserve as synchronization signals and thus have to be as steepas possible Other sources of error for example stationarymagnetic fields as the earth magnetic field can be canceledout by either standard AMR-sensor flipping or the ternarycoil switching introduced in this work which ismore efficientfrom the point of view of energy conservation in the sensorynode [28]

The substantially lower resolution of the 120583C ADCrequired a more sophisticated read-out approach to avoidingloss of distance resolution A zooming technique was appliedthat by differential measurement offset autozeroing andscaling to full scale makes maximum use of the 120583C ADC12-bit resolution [24] Thus competitive localization resultsto the DAQ could be achieved on the integrated data loggertarget platform which was employed to acquire HMI dataset


25 Synchronization Issues The introduced magnetic local-ization concept and system crucially depends on the knowl-edge of the timing of each coilrsquos activation in the respectiveautonomous wireless sensor node This requires a synchro-nization between the clock in the coil switching unit and theclock in each sensor node As timebases commonly show asignificant uncertainty in particular when they are expectedto be small cheap and low-power repeated synchronizationis required In our case the tolerable or recoverable deviationlimit is determined by 50 of the duration of a singlecoilrsquos switching cycle In wired versions the synchronizationinformation easily can be made available by an extra triggerline Also in RF-based wireless sensor networks synchro-nization can be achieved by communications However inthe given container scenario deficiencies of RF hamperdata communication in general and localization as well assynchronization in particular A very straightforward ideais now to derive the coveted synchronization informationalso from the emitted magnetic field Indeed this has beeninvented already in [8] however with the sensor denotedas sync pick-up coil stationarily located very close to theemitting coil and attached by long wires to the sensor itselfA lock-in amplifier is used for the synchronization stepthere

The industrial scenario investigated in our case does notallow such a fortunate arrangement The magnetic sensoremployed for localization has to be employed also tomeasurethe data for synchronization and thus is remote and atvarying distances and orientations with regard to each of thecoilsThis scenario aggravation requires additional engineer-ing effort A resource hungry sampling of a sufficient timewindow around the expected first rising edge in the magneticfield has to be carried out In the very first-cut solution aheuristic threshold detector had been conceived in our pre-vious work which detects the magnetic field rising edge of acoil being switched on Based on the difference of the detectededge and timestamp to the expected timestamp the localwireless autonomous sensor nodersquos clock will be cyclicallyreadjusted The underlying technical problem of finding anedge or pulse in substantially noisy electrical ormagnetic fielddata has been visited before in communications networkingand most important magnetic head data reading in massstorage for example in [36] The task mentioned last comesclosest to our interest and activities In the work presentedhere we investigate the SVM classifier (SVM-C) techniqueas trainable edge detector It is applied with the parametersettings of unnormalised data obtained from the learning taskof 119862 = 10000 and kernel function is RBF with 120574 = 001 Theinput feature space is represented by a 2000 samples wideslidingwindow at an increment of 250 samples and the outputof the classifier represents the two classes ldquoedgerdquo and ldquonoedgerdquoThe processing structure of SVM based edge detectionsystem is illustrated in Figure 9The experimental data for thesynchronization investigations has been extracted from thewireless sensor node prototype in the HMI demonstrator incontinuous sampling mode that is whole localization cycleswere sampled whereas in contrast to this for localizationonly parts of the coil switched-on plateaus have to be sam-pled Three recorded raw data sets (ldquosyncraw1rdquo ldquosyncraw2rdquo

Table 3 Edge classification results

Method Heuristic SVM-CGenerated edges 66Detected edges 35 (5303) 41 (6213)Missed edges 31 (4697) 25 (3769)Spurious detections 14 (2121) 0 (00)

and ldquosyncraw3rdquo) of localization cycle each contains 262144samples of acquired ADC 12-bit values were used in theexperiment Each raw data set contains 33 different ldquoedgerdquoshapes and levels and 1028 ldquono edgerdquo events includingsome spurious switching activities from other sources in theenvironment that superpose like crosstalk These sampleshave been extracted from several localization cycles andlabeled by a human supervisor Figure 10 shows in the topstrip the sampled data of one localization cycle In thelearning phase ldquosyncraw1rdquo was split into two parts by hold-out sampling method resulting in two subdata sets withsimilar class distribution and data size in order to generatethe classifier with optimum parameters The remaining tworaw data sets (ldquosyncraw2rdquo ldquosyncraw3rdquo) were employed in thetesting phase to analyze performance of trained classifierThis gives 66 examples in ldquoedgerdquo class and 2056 in ldquonoedgerdquo class The results are shown in Table 3 The overallclassification rates of SVM-C and the heuristic method are98822 and 9788 respectively But these results look a bittoo optimistic as just the ldquono edgerdquo events are ruled out wellwhile the ldquoedgerdquo events still lack a comprehensive number ofcorrect classifications or detections which means that syn-chronization cycles occasionally might be missed Howeverthis is not a major problem as the system does not needsynchronization for each localization cycle Neverthelessimprovement of this classification subsystem is aspired and isunderway

Figure 10 shows an excerpt from ldquosyncraw2rdquo and ldquosyn-craw3rdquo data of the length of one localization cycle in the upperstrip and the edge detections of SVM-C versus heuristicmethod as well as the coil switching control signal timepoints in the lower strip The visible constant lag betweencoil switching control signal and the observed actual edgelocations is due to the delay in the currently used powerelectronics for coil driving Obviously the SVM-C solutionin the given straight form can already be dealing with noisespurious switching activities or crosstalk as well as coils invarious distances while the heuristics fails to do so in asignificantly higher number of cases

Future work has to tackle performance increase alongwith effort reduction with regard to energy consumptionfor example reducing sampling rate andor window sizeThe number of support vectors currently employed is cur-rently computed as 907 with 2000 features or dimensionseach Possible benefits of feature computation and sequentialapproaches [36] as well as larger data sets should be regardedfor a lean and efficient embedded implementation in follow-up work


3 Neural Virtual Sensors

Virtual sensors are an established engineering concept toobtain the equivalent of sensory registration that is notdirectly amenable to measurement either due to lack of phys-ical transduction principle or due to too expensive availablephysical transduction principle A well known example ofthe latter case is knock-detection in combustion engineswhere available but prohibitively expensive pressure sensingis replaced by a feasible acoustical sensing principle [37]The implied often nonlinear mapping task can be wellimplemented by suitable artificial neural networks such asfor example Multi-Layer-Perceptron with Backpropagationlearning (MLP) Fahlmanrsquos Cascade Correlation (CC) net-work Radial-Basis-Function (RBF) networks or Support-Vector-Regression (SVR) networks [37 38]

31 Motivation In this paper the most promising neuralnetwork candidates for example RBF and SVR networks areinvestigated as neural virtual sensors to improve localizationquality The basic idea of the localization process includingstandardmethod from Section 2 and two different enhancingapproaches with neural virtual sensors are illustrated inFigure 11 Twomain lines of investigation with the supervisedneural virtual sensor approach are depicted by two branchesin the figure The first one employs the model estimated dis-tances as input variables and remaps these to new correcteddistances followed by the standard localization algorithmsof Section 2 for coordinate calculation This method whichrequires the actual coil and sensor positions for groundtruth distance calculation will be denoted as the distance-to-distance (D2D) approach The second one directly mapsthe acquired sensor voltages to the sensor coordinates orposition completely omitting any model as well as omittingstandard localization algorithms This will be denoted as asthe voltage-to-coordinates (V2C) approach In both casesrepresentative training data must be provided for the super-vised mapping generation in the neural virtual sensors

The motivation of the proposed approach and its twovariations comes from the well known weakness of distanceestimation as expressed in (5) and (6) The employed modelassumes the sensor to be situated on the principal axis ofthe respective coil an assumption that is rarely met in actualsensor locations in container volumes This implies that thestronger the sensor position deviates from the principal axisof the regarded coil the larger the resulting error of theestimated distance from the sensor to the corresponding coilwill be Figure 12 illustrates this effect for one 119911-plane ofthe ISE demonstrator The error in the center is quite smallbecause the sensor comes closest to the principal coil axes dueto the cylindrical arrangement

The effect underlying the illustration in Figure 12 is wellknown and algorithmic correction schemes have long beensuggested [8 9] The advantage of the suggested supervisedlearning approach is that also a calibration of the localizationsystem with regard to instance specifics is achieved In thereferred to patents also the straight estimation of the sensorlocation frommagnetic sensor readings has been investigatedby look-up-table (LUT) mechanisms The advantages of RBF

or SVR approaches with regard to LUT in size generalizationand so forth are well known and obvious

32 RBF Networks Regarded RBF networks and tool imple-mentations in particular differ in determinationmechanismand size of the hidden layer and choice of the employed kernelfunction for example the Gaussian function

ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)

where 119894 is the index of the hidden layer 120583119894is the center of

the corresponding basis function and 120590119894is the spread which

determines the sensitivity of the neuron The output layerthen performs a linear transformation of the hidden neuronsactivations to the target output values It is calculated as

119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908

0being the weights The centers 120583

119894are learned

form the training set and the weights are optimized whiletraining [39 40] In this work the implementation fromMATLAB with the parameters spread and performance goalis employed A more resource efficient version of the RBFis Plattrsquos Resource-Allocating (RAN) Network for FunctionInterpolation [41] RAN allows the growth of the hiddenlayer from scratch and spread of every kernel function to beadjusted during training [41] and can be for future leanerrealizations

33 SVM Regression Support vector regression (SVR) [42]is an extension of the well established Support-Vector-Machines (SVMs) in order to solve the regression problemof learning and predicting continuous domain data SVRgenerates models from the training set (x119897 1199101) (x119897 119910119897)that perform with best fit in a linear function 119891(x) =

⟨w x⟩ + 119887 and result with a minimum 120598 deviation in theloss function Using 120598-insensitive loss function to reduce theerror to zero for all points that are smaller than 120598 in sometraining points however this error is beyond 120598 to deal withunfeasible constraints the slack variable 120585 is introduced inthe optimization problem The optimization problem of 120598-insensitive support vector regression (120598-SVR) [42] can beformulated as

minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)

subject to 119910119894minus ⟨w xi⟩ minus 119887 le 120598 + 120585

119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)

where 119862 determines the trade-off between the model com-plexity and the tolerance of the deviations larger than 120598 Theregression function is given by transforming the problem in


(13) into its dual problem subject to 0 lt 120572119894 120572lowast

119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)

where 119899SV is the number of support vectors (SVs) and120572119894and 120572

lowast

119894are Lagrangian multipliers The kernel function

119870(xi xj) = Φ(xi)sdotΦ(xj) can be chosen as radial basis function(RBF) Applying the so-called kernel trick allows tacklingof a nonlinear regression problem with linear estimation bymapping the data set into a higher dimensional space TheRBF kernel function is computed as

119870(xi xj) = exp (minus12057410038171003817100381710038171003817xi minus xj

10038171003817100381710038171003817

2

) 120574 gt 0 (15)

The optimum generalization performance of SVR is based onthe setting of model parameters 120598which is usually assigned aslevel of typical noise in the training data as well as parameter119862 and the kernel parameter 120574 For finding a convergencepoint of the optimum SVR prediction performance a grid-search method is commonly suggested [43] as independentcharacteristics to prediction model of 119862 and 120574

4 Experiments and Results

The data sets introduced in Section 24 will serve now forexperimental validation according to the outline in Figure 11of the proposedmethods For this aim the data sets have to besampled to generate appropriate training and test sets for thesupervised learning of the neural virtual sensorsWith regardto the moderate but sufficient available data size the hold-out approach was adopted Table 4 summarizes the selectedtraining setsThe residual data of each demonstrator are savedas test sets

For the ISEL1data set the measured points are orthogo-

nally located in one 119911-plane which can be seen in Figure 12The training data contains 25 input-target pairs which aremarked by the filled circles in the corresponding followingerror maps (Figures 14 and 16) The BREW data set positionsare spatially less regularly distributed (see Figure 8) Everypositionwith even index is used for training and the positionswith odd index are used for test set resulting in a training dataset size of 165 trials and a test data set size of 160 trials Forthe HMI data set there are 44 different positions whereasat each height (119911-position) 4 different 119909-119910-positions whereacquired This results in 11 119911-planes of 4 119909-119910-positions eachThe training data set is composed of 6 119911-planes and the testset contains the remaining 5 119911-planes whereby test and train119911-planes alternate

For D2D remapping networks which correspond topath 2 in Figure 11 two different network architectures withsuitable parameter setting ranges have been investigatedbased on a standard MATLAB implementation The variedparameters are the spread (120590) and the performance goalwhich is defined as the mean squared error of the trainingdata The architecture examined first is a network with inputand output layer size equal to the number of coils With

Table 4 Training data sets

ISELtrain set

BREWtrain set

HMItrain set

Number of positions 169 30 44Number of trials per position 1 min 10 3Total number of trials 169 325 132Number of trained positions 25 15 24Number of trained trials 25 165 72

119872 being the number of coils and 119873 being the numberof hidden layer neurons the network architecture can bereferred as 119872119909119873

119894119909119872 The second architecture consists of

119872 individually trained networks of 1198721199091198731198941199091 topology The

number of networks grows linearly with the number ofcoils and can be more greedy with regard to resourcesbut hidden layers can be individually grown with somesimilarity to RAN [41] and convergence commonly is easierThis architecture will be denoted as 119872119909(119872119909119873

1198941199091) in the

followingFor V2C mapping the same approach will be pursued

However in the case of the multinetwork architecture onlythree coordinates have to be generated independent of thenumber of coils So the architecture for V2C mapping andone single net is 1198721199091198731199093 and for multiple networks it is3119909(3119909119872119909119873

1198941199091) obviously alleviating resource issues and

the training process The V2C approach is illustrated bypath 3 in Figure 11 All the presented results are achievedusing the multiple network architectures for both D2D andV2C

For determining an optimum RBF parameter set abasic sensitivity analysis has been carried out with regardto mean localization error minimization and generalizationmaximization The investigated RBF parameters are the per-formance goal and the spread First the performance goal isset to fixed values of either 1 01 or 001 to limit the effort to aone-dimensional search For these three different settings thespread is swept With this approach a local suitable optimumcombination of performance goal and spread quality canbe achieved which returns a minimized distance error andhence localization error Figure 13 shows one example of aspread sweep for the BREWdata set andD2D remappingThelocalization error is computed for either the entire data set(training+ test data set) and for the test data setTheoptimumspread settings for those two data sets and analysis runs arenot identical Currently the RBF spread which performs bestfor the test set is chosen This approach can be applied forall network architectures for D2D remapping and for V2Cexcept for D2D with multiple network architecture case Thespread is swept for each network individually to make surethat an optimum spread can be found for each coil If thecriteria would be the localization error there would be noway to extract the best spreads because the multilaterationperforms a transformation from an M-dimensional input tothe 3-dimensional output So in case of D2D remapping with119872119909(119872119909119873

1198941199091) architecture the criteria are the distance error

which can be calculated before computing multilateration


Table 5 Results for raw data using advanced algorithms as described in Section 23 The parameter settings can be found in Figure 6 Theresults are a mean of five runs

Error Raw brew data Raw ISEL1 data Raw HMI DataGD SA PSO ML GD SA PSO ML GD SA PSO ML

Results for Raw data set in [cm]Loc error 120583 881 867 87 1318 292 289 288 365 1001 1006 985 1181 237 233 234 354 105 104 104 132 1641 1649 1615 1936Loc error 120590 417 417 415 1197 19 194 188 22 95 946 956 128 112 112 112 322 069 07 068 079 1557 1551 1567 2098Max loc error 355 3705 3534 13566 1115 1157 1131 1445 6745 6702 6737 13725 954 996 95 3647 403 418 408 522 11057 10987 11044 2250

Interpoint distances preservedCentralised

Gradient descentStart

Acquire rangeNLM using Sammon stress

Conformal transformReturn location

Stop

Flow

Sammons mapping

Localization algorithms

Distributed methodDeterministic

More anchors give better resultStart

Get anchor node locationsGet distances

Find euclidean distances from coilsSolve resulting equations

Stop

Flow

Multilateration

Dimensionality reductionSparse distance matrix (S)Distributed localization

Start

Flow

In anchors S point from heuristicFitness = NLMR stress funcIterate to improve fitnessReturn location

Stop

NLMR Gradient descent

GD in NLMLoop size = 500

MF = 1

Mf = MF lowast 09 if fitness reduces

Steps = 500

Accept id p(0 1) lt

MF = random(minuse e)

ex = e(x minus 1) lowast 0820 cycles

Fitness = NMLR stress fn

PSO Particles = 40

Generations = 150

C1 = C2 = Inertia = 1

T0 = 1

Tx

Tx

= T(xminus1) lowast 0820 cycles

Simulated annealing

Figure 6 Survey of employed algorithms and corresponding parameter settings

For each coil there is a specific RBF spread which results in aminimum distance error

SVR is employed as the second method in the entireexperiments with identical train and test data sets to RBF partof the work Here the LIBSVM [44] library was implementedon MATLAB platform Input and supervised learning datafor D2D and V2C investigations were identical to the RBFcase too Applying a grid search method to cover a widespectrum of parameter space in searching model parameters119862 and 120574 are determined in the range of [1 100000] and[01 100] respectively Parameter 120598 is usually defined to thelevel of typical noise in the training data In the trainingphase the pair of parameters 119862 and 120574 delivering the minimalmean square error of the model validation process will beselected to generate the prediction model The particularsetting values of 120576 for the ISEL1 BREW and HMI data are003 001 and 004 for D2D and 001 001 and 003 for V2Crespectively

The outlined experiments are conducted for each data setwith RBF and SVM each performing D2D and V2C map-ping Each best performing network is trained and recalled atleast 3 times to make sure that random initialization effectsdo not affect the results The results are presented in thefollowing two subsections

To put the upcoming results and improvements intoperspective in addition to standard multilateration we haveapplied the advanced methods from Section 23 to all threeraw 120572-corrected distance data sets (see (6)) The achievedlocalization quality is shown in Table 5 which shows substan-tial improvements to multilateration for all methods but inparticular for the PSO based method

41 Distance to Distance The ISEL1data set has amean local-

ization error of 2280 cm and amaximum localization error of4127 cm applying standardmultilateration By setting the coildistance scale factor 120572 to its optimum value of 135 the mean


AMR sensor RAW data of X-axis

AMR sensor RAW data of Y-axis

AMR sensor RAW data of Z-axis

Neg

ativ

e

Posit

ive

Zero

Coil 1 Coil 2 Coil 3 Coil 4 Coil 5 Coil 6

Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19

Figure 7 3D-AMR-sensor raw data sketch from ISEL 1 data set for a six coil cycle

0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12

Ground truth positions measured at Technikum Warsteiner

y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm

Figure 8 The 30 positions measured for the brewery data set arevisualized hereThe ground truth positions of the sensor aremarkedby the rectangles the circles determine the positions of the 12 coils

error can be reduced to 360 cm and the maximum error isreduced to 1503 cmTheD2D remapping approach applied tothe ISEL

1data set leads to a further improvement The error

map in Figure 14 shows that the maximum localization erroris reduced by a factor of 8 compared to the initial results of

Figure 12 which are achieved without any scaling factor orneural virtual sensor The mean error is reduced by a factorof 21 to just 105 cm for the test data set

Table 6 summarizes the results for RBF and SVR in D2Dmapping of ISEL

1data The two networks are compared side

by side for each of the data setsWithout D2D remapping the mean localization error for

the BREW data set is 1318 cm and the maximum error is13566 cm By comparing themean localization errors of bothapproaches for the test sets from Table 6 it can be seen thatthe RBF generalizes better than the SVR

The mean localization without D2D remapping for theHMI data set is 1175 cm and maximum error is 12161 cmCompared to the actual demonstrator dimensions (seeTable 1) which is the smallest of all three demonstrators theinitial error for the standardmethod (multilateration withoutD2D remapping) is very high This is due to the use of thebuilt-in ADC of the 120583C which has a resolution of 12 bitcompared to 16 bit of the DAQ and a different sensor whichis less sensitive than the one used with the first two data setsBoth methods improve the localization result See Table 6 formore details

To better assess these results and improvements inaddition to standard multilateration we have applied theadvanced methods from Section 23 to all three 120572-correctedD2D remapped distance data sets This has been done for


window data250new

No

No

Yes Yes

Sliding window

SVM classificationEdge Update

Start measurement

detectedsamplesProcessing

collectionmeasurement

timing

Figure 9 Processing structure of SVM based edged detection system

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge

EdgeEdge detection output signal

Sample

Clas

s

SVM classificationHeuristic method

Coil switching activity

times104

times104

Figure 10 Edge detection result based on SVMclassification formagnetic synchronization top strip shows exemplary rawdata fromcompletelocalization data from 3D-AMR-sensor and 12-bit ADC of 120583C and bottom strip shows edge detection times of SVM and heuristic method aswell as coil switching control signal for the top data

Magnetic field generation

Step

Errors Electrical current source noise current error coil

displacement

Magnetic field measurement

Noise gain error missing calibration

Coil distance calculation

B-fi

eld

Inaccurate B-field model axis error and far-field error

Location determination

Loc algorithmDistance

Volta

ge

XY

Z

3-dimensionalcoordinates

3-axis AMR sensor

InAmpDistance

Coil model

Hardware

Neural virtual sensor

D2D remapping

V2C mapping

Bypassing B-field model and loc algorithm with RBF or SVR

Remapping of distances with RBF or SVR

11

2 2

2

3 3

Basic approach with error prone B-field model and localization algorithm

1

Distance-2-distance remapping to correct distance error2Voltage-2-coordinates mapping to bypass distance calculation and localization algorithm

3

12

120583C ADC or DAQ

Figure 11 The three different methods of determining the position of the sensor are illustrated here The first approach is straight forwardwhereas the second method minimizes the distance error by remapping the distances before coordinate determination Sensor voltages aredirectly mapped to coordinates with the third method to bypass model-based distance calculation and the localization algorithm


Mean square error (cm) for sensor node 501

20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40

Mean square error (cm)Sample point

Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup

Figure 12 Error map for ISE demonstrator and using simple multi-lateration The localization error increases with increasing distanceto the center of the volume

1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)

Loc error just for interpolated pointsLoc error for entire dataset

X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45

Figure 13 Dependent on the RBF spread the resulting localizationerror varies and a minimum can be determined

RBF and SVR for complete data sets as well as test dataonly (Figure 15) The achieved localization quality is given inTable 7 which again shows substantial improvements bothto the results before D2D remapping as well as to standardmultilateration application for all methods This has beensummarized in Figure 15 As before the PSO based methodis taking the lead in result quality

20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5

Localization error (cm)Training point

Test point

y-axis (cm)

x-a

xis (

cm)

Localization error for ISEL1 data set and RBFremapping + multilateration

05

15

25

35

45

Figure 14 Employing RBF-D2D remapping andmultilateration themean localization error can be reduced to 090 cm

Table 6 Results for all experiments employing D2D and MLcomputation for path 2 in Figure 11

Data set ISEL1 BREW HMINetwork type RBF SVR RBF SVR RBF SVRsum119873119894

139 150 333 492 162 216Results for test and training data set in [cm]

Loc error 120583 090 084 352 351 286 221 032 03 095 094 469 362Loc error 120590 080 065 413 447 346 330 029 023 111 12 567 541Max loc error 504 313 3704 3562 2141 2141 182 113 996 958 351 351

Results for test with test data set in [cm]Loc error 120583 105 091 560 624 484 436 038 033 151 168 793 715Loc error 120590 078 064 501 499 426 382 028 023 135 134 698 626Max loc error 504 313 3704 3562 2141 2141 182 113 996 958 351 351

42 Voltage to Coordinate The results for V2C mappingapproach are found to be comparable in terms of localizationerror to the previous approach Figure 16 shows the errormap for RBF-V2C applied to ISEL

1data set The mean

localization error for ISEL1data set is higher than the one

of D2D followed by standard multilateration but still is inan acceptable range of just 214 cm which is in the order ofthe current sensorrsquos dimensions and thus sufficient for theregarded application Table 8 summarizes and compares RBFand SVR for V2C in the same way as previously providedfor the D2D investigationsThe SVR approach for ISEL

1data


Table 7 Results after D2Dmapping using advanced algorithms as described in Section 23 The parameter settings can be found in Figure 6The results are a mean of five runs

Error Brew data ISEL1 data HMI dataGD SA PSO ML GD SA PSO ML GD SA PSO ML

Results for D2D [Rbf] train + test data set in [cm]Loc error 120583 372 402 32 352 092 094 092 09 30 296 267 286 10 108 086 095 033 034 033 032 492 485 438 469Loc error 120590 31 301 325 413 07 066 067 08 333 322 327 344 083 081 087 111 025 024 024 029 546 528 536 564Loc error max 1871 1873 1898 3704 383 389 397 504 2033 2065 2032 2118 503 503 51 996 138 14 143 182 3333 3385 3331 3472

Results for D2D [Rbf] test data set in [cm]Loc error 120583 515 532 473 514 158 158 161 176 46 459 427 454 138 143 127 138 057 057 058 064 754 752 70 744Loc error 120590 354 351 374 435 093 094 089 12 421 406 415 429 095 094 101 117 034 034 032 043 69 666 68 703Loc error max 1871 1873 1898 3215 367 373 376 494 2033 2065 2032 2118 503 503 51 864 132 135 136 178 3333 3385 3331 3472

Results for D2D [SVR] train + test data set in [cm]Loc error 120583 373 385 301 351 08 089 076 084 242 248 228 221 10 103 081 094 029 032 027 03 397 407 374 362Loc error 120590 32 299 341 446 052 052 051 065 314 313 325 329 086 08 092 12 019 019 018 023 515 513 533 539Loc error max 1798 1898 1852 3562 292 291 307 314 2026 2062 2054 2141 483 51 498 958 105 105 111 113 3321 338 3367 351

Results for D2D [SVR] test data set in [cm]Loc error 120583 526 497 476 561 078 089 074 081 419 425 418 422 141 134 128 151 028 032 027 029 687 697 685 692Loc error 120590 367 362 382 451 052 052 05 064 388 387 395 389 099 097 103 121 019 019 018 023 636 634 648 638Loc error max 1798 1898 1852 2383 292 291 307 314 2026 2062 2054 2141 483 51 498 641 105 105 111 113 3321 338 3367 351

20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test

Demonstrators and methods

Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM

Figure 15 Graphical comparison of the raw results with the resultsafter application of RBf and SVR based on Tables 5 and 7

performs superior to the RBF approach but both approacheslag behind all previously obtained D2D results

For the BREW data set the mean localization error forV2C and RBF is nearly twice the one of D2D (RBF) withML The maximum error unfortunately is also increasedNeverthelessone advantage of the V2C approach is thesignificantly smaller number of neurons of just 27 while D2D(RBF) and ML required 333 neurons A trade-off of resultquality and computational resource can be considered TheSVR approach for BREW data performs superior to RBFapproach but also lags behind D2D results

For the HMI data set an increase in mean localizationerror can also be observed but is not so expressed as observedfor the first two regarded data sets Comparing the resultsfrom Table 8 with those from Table 6 results do not differsignificantly except for themean localization error for the testdata set where D2D (RBF) and ML perform 093 cm betterthan V2C However the SVR V2C approach outperforms



Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4

Mean square error (cm) of sensor node 501

20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)

with RBF-NN (voltage-to-coordinates)

Figure 16The localization error with RBF-V2Cmapping is reduceddown to 214 cm

Table 8 Results for all experiments employing V2C computationfor path 3 in Figure 11


21 50 27 495 192 213Results for test with test and training data set in [cm]



RBF-basedmethods andD2D approaches in general for HMItest data

43 Discussion The overall results given in Tables 6 and8 show that all proposed methods are feasible and providesubstantial result improvements with regard to raw modeloutput data and standard multilateration The methods fromSection 23 are already powerful and completely unsuper-vised However they have to rely on the model output andoffer no calibration options The D2D extension in partic-ular when combined with the methods from Section 23offers calibration options and remarkable result improve-ment at substantial computational cost dependence on themodel for distance calculation and the necessity to obtain

Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Performance D2D with ML testPerformance V2C test

Effort D2DEffort V2C

0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns

Figure 17 Comparison of performance versus effort for D2D andV2C approaches employing RBF neural network (see Tables 6 and8)

Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0

Performance D2D with MIPerformance V2C


Figure 18 Comparison of performance versus effort for D2D andV2C approaches employing SVR (see Tables 6 and 8)

representative supervised data for each application scenarioThese methods are best sited for host-based postmeasure-ment localization computation

The V2C approach though it did not give top perfor-mance in most of the investigations still is appealing as it isnot depending on a model and is computationally much lessdemanding because V2C is linear in complexity with regardto the number of coils and requires smaller network sizes (seefirst row of Table 6 and of Table 8 resp) Thus it is bettersuited for on-line node-based localization computation andoffers calibration options with the same need met in D2D ofobtaining representative supervised data for each applicationscenario Also sometimes mediocre results of V2C are partlydue to lack of rotation invariance with regard of the rotationof the sensor node itself Either sufficient rotated exampleshave to be provided or an invariance transform has to beadded in future improvements

Clearly a trade-off in result quality and resource demandis offered by the different proposed methods This is illus-trated in Figures 17 and 18 by putting the performance andrequired cost for both methods D2D and V2C side by sidefor RBF and SVR respectively This looks on first sight toomuch in favor of D2D as existing overhead of computing


the distances from magnetic measurements and computingcoordinates from transformed distances is not yet includedin the given effort calculation V2C approach does not needthese steps at all The final choice of method depends on theapplications requirements on localization accuracy allowableresource expenses and the potential need for node-basedlocalization computation during measurement

5 Conclusion

This paper presented our work on a artificial neural networkbased enhancement of a dedicated magnetic localizationsystem for a wireless integrated autonomous sensor swarmfor distributed process parameter measurement in industrialenvironment such as for example large scale stainless con-tainers or fermentation tanks The concept has no limitationon the sensor swarm size The focus of our work was on theimprovement of the initially achieved mediocre localizationaccuracy of the basic electronic system by means of alearning system based on neural virtual sensors adapting tothe regarded scenario and system instance RBF and SVRtechniques were investigated in D2D along with standardand advanced distance to coordinate computation and V2Capproaches for three different demonstrators from lab toindustrial scale

The supervised learning approach achieved significantimprovements even for uncalibrated sensors and measure-ment set-up in all investigated configurations The mostfortunate method combination of D2D by SVR followedby PSO-based distance to coordinate computation returneda factor large than 4 of improvement for the BREW datafrom industrial scenario The mean error of about 3 cm isless than the size of the currently employed sensor nodebringing the localization results well in the order of theexpectation met for example in brewery industry as wellas in challenging smart-environment applications Howeverthe presented learning system could also be abstracted to thebenefit of nonmagnetic that is RF-based localization

The mandatory synchronization for the pursued mag-netic localization approach motivated the extension of thedescribed approach by a learning SVM-based edge detectorfor coil switching time detection and sensor clock correctionSimulations on data from the HMI demonstrator showed theviability of the approach and thus the overall system

Future work will improve the system with regard toartificial neural network size reduction robustness issueslean synchronization techniques swarm visualization self-xmechanisms improved coil-switching power electronics and3D integration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to gratefully acknowledge the supportof the German BMBF mst-AVS Project PAC4PT-ROSIG

Grant no 16SV3604 for funding the baseline of this follow-upwork and the contributions of L Rao to the first-cut sensornode SW and of S Carrella for collecting the raw data forthe BREW data set in Warsteiner brewery together with DGroben

References

[1] T Selker Counter-intelligence project 2008 httpwwwmediamiteduci

[2] B Warneke M Scott B Leibowitz et al ldquoAn autonomous 16solar-powered node for distributed wireless sensor networksrdquoin Proceedings of the 1st IEEE International Conference onSensors (IEEE Sensors rsquo02) vol 2 pp 1510ndash1515 June 2002

[3] K Pister J Kahn and B Boser ldquoSmart dustmdashautonomoussensing and communication in a cubic millimeterrdquo 2001 httproboticseecsberkeleyedupisterSmartDust

[4] International Technology Roadmap for Semiconductors httpwwwitrsnet

[5] W Arden M Brillouet P Cogez M Graef B Huizing andR Mahnkopf ldquomore-than-moorerdquo White paper 2013 httpwwwitrsnetLinks2010ITRSIRC-ITRS-MtM-v2203pdf

[6] ldquoSensornetzwerkerdquo Tech Rep 2013 httpwwwizmfraunho-ferde

[7] A Reinecke U Popping and U Hampel ldquoAutonome Sensor-partikel zur raumlichen Parametererfassung in groszligskaligenBehalternrdquo in GMAITG-Fachtagung Sensoren und Messsys-teme pp 513ndash521 VDE June 2012

[8] C V Nelson and B C Jacobs ldquoMagnetic sensor system forfastresponse high resolution high accuracy three-dimensionalposition measurementsrdquo PCT patent application WO 2000 017603A1 applicant The John Hopkins University USA 1998

[9] J S Bladen and A P Anderson ldquoPosition location systemrdquoPCT patent application WO 1994 004 938A1 August 14 1992applicant for all states except US British TelecommunicationsPub Ltd US Inventors

[10] Motilis Innovative Pill Technology 2009 httpwwwmotiliscom

[11] Matesy GmbH 3d-magtrack 3d-magma httpwwwmatesydede

[12] Polhemus2012httpwwwpolhemuscompageMilitaryWhy-MagneticTracking

[13] Ascension Technology Corporation Products ApplicationOctober 2014 httpwwwascension-techcommedicalindexphp

[14] ldquoVector projectrdquo 2010 httpwwwvector-projectcom[15] G Pirkl and P Lukowicz ldquoRobust low cost indoor positioning

using magnetic resonant couplingrdquo in Proceedings of the ACMConference on Ubiquitous Computing (UbiComp rsquo12) pp 431ndash440 ACM Press New York NY USA 2012

[16] M Barry A Grnerbl and P Lukowicz ldquoWearable joint-angle measurement with modulated magnetic field from lcoscilatorsrdquo in Proceedings of the 4th International Workshop onWearable and Implantable Body Sensor Networks (BSN rsquo07) SLeonhardt T Falck and P Mhnen Eds vol 13 chapter 7 ofIFMBE Proceedings pp 43ndash48 Springer New York NY USA2007

[17] J Blankenbach and A Norrdine ldquoPosition estimation usingartificial generated magnetic fieldsrdquo in Proceedings of the Inter-national Conference on Indoor Positioning and Indoor Naviga-tion (IPIN rsquo10) pp 1ndash5 September 2010


[18] J Blankenbach A Norrdine and H Hellmers ldquoAdaptivesignal processing for a magnetic indoor positioning systemrdquo inProceedings of the International Conference on Indoor Positioningand Indoor Navigation (IPIN rsquo10) Short paper pp 15ndash17 2010

[19] J Agila B Link G Fabritius M H Alizai and K WehrleldquoBurrow viewmdashseeing the world through the eyes of ratsrdquo inProceedings of the IEEE International Workshop on InformationQuality and Quality of Service for Pervasive Computing IQ2S

[20] Asensor Technologies ABHe444 Series 3d Analog Hall SensorsDatasheet SENSOR+TEST 2013 Asensor Technologies ABNurnberg Germany 2013

[21] Bosch Sensortec BMX055 BNO055 2013 httpwwwbosch-sensorteccomenhomepageproducts 39 axis sensors 59-axis sensors

[22] Invensense ldquoMPU-9150 Nine-Axis (Gyro + Accelerometer +Compass) MEMS Motion Tracking Devicerdquo 2013 httpwwwinvensensecommemsgyrompu9150html

[23] Sensitec ldquoAFF755B datasheetrdquo 2011 httpwwwsensiteccomenglishproductsmagnetic-fieldaff755html

[24] A K D Groben A C Kammara and K Thongpull ldquo3dlocalization of low-power wireless sensor nodes based on amrsensors in industrial and ami applicationsrdquo in Proceedings ofthe 16th International Conference on Sensors and MeasurementTechnology (SENSORS rsquo13) pp 346ndash351 AMA ServiceGmbHNurnberg Germany May 2013

[25] ldquoHofmann Leiterplatten GmbHrdquo 2013 httpwwwhofmannde

[26] R Akl K Pasupathy and M Haidar ldquoAnchor nodes placementfor effective passive localizationrdquo in Proceedings of the Inter-national Conference on Selected Topics in Mobile and WirelessNetworking (iCOST rsquo11) pp 127ndash132 October 2011

[27] B Tatham and T Kunz ldquoAnchor node placement for localiza-tion inwireless sensor networksrdquo in Proceeedings of the 7th IEEEInternational Conference on Wireless and Mobile ComputingNetworking and Communications (WiMob rsquo11) pp 180ndash187October 2011

[28] S Carrella K Iswandy and A Konig ldquoA system for localizationof wireless sensor nodes in industrial applications based onsequentially emitted magnetic fields sensed by tri-axial amrsensorsrdquo in Proceedings of the 11th SymposiumMagneto-ResistiveSensors and Magnetic Systems Lahnau Germany March 2011

[29] M Leonardi A Mathias and G Galati ldquoTwo efficient local-ization algorithms for multilaterationrdquo International Journal ofMicrowave and Wireless Technologies vol 1 no 3 pp 223ndash2292009

[30] A Wessels X Wang R Laur and W Lang ldquoDynamic indoorlocalization using multilateration with RSSI in wireless sensornetworks for transport logisticsrdquo Procedia Engineering vol 5pp 220ndash223 2010

[31] Many Authors ldquoMultilateration and ADS-B an executive ref-erence guiderdquo 2013 httpwwwmultilaterationcomresourceshtml

[32] K Iswandy and A Konig ldquoSoft-computing techniques toadvance nonlinear mappings for multi-variate data visualiza-tion and wireless sensor localizationrdquo e-Newsletter IEEE SMCSociety vol 29 2009

[33] A Konig ldquoInteractive visualization and analysis of hierarchicalneural projections for data miningrdquo IEEE Transactions onNeural Networks vol 11 no 3 pp 615ndash624 2000

[34] A C Kammara and A Konig ldquoAdvanced methods for 3Dmagnetic localization in industrial process distributed data-logging with a sparse distance matrixrdquo in Soft Computing

in Industrial Applications vol 223 of Advances in IntelligentSystems andComputing pp 149ndash156 Springer Berlin Germany2014

[35] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995

[36] J Cioffi W Abbott H Thapar C Melas and K D FisherldquoAdaptive equalization in magnetic-disk storage channelsrdquoIEEE Communications Magazine vol 28 no 2 pp 14ndash29 1990

[37] K Iswandy and A Konig ldquoHybrid virtual sensor based onRBFN or SVR compared for an embedded applicationrdquo inKnowlege -Based and Intelligent Information and EngineeringSystems A Konig A Dengel K Hinkelmann K Kise RHowlett and L Jain Eds vol 6882 ofLectureNotes inComputerScience chapter 34 pp 335ndash344 Springer 2011

[38] H Pasika S Haykin E Clothiaux and R Stewart ldquoNeuralnetworks for sensor fusion in remote sensingrdquo in Proceedings ofthe International Joint Conference on Neural Networks (IJCNNrsquo99) vol 4 pp 2772ndash2776 1999

[39] S Haykin Neural Networks edited by S Haykin MacmillanNew York NY USA 1994

[40] P D Wasserman Advanced Methods in Neural Computing VanNostrand Reinhold New York NY USA 1st edition 1993

[41] J Platt ldquoA resource-allocating network for function interpola-tionrdquo Neural Computation vol 3 no 2 pp 213ndash225 1991

[42] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[43] C-C Chang and C-J Lin A practical guide to support vectorclassification 2010 httpwwwcsientuedutwsimcjlinpapersguideguidepdf

[44] C-C Chang and C-J Lin ldquoLibsvm a library for supportvector machinesrdquo ACM Transactions on Intelligent Systems andTechnology vol 2 no 3 pp 271ndash2727 2011

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



distributed measurement in industrial applications in themeasurement and instrumentation field [6 7]

One important aspect in the practical application ofsensory networks or swarms with multisensory processparameter registration for example of temperature pressurehumidity conductivity or impedance spectrum is the log-ging of time and location context A synchronized timebasepotentially addional location sensors and apt signal process-ing are required for the task of context acquisition Evaluationof distributed swarm measurements will be of value onlyif time and location of the registration are available forswarm data visualization and analysis In many applicationscenarios including indoor outdoor or even maritine tasksthe radio signal itself and its attenuation (Received-Signal-Strength-Indicator (RSSI)) can serve as sensory source andbaseline for localization

However in industrially relevant scenarios of closedlarge-scale containers for example stainless-steel fermen-tation tanks in brewery industry shown in Figure 1 strongattenuation in the medium and reflections from containerwalls hamper communication itself and thus also localiza-tion

In our research an alternative localization system hasbeen conceived to locate the units of the sensor swarm basedon magnetic technology and inspired by existing trackingsystems and technology for example helmet tracking inmilitary applications or instrument or pill tracking inmedicalapplications The developed approach and system scales tothe required industrial tank sizes It employs integratedmagnetic sensors together with algorithms from compu-tational intelligence to robustly calculate the sensor nodelocalization from magnetic field emitting beacons In thispaper the basic electronic system and an extension by neuralnetworks as virtual sensors in a supervised approach forthe significant improvement of the localization quality andthe simplified adaptation to changed or new applicationscenarios are presented In Section 2 we will outline ourapproach system architecture and electronics scenariosdata acquisition and the synchronization approach with thecorresponding classification experiments In Section 3 virtualsensormethods and corresponding parameter settings will begiven In Section 4 before concluding our experiments andresults will be presented

2 Magnetic Localization System

Magnetic localization systems are in widespread use sincemore than two decades and related publication and patentactivity for example [8 9] can be observed Numerousconcepts and systems solutions can be found which achievea localization or a tracking of one or potentially severalobjects These systems can be conceived in two dual ways byeither employing an potentially integrated magnetic markerwhich is located by an external stationary sensor systemor sensor array or alternatively employing a plurality ofexternal stationary magnetic field generator units workingas beacons which are detected by magnetic sensors withinthe regarded mobile sensory nodes The first approachis commonly employed in medical tracking systems for

Figure 1 Fermentation tanks example of twenty meters height andsix meters diameter from brewery industry (Courtesy Warsteiner)

example in systems of Motilis [10] or Matesy [11] whichemploy permanent magnets as markers for example ina pill size arrangement moving through the human bodyTracking takes place at rather short distance Application to asensor swarm faces difficulties as the discerning of multiplemarkers that is sensor nodes in the swarm has not been sat-isfactorily solved so far Naturally instead of deploying per-manentmagnets in the sensory nodes also actively controlledmagnetic field generation by coil setups or spinning magnetsetups could have been considered However with regard tosize and power budget of autonomous miniaturized systemsThe second approach with active beacons and integratedmagnetic sensing in the swarm nodes thus is preferredin most applications for example in systems Polhemus[12] and Ascension [13] as well as medical applications ofinstrument or endoscopic task tracking Also this variant ismore fortunate for and compatible with the development ofSmart-Pills for example in the Vector-project [14] Basicallytwo beacon controlmethods can be distinguished employingAC-fields (eg systems of Polhemus [12]) or DC fields (egsystems of Ascension [13]) which in the latter casemeans thatthe beacons work in a timemultiplexing scheme that is eachbeacon emits a field at a defined time frame which allowsthe sensor and the the localization algorithms to uniquelyidentify the source However this feature also gives rise tothe synchrony of the beacon control and sensor swarm unitstime bases that is requiring an approach for maintainingsynchronization

AC-field generation additionally allows the use of fre-quencymultiplexing that is the simultaneous activity of sev-eral beacons at different frequencies However this requiresmore effort on the receiver side Also quasi-DC approachesare less vulnerable to the presence of magnetic materials andeddy-current induced fields


Sensornode 1

Sensornode 2

Sensor

Gateway(IMST)




Wirelessor UART


d1

d2

d3d4

d5

d6

Coil 1

Coil 2

Coil 3

Coil 4

Coil 5

Coil 6

15

15

151

1

105

05

050

0

0Y (m) X (m)

Z(m

)



node n

120583CDAQPython)

8

22

1

7

1

9 9 1010

6 6 55 4 4

3 88

77 2 9

6

510 4

3 3

1







119901

119894

and 119881119899


119898is


119881119894=

119881119901

119894minus 119881119899

119894

2 119894 = 119909 119910 119911 (1)

119881119898

= radic1198812119909+ 1198812119910+ 1198812119911 (2)

119861119898

= radic1198612119909+ 1198612119910+ 1198612119911=

119881119898

119878 sdot 119881119904sdot 119866

(3)





119861119898

=1205830

2sdot

119899 sdot 119868 sdot 1198772

(1198772 + 1198892)32

(4)

119889 = radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (5)





ISEdemonstrator

Brewerydemonstrator

HMIdemonstrator



119889 = 120572 sdot radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (6)






coils















2



119894(119898) with 119898 as


119864119894(119898) =

1

119888

119870

sum

119895=1

(119889119883119894119895

minus 119889119884119894119895

(119898))2

119889119883119894119895

(7)

where

119889119883119894119895

= radic

119898

sum

119902=1

(V119903119894119902

minus V119905119895119902)2

119888 =

119870

sum

119895=1

119889119883119894119895

(8)

where 119889119883119894119895




119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)






0= 1) which is reduced (119879119909 = 119879







1=






ISEL1 2data set

BREWdata set

HMI dataset


Std PCBAFF755B

Std PCBAFF755B

AMLAFF756




XMEGA256A3




1and ISEL

2in the following



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Sensornode 1

Sensornode 2

Sensor

Gateway(IMST)




Wirelessor UART


d1

d2

d3d4

d5

d6

Coil 1

Coil 2

Coil 3

Coil 4

Coil 5

Coil 6

15

15

151

1

105

05

050

0

0Y (m) X (m)

Z(m

)



node n

120583CDAQPython)

8

22

1

7

1

9 9 1010

6 6 55 4 4

3 88

77 2 9

6

510 4

3 3

1







119901

119894

and 119881119899


119898is


119881119894=

119881119901

119894minus 119881119899

119894

2 119894 = 119909 119910 119911 (1)

119881119898

= radic1198812119909+ 1198812119910+ 1198812119911 (2)

119861119898

= radic1198612119909+ 1198612119910+ 1198612119911=

119881119898

119878 sdot 119881119904sdot 119866

(3)





119861119898

=1205830

2sdot

119899 sdot 119868 sdot 1198772

(1198772 + 1198892)32

(4)

119889 = radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (5)





ISEdemonstrator

Brewerydemonstrator

HMIdemonstrator



119889 = 120572 sdot radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (6)






coils















2



119894(119898) with 119898 as


119864119894(119898) =

1

119888

119870

sum

119895=1

(119889119883119894119895

minus 119889119884119894119895

(119898))2

119889119883119894119895

(7)

where

119889119883119894119895

= radic

119898

sum

119902=1

(V119903119894119902

minus V119905119895119902)2

119888 =

119870

sum

119895=1

119889119883119894119895

(8)

where 119889119883119894119895




119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)






0= 1) which is reduced (119879119909 = 119879







1=






ISEL1 2data set

BREWdata set

HMI dataset


Std PCBAFF755B

Std PCBAFF755B

AMLAFF756




XMEGA256A3




1and ISEL

2in the following



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





ISEdemonstrator

Brewerydemonstrator

HMIdemonstrator



119889 = 120572 sdot radic((12) sdot 120583

0sdot 119899 sdot 119877

2

sdot 119868

119861119872

)

23

minus 1198772 (6)






coils















2



119894(119898) with 119898 as


119864119894(119898) =

1

119888

119870

sum

119895=1

(119889119883119894119895

minus 119889119884119894119895

(119898))2

119889119883119894119895

(7)

where

119889119883119894119895

= radic

119898

sum

119902=1

(V119903119894119902

minus V119905119895119902)2

119888 =

119870

sum

119895=1

119889119883119894119895

(8)

where 119889119883119894119895




119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)






0= 1) which is reduced (119879119909 = 119879







1=






ISEL1 2data set

BREWdata set

HMI dataset


Std PCBAFF755B

Std PCBAFF755B

AMLAFF756




XMEGA256A3




1and ISEL

2in the following



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in












2



119894(119898) with 119898 as


119864119894(119898) =

1

119888

119870

sum

119895=1

(119889119883119894119895

minus 119889119884119894119895

(119898))2

119889119883119894119895

(7)

where

119889119883119894119895

= radic

119898

sum

119902=1

(V119903119894119902

minus V119905119895119902)2

119888 =

119870

sum

119895=1

119889119883119894119895

(8)

where 119889119883119894119895




119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)






0= 1) which is reduced (119879119909 = 119879







1=






ISEL1 2data set

BREWdata set

HMI dataset


Std PCBAFF755B

Std PCBAFF755B

AMLAFF756




XMEGA256A3




1and ISEL

2in the following



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119910119894119902(119898 + 1) = 119910

119894119902(119898) minusMF times Δ119910

119894119902(119898) (9)

with

Δ119910119894119902(119898) =

(120597119864119894(119898) 120597119910

119894119902(119898))

(1205971198642

119894(119898) 120597119910

119894119902(119898)2

)

0 lt MF le 1 (10)






0= 1) which is reduced (119879119909 = 119879







1=






ISEL1 2data set

BREWdata set

HMI dataset


Std PCBAFF755B

Std PCBAFF755B

AMLAFF756




XMEGA256A3




1and ISEL

2in the following



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



















ℎ119894(119909) = exp(minus

1003817100381710038171003817119909 minus 120583119894

1003817100381710038171003817

2

21205902

119894

) (11)




119891 (119909) =

119896

sum

119894=1

119908119894ℎ119894(119909) + 119908

0(12)

with 119908119894and 119908


119894are learned




minimize 1

2w2

+ 119862

119897

sum

119894=1

(120585119894+ 120585lowast

119894)


119894

⟨w xi⟩ + 119887 minus 119910119894le 120598 + 120585

lowast

119894

120585119894 120585lowast

119894ge 0 119894 = 1 2 119897

(13)




119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119894lt 119862 and

sum119897

119894=1(120572119894minus 120572lowast

119894) = 0

119891 (x) =

119899SV

sum

119894119895=1

(120572119894minus 120572lowast

119894)119870 (xi xj) + 119887 (14)


lowast




10038171003817100381710038171003817

2

) 120574 gt 0 (15)








ISELtrain set

BREWtrain set

HMItrain set






1198941199091) in the
















Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











Stop

Flow

Sammons mapping






Stop

Flow

Multilateration


Start

Flow


Stop



MF = 1


Steps = 500

Accept id p(0 1) lt




PSO Particles = 40

Generations = 150


T0 = 1

Tx

Tx


Simulated annealing












Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







Neg

ativ

e

Posit

ive

Zero


Volta

ge (V

)Vo

ltage

(V)

Sample

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18times104

183182181

18179

177176175174173172

Volta

ge (V

)

196195194193192191

19


0 100 200

0100

100

150

200

250

300

350

400

450

19 51226 30

1 23 111825 29

101724

491623 28381522271421

5

4

67

8161320 27

9 1011 12


y-ax

is (cm

)

x-axis (cm)

z-ax

is (c

m)

minus200minus100

minus100

100 cm

150 cm

200 cm

250 cm

300 cm

350 cm

400 cm

450 cm













window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




window data250new

No

No

Yes Yes

Sliding window


Start measurement



timing


1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9

200400600800

Input signal

Sample

AD

C va

lue

1 15 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9No edge


Sample

Clas

s



times104

times104



Step


displacement




B-fi

eld




Volta

ge

XY

Z


3-axis AMR sensor

InAmpDistance

Coil model

Hardware


D2D remapping

V2C mapping



11

2 2

2

3 3


1


3

12

120583C ADC or DAQ




20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

5

0

10

15

20

25

30

35

40


Y-axis (cm)

X-a

xis (

cm)

15

15

1515

15

15

20

20

20

2020

20

20

20

10

10

10

10

25

25

25

25

25

25

5 5

3030

30

25

35 3530

40

25

30

in circular setup


1 2 3 4 52

4

6

8

10

12

14

16

18

20

Mea

n lo

caliz

atio

n er

ror (

cm)


X 438Y 5876

X 435Y 3575

120590

120590 Sweep

05 15 25 35 45



20 30 40 50 60 70 80 90 100 110 120 130 1405

152535455565758595

105115125

1

2

3

4

5


Test point

y-axis (cm)

x-a

xis (

cm)


05

15

25

35

45








1data set The mean



1data








20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










20

15

10

5

0

Erro

r (

)

RawRBF test

SVR test


Brew

GD

Brew

SA

Brew

PSO

Brew

M

ISE

GD

ISE

SA

ISE

PSO

ISE

M

HM

IG

D

HM

ISA

HM

IPS

O

HM

IM







Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





Test point

2

2

222

2

22

2

2

2

4

4

4

6

6

62

2

2

2

884

4

2

2

10

4

44

6

422

2

6

4

4

4


20 30 40 6050 70 80 90 100 110 120 130 1405

152535455565758595

105115125

0

5

10

15

y-axis (cm)

x-a

xis (

cm)










Erro

r (

)

10

8

6

4

2

0ISE Brew HMI



0

10000

20000

30000

40000

50000

Tota

l num

ber o

f neu

ral c

onne

ctio

ns


Erro

r (

)

10

8

6

4

2

0ISE Brew HMI

Tota

l num

ber o

f sup

port

vec

tors500

400

300

200

100

0









5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





5 Conclusion







Acknowledgments



References






















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article Neural Virtual Sensors for Adaptive Magnetic...

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