st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand Investigation of advanced data pocessing technique in magnetic anomal detection sstems. Ginbug (, A. Sheinke (, L. umkis (,.Z. Kaplan (, N. Salomonski ( ( Soeq NRC, Yavne, 88, Isael, bogin@soeq.gov.il ( en-guion Univesit of the Negev, P.O. o 65, ee-sheva, 85, Isael Abstact Advanced methods of data pocessing in magnetic anomal detection (AD sstems ae investigated. Raw signals of AD based on component magnetic sensos ae tansfomed into eneg signals in the space of speciall constucted othonomalied functions. This pocedue povides a consideable impovement of the SNR thus enabling eliable taget detection. Estimation of the taget paametes is implemented with the help of Genetic Algoithm. Numeous compute simulations show good algoithm convegence and acceptable accuac in estimation of both taget location and its magnetic moment. Kewods: agnetomete, agnetic Anomal Detection, Othonomal asis, Genetic Algoithm Intoduction The necessit to detect hidden feomagnetic obects (e.g. mines, undewate wecks, and sunken ships etc has led to seveal detection techniques, one of which is the agnetic Anomal Detection (AD. The pinciple of the AD is based on the abilit to sense the anomal in Eath magnetic field poduced b the taget. [-] Thee ae two basic tpes of AD: seach and alam sstems. In the fist case, magnetic sensos ae installed on the moving platfom seaching fo hidden feomagnetic taget b suveing specific aea along pedefined paths (usuall staight lines. Taget pesence is evealed as a spatial magnetic anomal along the suve line passing in the vicinit of the taget. AD of alam tpe makes use of stationa instuments poducing an alam signal when feomagnetic taget passes neab the magnetic senso. We assume the distance between the taget and the senso noticeabl eceeding taget dimensions so that taget magnetic field is descibed b dipole model. AD signal is time-depending magnetic field caused b mutual motion of magnetic dipole and the senso. Theefoe, ou appoach to signal pocessing is equall applicable fo both tpes of AD sstems. agnetometes of vaious tpes ae widel used fo detection and chaacteiation of hidden feomagnetic obects b analing small Eath s magnetic field anomalies. The basic poblem, which aises when measuing weak magnetic field anomalies, is a poblem of small signal detection and estimation of taget paametes in the pesence of noise and intefeence. In the pesent wok we anale diffeent signal pocessing methods fo AD based on vecto magnetic sensos. Ou investigation coves two basic tpes of such sensos, whee the fist one (e.g. flugate povides a diect eading of a field component and the second one (seach coil in low-fequenc mode esponds to time-deivative of magnetic field. Pesentation of field component signals with the aid of othonomal functions Let magnetic dipole whose moment components ae, and be located at the oigin of the, Y, Z coodinate sstem. The line of the senso platfom movement is paallel to the ais. Each of thee mutuall othogonal component sensos is aligned in paallel to one of the coodinate aes (ig.. Z Line of sensos movement s Sensos (,s,h R igue. Relative position of the magnetic dipole and the sensos. The distance between the line of the senso movement and the Z ais is s, and the distance between this line and the Y plane is h. R is the distance between the dipole and the line of the senso movement. It is the so-called CPA (closest poimit appoach distance, R = s + h. ( The magnetic field geneated b a point dipole with a moment at some distance R fom the dipole is µ = [R ( R R- ] π ( whee µ о = π* -7 H/m is the pemeabilit of fee space. R h Y 56
st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand Equation ( can be ewitten in mati fom (see, fo instance, [] µ = π R 5 R and afte nomaliing R R ( w = / R m = /, m = /, m = /, = + + a = s / R a = h / R a = s / a = sh / R a 5 = h / R Equation ( takes the fom: R ( (5 (6 µ = πr a a a a a a a m m a m 5 (7.5 = ( + w.5 = w( + w 8 π.5 = ( + w.5 = ( + w.5 = w ( + w ] 8.5 5.5 = [( + w ( + w ] 5π 6 ( 8.5 = w( + w 5π satisfing the usual othonomaliation conditions: i = fo i, and i, =,,. ( =..5. -.5 whee unctions (w, (w and (w ae lineal independent, while (w can be ecluded basing on = ( w ( w (w (w (w -. - - (8 (9 Appling Gam-Schmidt othonomaliation pocedue [5] we get tiplet of mutuall othogonal. functions (w, (w, and (w The othonomal functions (w, (w, and (w ae shown in ig. w igue. The set of othonomal functions: (w, (w, and (w fo pesentation of field component signals. The field components (7 as a function of senso platfom movement can now be epessed as a linea combination of basis functions i (w = A A = i i i=,, ; =,, ( It is impotant to undeline that (, ae coect not onl fo an dipole position and oientation but fo an diection of senso platfom and its oientation as well. This gives us an oppotunit to implement a unified algoithm fo pocessing of AD signal as it will be shown below. It is woth to note that basic functions ( coincide with the same functions which can be emploed fo the case of AD based on scala magnetomete [6, 7]. S d, = K dt d,, = K d d dt,,, = K V R d,, ( whee A is mati which coefficients depend on a paticula dipole position and oientation and can be obtained in the following wa: Pesentation of time deivatives of field component with the aid of othonomal functions Seach-coil magnetometes ae widel used fo component measuements in AD sstems. o diect mode of opeation the output signal of seachcoil magnetomete is popotional to the ambient field. o that case all esults of pevious section ae applicable. The diect mode of opeation is usuall a esult of elativel lage self capacitance of the coil windings, and/o electonics coection measues. Howeve, in the lowe pat of opeation fequenc band seach coil senso opeates in deivative mode [8]. In this case senso signals S,, can be witten as ( 56
st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand whee K is coefficient depending on pemeabilit of seach-coil coe, numbe of tuns, and coil geomet, while V is the velocit of the senso platfom. Implementing mathematical tansfomations like in pevious section it is eas to show that signals of seach-coil magnetometes ( can be pesented b linea combination of fou functions.5 ψ = w( + w,.5.5 ψ = w( + w, ψ = ( + w,.5 ψ = w ( + w (5.5..5. -.5 ν (w ν (w ν (w ν (w -. - - D Afte implementation of Gam-Schmidt pocedue we get quatet of mutuall othogonal. functions: v = ψ, v = ψ, 7π π 8 v = ( ψ ψ, π 8 v = ( ψ ( w ψ. (6 π The othonomal functions v (w, v (w, v (w, and v (w ae shown in ig. ig.. The set of othonomal functions: v (w, v (w, v (w, and v (w fo pesentation of time deivatives of field component signals. Now the vecto of time deivatives d/=(d /, d /, d / can be witten in mati fom as d d d = ( w i i w ν ( w ν = D ν ( w ( w ν ( w (7 whee D is mati which coefficients ae epessed simila to ( i=,,, =,, (8 Emploment of the othonomal functions fo enhancement of signal to noise atio Decomposition of the senso signal in the space of othonomal basis ( o (6 povides us with an effective wa fo enhancement of signal to noise atio. ollowing [6,7] we constuct a citeion function E fo pima detection algoithm as E = A + A + A E = D + D + D + D These epessions can be intepeted as the eneg of the signal in the space of chosen basis. Coefficients in (9, ae calculated as convolutions of the aw signal of the senso with appopiate basic functions fo each point w of the senso platfom tack. ~ A w = ( w + w ( w D i, ( i ~ i, ( w ν i ( w + w S =,, (9 fo the sensos which signals ae popotional to field components and =,, ( i=,, ; =,, ( = i=,,, =,, ( In pactice integation in (, is confined within finite obsevation window (integation limits which length is chosen basing on the epected value of CPA so to enable eal-time detection scheme. An eample of application of given algoithm fo taget detection is shown in ig.. Raw data acquied b Z- flugate (ig. a contain bell-shaped dipole signal (m =.7, m =.5, m =.8 with SNR equal to.. Data pocessing accoding to (9, (ig. b inceases SNR up to which is much bette than simple band-pass filteing (ig c. It is a consequence of the pinciple of algoithm (9 - which is based on pio guess of magnetic dipole stuctue of the taget signal. 5 Poblem of taget localiation and estimation of its magnetic moment Afoementioned algoithm povides effective tool fo taget detection. Howeve, it does not pemit acceptable estimation of the taget location and its magnetic moment. Aiming to advance the subect of taget paametes estimation we have poposed and analed application of Genetic Algoithm (GA. To stat with it, let us fist note that in pactice magnetic measuements ae pefomed in a sequentiall discete manne while the magnetomete moves along the tack. taking N samples of the measued magnetic field (, (,... ( N we get a nonlinea ovedetemined set of equations (fo lage enough N, 56
a b c st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand - ( - ig.. Illustation of the data pocessing algoithm: a aw signal sensed b the Z-flugate, b eneg calculated accoding to (9,, c The aw signal afte a band pass filte ( = ( m, ( = ( m, +... ( ( N = ( m, + N We aim to solve equation ( fo m and, which ae the taget magnetic moment, and the vecto fom the taget to the fist sample point espectivel. The displacements,... N ae the vectos fom the position of the fist sample to the position of samples,,...,n espectivel. These displacements can be measued pecisel using advanced navigation sstems and theefoe ae consideed as known. Solving equation ( analticall is not tivial especiall in the pesence of noise. That is wh we have divided the poblem domain into cells of pedetemined esolution. Each of the vectos m and, consists of thee Catesian components, Hence, one can define a single si element solution vecto, = ( m, = ( m, m, m,,, T ( o each component of m and thee should be set a ange accoding to pactical consideations concening taget possible location and magnetic dipole ange. Then, fo each component of m and thee should be defined a esolution accoding to the needed accuac. A shot eample illustates the pocess. Conside a seach fo a taget, whose magnetic moment anges fom - Am to+ Am. The needed accuac fo estimating the taget magnetic field is. Am. Assume that the seach takes place in a cube with a side length of m, and we would like to localie taget with accuac of cm. o each element of the solution vecto, w thee ae possibilities, esulting in a finite solution space of a total 6 possible solutions, fom which we have to choose the neaest to actual one. As we see the poblem becomes that of seaching the (sub optimal solution out of a finite solution space instead of solving equation ( analticall. The limited ange of possible solutions and the esticted esolution esult in sub optimal solutions athe than optimal, that is, howeve, acceptable fo man applications. Checking all possible solutions one b one would consume enomous time, which is not available in eal time sstems. o this eason we popose the Genetic Algoithm as a apid seach method. 6 Application of Genetic Algoithm fo taget localiation and estimation of its magnetic moment Genetic algoithms povide an effective wa to solve poblems such as taveling salesman (the shotest oute to visit a list of cities [9]. In this wok we focus on GA as a seach method to find the maimum of an obect function, also called fitness function. The GA mimics the evolutiona pinciple b emploing thee main opeatos: selection, cossove, and mutation. As a fist step we build a chomosome, which has the genotpe of the desied solution. In the case of localiation of a magnetic dipole, the chomosome has the fom of (. Each element of the chomosome is called gene and ma take onl esticted values that wee defined peviousl b ange and esolution as is eplained in the fome eample. Implementing the evolutiona pinciple obligates a collection of L chomosomes, which is entitled as population. At fist, andom values ae set fo each chomosome of the population. A fitness value is calculated fo each chomosome b substituting fo the chomosome into the fitness function. The chomosomes can be aanged in a list fom the fittest chomosome (with the lagest fitness esult to the least fit one. Then the selection opeato is applied, selecting onl the K fittest chomosomes fom the list. Thee ae seveal was to pefom the selection, which would not be descibed hee. Afte selection, the cossove opeato is utilied esembling a natual beeding action. Onl the K fittest chomosomes of the list ae allowed to beed amongst themselves b the following mathematical opeation, new = λ i + ( λ (5, ae andoml chosen fom the Chomosomes i list of the K fittest chomosomes. λ is a cossove paamete (usuall.5, and is a newbon chomosome. The pocess is epeated until a population of K newbon chomosomes is eached. Aftewad mutation opeato is implemented b andoml selecting a chomosome fom the newbon population, and changing a andom gene to a andom new 56
st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand pemitted value. The andomness popet enables the GA to ovecome local minima. Afte mutation is applied, fitness evaluation is pefomed on the mutated newbon population. The pocess of fitness evaluation-selection-cossove- mutation is epeated fo a pedetemined numbe of geneations o until the fittest chomosome eaches a pedefined fitness value. The convegence of the GA is epessed b incease in the aveage fitness of the population fom geneation to geneation. The chomosome with the lagest fitness value is chosen as the solution, accoding to suvival of the fittest pinciple. Defining an appopiate fitness function is an impotant step in utiliing GA. We have poposed the following fitness function fo magnetic dipole localiation b a -ais magnetomete (without consideing noise chaacteistics: fitness( = N n= ( n + ( n + [ ( n ] + [ ( n ] ( + [ n ( n ] (6 whee,, (n epesents the n-th measuement sample while,, is calculated magnetic field poduced b chomosome. Note that the fittest chomosome fitness value is closest to eo. In ode to investigate magnetic dipole localiation b Genetic Algoithm, we pefomed numeous compute simulations. To illustate some of simulation esults we have chosen magnetic dipole with =.7 A m, =.5 A m, =.8 A m located at the oigin of coodinate sstem (,,. The samples wee taken eve. m fom - 7.m to +7.m along the -ais (south-noth at a constant -ais coodinate of s=6.7 m (see ig. and a constant height h=. m. This esults in a CPA distance of R = 7 m. Random noise was added to the magnetic dipole signal to ensue SNR of. (ig. a. The GA was set to a population of chomosomes and a stop condition of, geneations. The mutation pobabilit was set to 5% and the cossove pobabilit to %. Statistical pocessing of the simulation esults afte eecutions leads to the following esults. oment estimation Total magnetic moment of the taget dipole is A m. Estimated magnetic moment aveaged ove eecutions of GA algoithm was. A m elative biased estimate value of %. Statistical distibution of the obtained moment values is shown in ig. 5. Taget localiation Estimated taget location aveaged ove eecutions of GA algoithm was (-.6m, -.5m,.7m so that absolute biased estimate length was.5m which makes up less than% eo elative to CPA distance. Spatial distibution of the obtained taget locations is shown in ig. 6. 7 Conclusion In the pesent wok we have investigated two appoaches to the data pocessing of the AD signals. ig. 5 Distibution of magnetic moments obtained as a esult of GA algoithm eecutions. Tack of the sensos platfom ig. 6 Spatial distibution of taget locations obtained as a esult of GA algoithm eecutions. Ou fist appoach to AD signal pocessing elies on the decomposition of the AD signal in the space of speciall constucted othonomalied functions. It tuns out that the signals of flugate senso can be 565
st Intenational Confeence on Sensing Technolog Novembe -, 5 Palmeston Noth, New Zealand pesented as a linea combination of thee othonomal functions while the seach coil signals need fou othonomal functions fo coect epesentation. The dipole eneg signal is intoduced in the basis chosen and is found to be a useful function fo the data pocessing algoithm based upon the esults of the modeling. It is impotant to undeline that this method woks equall well fo vaious oientations of taget moment elative to etenal Eath s magnetic field and diection of suve line. The afoementioned pocessing pocedue povides a consideable impovement of the SNR thus enabling eliable taget detection even with low values of SNR. To poceed with taget paametes estimation we poposed and tested anothe appoach to AD signal pocessing based on Genetic Algoithm. Tpical paametes of GA included: population of chomosomes; stop condition of, geneations; mutation pobabilit 5%; cossove pobabilit %. Statistical pocessing of the simulation esults afte eecutions shows good algoithm convegence and acceptable (<% elative eos of main taget paametes estimation even with athe low signal-tonoise atio in aw magnetomete signal. 8 Refeences fequenc thee-ais seach coil magnetomete fo []. Hiota, T. uuse, K. Ebana, H. Kubo, K. space eseach", Review of Sci. Inst., 76, Tsushima, T. Inaba, A. Shima,. uinuma pp 5- - 5- (5 and N. Too, agnetic detection of a suface ship b an aibone LTS SQUID AD, IEEE Tans. Appl. Supecond. pp 88-887 ( p.56 [] W.. Winn, in: C. E. aum (Ed., Detection and Identification of Visuall Obscued Tagets, Talo and ancis, Philadelphia, PA, (999, Chapte, pp 7-76. [] H. Zafi, N. Salomonski, Y. egman,. Ginbug, Z. Zalevsk,. aam, aine magnetic sstem fo high esolution and eal time detection and mapping of feous submeged UO, sunken vessels, and aicaft, in: Poc. UO/Countemine oum, New Oleans, LA, 9- Apil. [] R..Semevsk, V. V. Avekiev, V. V. Yaotsk, Special agnetomet, Nauka, St.-Petesbug, (, pp.8, (in Russian [5] G.A. Kon, T.. Kon, athematical Handbook fo Scientists and Enginees, cgaw Hill, New Yok, nd ed., (968, p. 9. [6] Y. D. Dolinsk, Vlianie osobennostei signala na stuktuu optimalnogo piemnika pi obnauhenii namagnichennkh tel, Geofiicheskaa Appaatua, 97 pp 9-8 (99 (in Russian. [7]. Ginbug, L. umkis and.z. Kaplan, Pocessing of magnetic scala magnetomete signals using othonomal functions, Sens. Actuatos A, pp 67-75 (. [8] H. C. Sean, P. egeau, "An optimied low- [9]. O. Kaa, C. DeSilva Soft Computing and Intelligent Sstems Design Theo, Tools and Applications, Addison Wesle, England, (, 566