[IEEE 2009 15th International Conference on Intelligent System Applications to Power Systems (ISAP)...

THREE-DIMENSIONAL LOCATION OFELECTROMAGNETIC SOURCES USING

INTELLIGENT SYSTEMSRafael Hernan Mira Perez, Instituto Tecnologico Metropolitano

Jesus Antonio Hernandez Riveros, Universidad Nacional de Colombia

Abstract—This paper proposes a method to determine the spatial location where an emitting electromagnetic source is.A magnitude, a vertical angle and a horizontal angle corresponding to the location of the source, regarding an arbitraryreference, are obtained while supplying an Artificial Neural Network (ANN) with experimental basic data from the sensorsinstead those of signal processing. The modeling methodology and the basic and most important concepts in applyingthe techniques of localization are taken into account. The behavior of the occurrence in the three-dimensional space isanalyzed detailing each step in obtaining the model of the ANN. Characterizing the system, finding its parameters, andmeasuring variables of interest for the development of practical analysis are made through a laboratory prototype builtfor these purposes and for validating the neural model. From the fitted model the efficiency of ANN is estimated.

Index Terms—sources location, neural networks, spatial location, low-cost technology.

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1 INTRODUCTION

Among the variety of situations generated byelectromagnetic sources, including natural phe-nomena such as lightning, the location of thesource is difficult to locate accurately. Thesource location can be achieved by training anANN, to calculate the distance and the verticaland horizontal angles which the electromagne-tic activity happened. Currently, natural pheno-mena manifested in lightning, affect the energytransmission, as well as the location of faultscaused by them. a proposal for detecting thearrival of more than one signal simultaneouslyto an array of antennas of linear or planar geo-metry using intelligent algorithms is presentedin [2]. In [5] is shown a way to detect traditionalperiodic radiation and records of frequencyvariations, extremely low of electromagneticfields, where these fields are of geophysicaland astrophysical origin. An algorithm to es-timate the location of a mobile or static useris presented in [6], base in electromagnetic-based technologies two localization algorithms

•

are proposed: estimation by selective fusion(SELFLOC) and region of confidence RoC. In[10] is found an application of ANN in cellularcommunications estimating the location andeliminating the interference cocanals. Moreo-ver, [9] shows that the radiation of the structureof an antenna is the sum of the obtained fielddue to the distribution, which is obtained bythe method of reconstruction of the source andthe field radiated by the current that it induceson the conductive structure. In [15] there is astudy on the characterization of a system capa-ble of capturing energy from the environmentusing electromagnetic systems, and [14] discus-ses new broadband radio carriers as candidatesfor future communications using electrical im-pulses. In [7] of sensors for low-power batteriesare studied. In [3] Bayesian filters are used toestimate the position of electromagnetic sour-ces, while in [16] the identification and locationof a WLAN system is studied, without usingextra hardware, by adding the values of thewireless network provided by located users.On the other hand [1] looks at the bordersof a time of arrival estimation error for ultraoperating in multipath environments. Another

978-1-4244-5098-5/09/$26.00 ©2009 IEEE

aspect is that [13] developed an algorithm totrack the arrival of a plane and estimate thetime of arrival and in [12] is shown in the di-gital oscilloscope a teaching application, whichcontains interactive tools to teach the characte-ristics of antennas. However, all these methodsare based on traditional signal processing te-chnology and demand a high cost. This paperpresents an ANN-based method that uses asinputs basic variables of the sensors to locate asource of RF in space.

2 MATERIALS AND METHODS.The data taken when stimulates the antennacoils with voltage sources show that the voltageand current are significant, in the order of10 hz to 2 MHz, were used. This sensors werestimulated by an electromagnetic source, gene-rating signals of current, voltage and power,proportional to the stimulation signal. Thesesignals are converted into data that feed theANN, which after proper training delivers thedistance and angles where the initial electro-magnetic phenomenon happened.

2.1 Gathering dataThe data taken when stimulates the antennacoils with voltage sources show that the voltageand current are significant, in the order of50mA a 100 mA, measurable and good power.Signals emitted by the microphone, being sti-mulated with sound sources, product of anelectromagnetic phenomenon, response wea-kly, but also offer possibility of measurementand power, although a little lower in the orderof 10 mA to 80 mA, However, data taken usingfilters to only pass signals that stimulate thereceptors when activated by an electromagneticsource, show that they respond quickly andhave very good power, of the order of 5 mAa 400 mA.

2.2 Mathematical analysisThe process of mathematical modeling of thesystem is presented in three stages as follows:

1) Antenna Modeling: in applications ofsignal processing is common to assumea Gaussian process in the design process,

however not Gaussian processes arise incertain situations and then you can ques-tion how to model data in a specificsituation and then raises the possibilityof monitoring continuous state space inwhich one works, another considerationis that problems can be divided into mainentrance, intermediate and weak signalcases [11]. The objective of this projectis to exploit existing techniques, to mo-nitor and select the proper detector toprocess the data. The detection of radar,for example, with knowledge of the staticenvironment is given when collecting aset of N samples represented in ”Eq.(1)”,{

r0, r1, .........rN−1

}(1)

a cell in a space, processing data by a re-ceiver Neyman-Person (LRT), which takethe form of a proof of the probability of(LRT) and is decided by which cell ornot a goal, the (r) represents the vectorcomposed of N samples, and the repre-sentation presented in ”Eq. (2) ”{

r = (r0, r1......, rN−1)T

}(2)

T represents the transpose, and the sam-ples represent the random variables des-cribed in ”Eq. (3)” respectively.{

R0, R1......, RN−1

}(3)

The probability compares a static λ, withthe threshold of a fixed η. The λ is thestatic relationship between the probabi-lity density function (PDF) represented by”Eq. (4) ”, {

pR( rH1

)}

(4)

N samples of a given target is presentand the joint PDF shown in Eq. (5) of Nsamples given, a goal that is not present.H1 and H0 represent the hypothesis thata target is present or absent. This rela-tionship is called LR. The threshold η isdetermined by restricting the probabilityof a false alarm (ATP) to a specified value.The binary hypothesis H1, H0 is set solow that H1, the sample collected KTH,(Rk), k = 0, 1, 0, ..........N − 1, consists of a

signal sampled target, (Sk), in addition,a sum of signs of disturbance sampleddk). The hypothesis H0, the sample KTH,(rk)(where k = 0, 1, ........ N-1) containsthe disturbance (dk) . Because, in ”Eq.(5)”, the disturbance of the sample (dk)consists of a noise (CL) (ck), shows a morenormal (nk).{

rk =

{sk + dk; H1

dk; H0K = 0, 1,..N − 1

}

(5)The probability ratio test then takes theform of ”Eq.(6) ”{

λ =pR(

(r)H1>

)H1

pR((r)

H0<)H0

η

}(6)

The above analysis shows that if the radaris one of the typical electromagnetic phe-nomena, which emits the signal and theresponse is expected to make a decision,but for the case being analyzed is not veryapplicable, these are techniques knownas passive and therefore discarded as astarting point for analysis and is directlyactive in the techniques, where the sourceemits the response signal and does not ex-pect to make a decision. The detection ofradio sources is a growing field of studyof interest, given the mobility of newtechnologies. There are some solutionsthat are distinguished by their high cost.There are tools such as the detector Finder(Germany) that has a working range from50 MHz to 6 GHz. The company Inter-connection Electrical SA (ISA) Colombia)is implemented in strategic areas, detec-tors sources that emit electromagnetic sig-nals to a global positioning system (GPS).To characterize a radio source parame-ters have been found as radiated powerdensity, defined as output per unit areain a certain direction, which in terms ofspherical coordinates is a mathematicalbehavior as shown in ”Eq.(7)”{ −→

P (θ, φ) = Re(−→Ex

−→H )

}(7)

Where: −→P = Radiated power density. θ=Angle formed by the electric field with

respect to the reference axes. φ= Angleformed by the magnetic field with respectto the reference axis. Re=Relationship bet-ween the electric field and magnetic field.−→E = Electric field. −→H= Magnetic Field.

2) Location of sources: a ANN is used toidentify the location of a radio frequencysource. A group of sensors that capturethe signal feed data to the ANN. Someinitial design parameters are needed totake into account, which determine theworking conditions of the system, suchas: the source signal, which should bedisposed within the frequency range setfor this case, corresponding to the ap-propriate scope, based on historical data.Figure 1 mimics the outline developed forthe purpose of testing and experimenta-tion of the system, with respect to a refe-rence initially established. In figure 1 lo-

Fig. 1. Work space

cated within the working space L x L, arethree detectors S1, S2,S3 and S4, locatedindistinctly, called sensors in this project,and a transmitter f, called in this projectas the source. The design of source andsensor array is one of the basic aspects,requiring the appropriate sensitivity, sothat the signals are captured within an es-tablished range. Interferences, noise, dis-turbances and obstacles are mixed withthe measured signal. Currents, voltages,power, distance and angle are measuredon actual data through tools that are com-mercially available.

3) Theoretical foundation on ANN: AnANN is a structure composed of a num-ber of interconnected units (artificial neu-

rons). Each unit features input/outputand implements a local calculation orfunction, the output of any unit is de-termined by the characteristics of in-put/output, interconnection with otherunits and external inputs. However, itis possible to develop a functionality th-rough one or more forms of training, [8].The human brain consists of more than100 billion items of processers called neu-rons, which communicate through con-nections called synapses. Each neuron iscomposed of three main parts: the body,axon and dentritas. The outer layer ofthe body, the dentritas, has the uniqueability to generate nerve impulses whichare like branches that leave the body,have some synaptic connections, whichusually receive signals from other axons.The axon is responsible for activating orinhibit other neurons, which in turn areactivated by hundreds of thousands ofother neurons. The operation of an artifi-cial neuron based on this design basicallyconsists of applying a set of entries, eachof which represents the output of anotherneuron, or an external input, performs aweighted sum of these values and filterthis value with a function. The ANN isa tool that presents viable alternatives tosolve a problem with elements that re-duce costs and save time, using the popu-lar principle of OCCAM, which holds thatif they are several possible explanationsfor a phenomenon is due to choose theeasiest to explain fully The RNA is a toolthat presents viable alternatives to solvethe problem with elements that reducecosts and save time, using the popularprinciple of OCCAM, which holds that ifthey are several possible explanations fora phenomenon is due choose the easiestto explain fully, [4], but requires a seriesof studies and signal conditioning in or-der to begin formulating a new theory.However, there is an option to locate asource of radio frequency, with differentsensors and not using traditional signalprocessing. This is the approach here pre-sented. Based on a working space, as

shown in Figure 2 and assuming that inreceptors, measurable excitation voltagesare activated by a radio source, a ANN forlocalization source was designed. Geome-tric measures are obtained by taking thetable 1, where the measured values canbe appreciate, which represent the voltageand the distance of each point. The fo-llowing terminology is used to identifyvariables df = distance from the source(event) to the receiver R, V S1, V S2, V S3,voltages corresponding to signals presentin receiver R, d1, d2, c correspond to therespectively equivalent distance as vol-tages generated by V S1, V S2, and V S3,respectively. The methodology used for

Fig. 2. Graphical simulation capturing data

making initial data has some drawbacks,because the reference situated in the fi-gure 2 is located in one of the axes andtherefore generates inconsistencies in theinterpretation. Then locating the referencein a fixed, predefined point, for which alltests are performed, as shown in part b ofthe figure 2, facilitates the location of thebody in working space using a sensor. Toanalyze the behavior of elements within

the working space may be consideredseveral states:

4) State 1: in this case has only one sensor,S1, which is currently known about thelocation and angle, with respect to thereference R, as shown in in Part B ofFigure 2, which f is the vector equivalentto the signal source, either in the quarters,df is the distance from the source to thereference, d1 represents the distance fromthe sensor S1 to the reference R, α1 re-presents the angle that generates f1, withrespect to the positive x axis, dependingon the reference R and V S1 correspondsto the voltage detected by the sensor S1,when stimulated by the source. In thisfirst condition is not enough informationto estimate df .

5) State 2: in this case there are two sensors,S1 and S2, of which it knows the exactlocation and angle α and φ, with respectto the reference R, as shown in Figure2, where f1 is the vector equivalent tothe signal source, df represents the dis-tance from the source to R, d1 representsthe distance from the sensor S1 to thereference R, α1 represents the angle thatgenerates f1, with respect to the axis ofpositive the x, depending on the referenceR, V S1, V S2 correspond respectively tothe voltages detected by the sensor S1

and S2 when they are stimulated by thesource. To analyze the process using geo-metric tools, the value of the angles α,φ, γ, β, α=arcsin xS2

d2, (φ+θ+α)=arcsin xS1

d1,

θ2=arcsin(d2 sin θV S2

). α For mapping, it is no-ted that when the source is located onthe first and second quadrant the systemresponds properly, but when it is positio-ned in the third or fourth show ambiguityin angular location and location. valuestaken for the study are shown in Table 1

6) State 3: now you have two sensors, S1

and S2, of which it knows the exact lo-cation and angle α and φ, with respectto the reference R, as shown in Figure3, where f1 is the vector equivalent tothe signal source, df1 represents the dis-tance from the source to R dS1 represents

the distance from the sensor S1 to thereference R, α1 represents the angle thatgenerates f1, with respect to the axis ofpositive x depending on the reference R,V S1, V S2 correspond respectively to thevoltages detected by the sensor S1 andS2 when they are stimulated by source,which moves a distance dz, on the z axisof the system.To analyze the process using geome-tric tools, the value of the angles α,φ, γ, β, α=arcsin xS2

d2, (φ+θ+α) =arcsin xS1

d1,

θ2=arcsin(d2 sin θV S2

)With these data we obtain the table 2,which represents the data on the physicalplane.

TABLE 1Random values taken from ideal

circumstances, considering two sensors andsources in three dimensional spaces

Source Ds1 df αz dfz dz VS1Z VS2f11z 4.1 8.6 18.5 12.6 4.0 0.1746 0.2096f21z 9.0 9.7 109.9 14.7 5.0 0.0971 0.0686f31z 15.0 8.2 205.0 14.2 6.0 0.0619 0.0592f41z 12.8 7.3 299.3 14.3 7.0 0.0685 0.0836f51z 5.0 5.0 40.0 14.0 9.0 0.0971 0.1039f61z 4.5 3.2 22.6 5.2 2.0 0.2031 0.1630f12z 4.8 10.5 25.6 18.5 8.0 0.1072 0.1084f22z 6.8 9.5 119.1 18.5 9.0 0.0887 0.0667f32z 8.0 8.0 186.4 9.0 1.0 0.1240 0.0644f42z 11.8 7.8 281.8 9.8 2.0 0.0836 0.1288f52z 8.1 6.4 112.6 10.4 4.0 0.1107 0.0791f62z 13.0 10.4 102.9 13.4 3.0 0.0750 0.0576f13z 1.5 9.0 14.5 12.0 3.0 0.2981 0.1397f23z 9.9 8.0 109.5 12.0 4.0 0.0937 0.0687f33z 14.1 7.4 203.8 12.4 5.0 0.0668 0.0644f43z 15.0 8.5 294.4 14.5 6.0 0.0619 0.0736f53z 8.5 1.1 227.0 4.1 3.0 0.1109 0.1098f63z 17.0 10.0 185.2 11.0 1.0 0.0587 0.0587f14z 10.2 10.2 19.2 15.2 5.0 0.0880 0.1715f24z 11.5 8.3 114.8 14.3 6.0 0.0771 0.0619f34z 13.2 6.0 212.6 13.0 7.0 0.0669 0.0685f44z 10.5 8.0 300.0 16.0 8.0 0.0758 0.1006f54z 8.1 1.6 315.6 5.6 4.0 0.1107 0.1176f64z 9.5 2.5 296.4 4.5 2.0 0.1030 0.1085

In this case resolves the ambiguity oflocation presented in the previous case, iewhen the source is located on the third orfourth quadrant, because the reference dz,change sign, but when distances are thesame values are the same and ambiguitycontinues.

7) State 4: another consideration is when

Fig. 3. Location of the source in space, detectedby two sensors

you have three sensors, S1, S2 and S3 forwhich the exact locations are known andthe angles α, ϕ and φ, with respect to thereference R, as shown in Figure 4, wheref1 is the vector equivalent to the signalsource, df represents the distance fromthe source to R, d1 represents the distancefrom the sensor S1 to the reference R, d2

represents the distance from the sensor S2

to the reference R, d3 represents the dis-tance from the sensor S3 to the referenceR, α1 represents the angle that generatesf1, with respect to the positive x axis,depending on the reference R, V S1, V S2

and V S3 correspond respectively to thevoltages detected by the sensor V S1, V S2

and V S3 when they are stimulated by thesource.To analyze the process using geometrictools, the value of the angles α1, β1, θ1, θ2,θ3, φ1, φ2, φ4 y γ1, entonces α1= arcsin(xS2

d2,

α+θ+ϕ) = arcsin xS1

d1, θ2 = arcsin(d2 sin θ

V S2).

For this condition, there are three sensorsthat capture three signals equivalent to astimulus delivered by the same source,are located in a two dimensional plane,but where exactly are located the samedistance in the third and fourth quadrant,the ambiguity remains.

8) State 5: now selects random values, ta-king measures in the work space andbased on this table is constructed 2,where the equivalence scale proportional

Fig. 4. Representation of vectors in state spaceusing three sensors

to comply with the measures taken to 6independent sources.


circumstances, considering two sensors andsources in three dimensional spacesFuente α df VS1 VS2 VS3f11 52,0 8,6 0,244 0,385 0,323f21 135,0 9,7 0,111 0,073 0,102f31 216,0 8,2 0,067 0,063 0,072f41 313,0 7,3 0,078 0,103 0,091f51 13,0 5,0 0,200 0,294 0,222f61 75,0 3,2 0,222 0,172 0,313f12 49,0 10,5 0,208 0,217 0,217f22 112,0 9,5 0,147 0,083 0,125f32 194,0 8,0 0,077 0,065 0,078f42 334,0 7,8 0,085 0,133 0,103f52 143,0 6,4 0,123 0,083 0,116f62 169,0 10,4 0,077 0,058 0,071f13 67,0 9,0 0,667 0,154 0,286f23 151,0 8,0 0,101 0,071 0,096f33 232,0 7,4 0,071 0,068 0,075f43 295,0 8,5 0,067 0,082 0,077f53 262,0 1,1 0,118 0,116 0,139f63 233,0 10,0 0,059 0,059 0,063f14 36,0 10,2 0,098 0,333 0,200f24 166,0 8,3 0,087 0,067 0,087f34 253,0 6,0 0,076 0,078 0,083f44 348,0 8,0 0,095 0,169 0,095f54 322,0 1,6 0,123 0,133 0,154f64 274,0 2,5 0,105 0,111 0,122

It is considered sensors S1, S2 and S3,located in the first quadrant, the sourcecan be presented in the first, second, thirdor fourth quadrant, as shown in Figure5, but located in space, we know thefollowing parameters:

1) f11=presence of source 1 in the firstquadrant,f21=presence of the source2 in the first quadrant

2) f31=presence of the source 3 in thefirst quadrant, f41=presence of thesource 4 in the first quadrant

3) f51= presence of 5 fountain in thefirst quadrant, f61=presence of thesource 6 in the first quadrant

4) f12= presence of source 1 in the se-cond quadrant, f22= presence of thesource 2 in the second quadrant

5) f32= presence of the source 3 in thesecond quadrant, f42= presence ofthe source 4 in the second quadrant

6) f52= presence of 5 fountain in thesecond quadrant, f62= presence ofthe source 6 in the second quadrant

7) f13= presence of the source 1 in thethird quadrant, f23= presence of thesource 2 in the third quadrant

8) f33= presence of the source 3 in thethird quadrant, f43= presence of thesource 4 in the third quadrant

9) f53= presence of 5 fountain in thethird quadrant, f63= presence of thesource 6 in the third quadrant

10) f14= presence of source 1 in thefourth quadrant, f24= presence of thesource 2 in the fourth quadrant

11) f34= presence of the source 3 in thefourth quadrant, f44= presence of thesource 4 in the fourth quadrant

12) f54= presence of 5 fountain in thefourth quadrant, f64= presence of thesource 6 in the fourth quadrant

13) VS11= voltage corresponding to thesignal detected by the sensor 1, whenthe source in the first quadrant.

14) VS11=voltage corresponding to thesignal detected by the sensor 1, whenthe source in the first quadrant.



17) VS12=voltage corresponding to thesignal detected by the sensor 2, when

Fig. 5. Analysis of the system by placing sen-sors in the first quadrant and the source in anyof the quadrants of the plane

the source in the first quadrant.18) VS13=voltage corresponding to the

signal detected by the sensor 2, whenthe source in the first quadrant.






24) ds1= distance s1 R, ds2= distance froms2 R, ds3= distance from s3 R

25) α1=angle between the vector produ-ced by the source s1, with respect toR.

26) α2=angle between the vector produ-ced by the source s2, with respectto R. item α3=angle between thevector produced by the source f3,with respect to R.

When these conditions occur, it is a veryforward in terms of location and the an-gular location of the source, but when the

Fig. 6. Representation of the system by locatingthe source in space, three sensors in the planeof two dimensions and the fourth in space

source is exactly the same distance fromthe main positive and negative returnsand is ambiguity and information is suf-ficiently clear.

9) State 6: here are three sensors, S1, S2

and S3 for which the exact locations areknown and the angles α, ϕ and φ, tothe benchmark R, as shown in Figure 6,but located in three dimensional space,where f1z is equivalent to the vector sig-nal source, df1z represents the distancefrom the source to R, d1 represents thedistance from the sensor S1 to R(reference), d2 represents the distance from thesensor S2 to R reference, d3 representsthe distance from the sensor S3 to thereference R, α1z represents the angle thatgenerates f1, with respect to the positive zaxis, depending on the reference R, V S1z,V S2z and V S3z correspond respectively tothe voltages detected by the sensor S1,S2 and S3 when they are stimulated bysource.To analyze the process using geometrictools, the value of the angle α1z, by geo-metric methods, then α1z = arcsen( dz

dfz,

known as the distance from the sour-ces in two dimensions, the new dis-tance is calculated in the third dimension,and dfz=

√df 2 + dz2 and the table 3 table

shows the data obtained.10) State 7: here are three sensors, S1, S2,


circumstances, considering three sensors andthe source in three-dimensional spaces

α df αz dz VS1Z VS2Z VS3Z52 8,60 18,50 4,00 0,1746 0,2096 0,1976135 9,70 109,88 5,00 0,0971 0,0686 0,0909216 8,20 204,99 6,00 0,0619 0,0592 0,0661313 7,30 299,30 7,00 0,0685 0,0836 0,076713 5,00 40,00 9,00 0,0971 0,1039 0,099475 3,20 22,61 2,00 0,2031 0,163 0,26549 10,50 25,62 8,00 0,1072 0,1084 0,1084112 9,50 119,10 9,00 0,0887 0,0667 0,083194 8,00 186,30 1,00 0,124 0,0644 0,0779334 7,80 281,77 2,00 0,0836 0,1288 0,101143 6,40 112,61 4,00 0,1107 0,0791 0,1054169 10,40 102,93 3,00 0,075 0,0576 0,069867 9,00 144,77 3,00 0,2981 0,1397 0,2169151 8,00 109,47 4,00 0,0937 0,0687 0,0897232 7,40 203,78 5,00 0,0668 0,0644 0,0704295 8,50 294,44 6,00 0,0619 0,0736 0,0698262 1,10 227,02 3,00 0,1109 0,1098 0,1282233 10,00 185,21 1,00 0,0587 0,0587 0,062836 10,20 19,20 5,00 0,088 0,1715 0,1109166 8,30 114,80 6,00 0,0771 0,0619 0,0771253 6,00 212,57 7,00 0,0669 0,0685 0,072348 8,00 300,00 8,00 0,0758 0,1006 0,0758322 1,60 315,58 4,00 0,1107 0,1176 0,131274 2,50 296,38 2,00 0,103 0,1085 0,1185

S3 and S4, of which the exact locationsare known and the angles α, ϕ , φ, φ,φ, with respect to the reference R, asshown in Figure 6, but located in threedimensional space, where f1 is the vectorequivalent to the signal source, df repre-sents the distance from the source to R, d1


reference to R, d2 represents the distancefrom the sensor S2 to the reference R, d3


to reference R, d4 represents the distancefrom the sensor S4 to the reference R,α1 represents the angle that generates f1,with respect the positive axis of x, depen-ding on the reference R, V S1, V S2 , V S3

and V S4 correspond respectively to thevoltages detected by sensor S1, S2 y S3

and S4 when they are stimulated by thesource.To analyze the process using geometrictools, the value of the angles α1,β1, θ1, θ2, θ3, φ1, φ2, φ4 y γ1,thenα1=arcsin(xS2

d2,α+θ+ϕ)=arcsin xS1

d1,

θ2=arcsin( d2

sinθV S2).


circumstances, considering the source, andfour sensors located in space

Source α df VS1 VS2 VS3f11 52.0 8.6 0.244 0.385 0.323f21 135.0 9.7 0.111 0.073 0.102f31 216.0 8.2 0.067 0.063 0.072f41 313.0 7.3 0.078 0.103 0.091f51 13.0 5.0 0.200 0.294 0.222f61 75.0 3.2 0.222 0.172 0.313f12 49.0 10.5 0.208 0.217 0.217f22 112.0 9.5 0.147 0.083 0.125f32 194.0 8.0 0.077 0.065 0.078f42 334.0 7.8 0.085 0.133 0.103f52 143.0 6.4 0.123 0.083 0.116f62 169.0 10.4 0.077 0.058 0.071f13 67.0 9.0 0.667 0.154 0.286f23 151.0 8.0 0.101 0.071 0.096f33 232.0 7.4 0.071 0.068 0.075f43 295.0 8.5 0.067 0.082 0.077f53 262.0 1.1 0.118 0.116 0.139f63 233.0 10.0 0.059 0.059 0.063f14 36.0 10.2 0.098 0.333 0.200f24 166.0 8.3 0.087 0.067 0.087f34 253.0 6.0 0.076 0.078 0.083f44 348.0 8.0 0.095 0.169 0.095f54 322.0 1.6 0.123 0.133 0.154f64 274.0 2.5 0.105 0.111 0.122

The analysis shows that the four sensorsystem is a prism in a plane and thisresults in optimizing the system angularlocation and location, without any ambi-guity, the data are shown in Table reftabla6 with which you train the ANN again,with very satisfactory results ideals areproposed, and expected the trend of thestudy. With the above data, it feeds theRNA, which delivers location informa-tion of the source angle and distance. Asstated in the previous section, the dataobtained allowed to train the ANN withresults of 98 % representative and the-refore is accepted as a result with goodprecision and accuracy.

2.3 Analysis of results

After doing the mapping and analytical dataobtained are training a neural network with theparameters, yields the results shown in Table 5and the errors shown in the table 6

TABLE 5Securities issued by the network, to angle inspace, angle in two dimensions, the source

distance and position in spacef1 f2 f3 f4 f5 f6

αfxy 20,02 15,15 28,40 29,98 33,03 37,52αfz 35,01 10,02 11,51 14,00 178,36 179,99dfz 3,78 4,89 2,55 2,32 1,99 1,42dfz 0,60 0,60 0,60 0,60 0,60 0,60

TABLE 6Errors made by the artificial neural network inthe space angle, angle in two dimensions, the

source distance and position in spacef1 f2 f3 f4 f5 f6

αfxy -0,03 -0,15 1,59 0,02 -3,03 2,47αfz -0,02 -0,02 -0,13 -0,08 1,63 0,00dfz 0,42 1,14 -0,81 -0,13 -0,40 -0,42dfz 0,00 0,00 0,00 0 0,00 0,00

2.4 Conclusions

1) The study of electromagnetic phenomenarequires elements with very good res-ponse rate because the high speed of thephenomena. However, has been shownthat is possible to locate an electromagne-tic source by means of basic signals fromthe detectors. Thereby, induced voltagewas used as the basic variable.

2) Ambiguity elimination was also achievedand besides in the whole space.

3) The data were disturbed with white noisebut the results had a satisfactory preci-sion, so the neural system could be usedin any environment.

2.5 Future work

1) Despite obtaining good results would beimportant to perform experiments othermodels of infrastructure and of ANN tosee which of them provides better res-ponse.

2) Using the same source applied, modelingthe system with several bandpass filtersto observe behavior stimulating with animpulse.

ACKNOWLEDGMENTS

The contributions made by Professors EdilsonDelgado Trejos, Fredy Bolanos and Javier He-rrera, have made possible the completion ofthis article.

REFERENCES

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complejos con tecnicas de reconstruccion de fuentes. InXVI Simposium Nacional de la Union Cientıfica Internacionalde Radio, pages 371–372, 2001.

[10] Javed Muhammad. Artificial neural networks for locationestimation and co-channel interference suppression incellular networks. Master’s thesis, University of Stirling,2007.

[11] Melvin M.Weiner. Adaptive Antennas and Receivers (Elec-trical and Computer Enginee). CRC Press, 2005.

[12] Daniel Perez, Arnau Cabedo, Lluıs Vicent, and JaumeAnguera. Herramienta educativa para el analisis deantenas microstrip: Impedancia de entrada y diagramasde radiacion. Revista IEEE America Lat, 2006.

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Researcher

Rafael Hernan MiraPerez, Instrumentation and Control En-gineering from Politecnico ColombianoJaime Isaza Cadavid from Medellın andM.Sc from Universidad Nacional de Colom-bia. He is an industrial automation profes-sor in the Instituto Tecnologico Metropo-litano de Medellın. His research interestsinclude computational intelligence in engi-

neering. email: [email protected]

Researcher

, Jesus AntonioHernandez Riveros Electrical Engineeringdegree from Universidad Nacionalde Colombia, M.S. degree in ComputerSciences from EAFIT University, Colombia,and Ph.D. degree in Computer Sciences(with Honors), from Universidad daCoruna, Spain. He has been working asa consultant engineer in the Colombian

electrical energy sector. In 1992 he joined Universidad Nacionalde Colombia as a Special Professor. He is currently a memberof the faculty staff. His research interests include computationalintelligence in engineering, evolutionary computation incontrol systems, and modeling of emergency systems. email:[email protected]

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