INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS

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1 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS. Ginburg (, L. Frumkis (,.Z. Kaplan (, A. Sheinker (,, N. Salomonski ( ( Soreq NRC, Yavne, 88, Israel, [email protected] ( en-gurion Universit of the Negev, P.O. o 65, eer-sheva, 85, Israel Abstract - Advanced methods of data processing in magnetic anomal detection (MAD sstems are investigated. Raw signals of MAD based on component magnetic sensors are transformed into energ signals in the space of speciall constructed orthonormalied functions. This procedure provides a considerable improvement of the SNR thus enabling reliable target detection. Estimation of the target parameters is implemented with the help of Genetic Algorithm. Numerous computer simulations show good algorithm convergence and acceptable accurac in estimation of both target location and its magnetic moment. Inde terms: Magnetometer, Magnetic Anomal Detection, Orthonormal basis, Genetic algorithm I. INTRODUCTION The necessit to detect hidden ferromagnetic subects (e.g. mines, underwater wrecks, and sunken ships etc has led to several detection techniques, one of which is the Magnetic Anomal Detection (MAD. The principle of the MAD is based on the abilit to sense the anomal in Earth magnetic field produced b the target. [-] There are two basic tpes of MAD: search and alarm sstems. In the first case, magnetic sensors are installed on the moving platform searching for hidden ferromagnetic target b surveing specific area along predefined paths (usuall straight lines. Target presence is revealed as a spatial magnetic anomal along the surve line passing in the vicinit of the target. MAD of alarm tpe makes use of stationar instruments producing an alarm signal when ferromagnetic target passes nearb the magnetic sensor. We assume the distance between the target and the sensor noticeabl eceeding target dimensions so that target magnetic field is described b dipole model. MAD signal is time-depending magnetic field

2 . GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS caused b mutual motion of magnetic dipole and the sensor. Therefore, our approach to signal processing is equall applicable for both tpes of MAD sstems. Magnetometers of various tpes are widel used for detection and characteriation of hidden ferromagnetic obects b analing small Earth s magnetic field anomalies. The basic problem, which arises when measuring weak magnetic field anomalies, is a problem of small signal detection and estimation of target parameters in the presence of noise and interference. In the present work we anale different signal processing methods for MAD based on vector magnetic sensors. Our investigation covers two basic tpes of such sensors, where the first one (e.g. flugate provides a direct reading of a field component and the second one (search coil in low-frequenc mode responds to time-derivative of magnetic field. II. PRESENTATION OF FIELD COMPONENT SIGNALS WITH THE AID OF ORTHONORMAL FUNCTIONS Let magnetic dipole whose moment components are M, M and M is located at the origin of the X, Y, Z coordinate sstem. The line of the sensor platform movement is parallel to the X ais. Each of three mutuall orthogonal component sensors is aligned in parallel to one of the coordinate aes (Fig.. Line of sensors movement Z s Sensors A(,s,h R M R M h Y X M M Figure. Relative position of the magnetic dipole M and the sensors. The distance between the line of the sensor movement and the Z ais is s, and the distance between this line and the XY plane is h. R is the distance between the dipole and the line of the sensor movement. It is the so-called CPA (closest proimit approach distance, R = s + h (

3 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 The magnetic field generated b a point dipole with a moment M at some distance R from the dipole is μ = R π [R ( M R R- M] where μ = π -7 H/m is the permeabilit of free space. Equation ( can be rewritten in matri form (see, for instance, [] ( R = μ R 5 πr R M M M ( and after normaliing, w = / R m = M / M, m M / M, = M = M + M + M m = M / M, ( (5 a = s / R h / R a = a = s R / a = R a = h R sh / 5 / (6 Equation ( takes the form: μ M = πr ϕ ϕ a ϕ a ϕ a ϕ a ϕ ϕ a ϕ a ϕ a ϕ m m a ϕ ϕ m 5 (7 where. 5 = ( + w. 5 ϕ ϕ = ( + w.5 ϕ = w( + w.5 ϕ = w ( + w (8 Functions ϕ (w, ϕ (w and ϕ (w are linearl independent, while ϕ (w can be ecluded basing on ϕ = ϕ( w ϕ( w (9

4 GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS Appling Gram-Schmidt orthonormaliation procedure [5] we get triplet of mutuall orthogonal functions F (w, F (w, and F (w: F ( 8 π.5 w = ( + w F = [( + w ( + w 5π 6 8 F 5π satisfing usual orthonormaliation conditions: + F F dw =.5 = w( + w + ( i for F w dw = ].5 ( i, and, i, =,,. ( The orthonormal functions F (w, F (w, and F (w are shown in Fig. w -.5 F (w..5 F (w F (w. Figure.The set of orthonormal functions: F (w, F (w, and F (w for presentation of field component signals. The field components (7 as a function of sensor platform movement can now be epressed as a linear combination of basis functions F i (w = A F F F (

5 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 where A is matri which coefficients depend on a particular dipole position and orientation and ma be obtained in the following wa: A = Fi ( w dw i=,, ; =,, ( i It is important to underline that (, keep true not onl for an dipole position and orientation but for an direction of sensor platform and its orientation as well. This enables us with an opportunit to implement unified algorithm for processing of MAD signal as it would be shown below. It is worth to note that basic functions ( coincide with the same functions which can be emploed for the case of MAD based on scalar magnetometer [6, 7]. III. PRESENTATION OF TIME DERIVATIVES OF FIELD COMPONENT WITH THE AID OF ORTHONORMAL FUNCTIONS Search-coil magnetometers are widel used for component measurements in MAD sstems. For direct mode of operation the output signal of search-coil magnetometer is proportional to the ambient field. For that case all results of previous section are applicable. The direct mode of operation is usuall a result of relativel large self capacitance of the coil windings, and/or electronics correction measures. However, in the lower part of operation frequenc band search coil sensor operates in derivative mode [8]. In this case sensor signals S,, can be written as ( S d, = K dt d, = K dw dw d d dt,,,, = K V R d,, dw where K is coefficient depending on permeabilit of search-coil core, number of turns, and coil geometr, while V is the velocit of the sensor platform. Implementing mathematical transformations like in previous section it is eas to show that signals of search-coil magnetometers ( can be presented b linear combination of four functions.5.5 ψ, ψ = w( + w, ψ = ( + w,.5 = w( + w ψ.5 = w ( + w (5

6 . GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS After implementation of Gram-Schmidt procedure we get quartet of mutuall orthogonal functions: v = ψ, v ( ( 7π w = ψ w, π v 8 8 w = ( ψ ( w ψ (, v = ( ψ ( w ψ. (6 π π ( w The orthonormal functions v (w, v (w, v (w, and v (w are shown in Fig..5 ν (w. ν (w ν (w.5 ν (w w Figure. The set of orthonormal functions: v (w, v (w, v (w, and v (w for presentation of time derivatives of field component signals. Now the vector of time derivatives d/dw=(d/dw, d /dw, d /dwcan be written in matri form as d d dw d dw dw ν ν = D ν ν (7 where D is matri which coefficients are epressed similar to ( D i Fi w = ( dw i=,,, =,, (8 5

7 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 IV. EMPLOYMENT OF THE ORTHONORMAL FUNCTIONS FOR ENHANCEMENT OF SIGNAL TO NOISE RATIO Decomposition of the sensor signal in the space of orthonormal basis ( or (6 provides us with an effective wa for enhancement of signal to noise ratio. Following [6,7] we construct a criterion function E for primar detection algorithm as E = A + A + A =,, (9 for the sensors which signals are proportional to field components and E = D + D + D + D =,, ( These epressions can be interpreted as the energ of the signal in the space of chosen basis. Coefficients in (9, are calculated as convolutions of the raw signal of the sensor with appropriate basic functions for each point w of the sensor platform track. A D + ~ i, ( w Fi ( w + w + ~ i, ( w ν i ( w + w S = dw = dw i=,, ; =,, ( i=,,, ; =,, ( In practice integration in (, is confined within finite observation window (integration limits which length is chosen basing on the epected value of CPA so to enable real-time detection scheme. An eample of application of given algorithm for target detection is shown in Fig.. Raw data acquired b Z-flugate (Fig. a contain bell-shaped dipole signal ( =.7, m =.5, =. 8 with SNR equal to.. Data processing according to (9, (Fig. m b increases SNR up to which is much better than simple band-pass filtering (Fig c. It is a consequence of the principle of algorithm (9 - which is based on prior guess of magnetic dipole structure of the target signal. m 6

8 . GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS a b c - ( - w Figure. Illustration of the data processing algorithm: a raw signal sensed b the Z-flugate, b energ calculated according to (9,, c The raw signal after a band pass filter V. PROLEM OF TARGET LOCALIZATION AND ESTIMATION OF ITS MAGNETIC MOMENT Aforementioned algorithm provides effective tool for target detection. However, it does not permit acceptable estimation of the target location and its magnetic moment. Aiming to advance the subect of target parameters estimation we have proposed and analed application of Genetic Algorithm (GA. To start with, it let us first note that in practice magnetic measurements are performed in a sequentiall discrete manner while the magnetometer moves along the track. taking N samples of the measured magnetic field (, (,..,(N and using equation ( we get a nonlinear over-determined set of equations (for large enough N, ( = ( M, R ( = ( M, R + ΔR... ( ( N = ( M, R + ΔR N We aim to solve equation ( for M and R, which are the target magnetic moment, and the vector from the target to the first sample point respectivel. The displacements ΔR, ΔR,, ΔR N are the vectors from the position of the first sample to the position of samples,,,n 7

9 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 respectivel. These displacements can be measured precisel using advanced navigation sstems and therefore are considered as known. Solving equation ( analticall is not trivial especiall in the presence of noise. That is wh we have divided the problem domain is into cells of predetermined resolution. Each of the vectors M and R, consists of three Cartesian components, hence, one can define a single si element solution vector, X = ( M, R = ( M, M, M, R, R, R T ( For each component of M and R there should be set a range according to practical considerations concerning target possible location and magnetic dipole range. Then, for each component of M and R there should be defined a resolution according to the needed accurac. A short eample illustrates the process. Consider a search for a target, whose magnetic moment ranges from - Am to+ Am. The needed accurac for estimating the target magnetic field is. Am. Assume that the search takes place in a cube with a side length of m, and we would like to localie target with accurac of cm. For each element of the solution vector X, there are possibilities, resulting in a finite solution space of a total 6 possible solutions, from which we have to choose the nearest to actual one. As we see the problem becomes that of searching the (sub optimal solution out of a finite solution space instead of solving equation ( analticall. The limited range of possible solutions and the restricted resolution result in sub optimal solutions rather than optimal, that is, however, acceptable for man applications. Checking all possible solutions one b one would consume enormous time, which is not available in real time sstems. For this reason we propose the Genetic Algorithm as a rapid search method. VI. APPLICATION OF GENETIC ALGORITHM FOR TARGET LOCALIZATION AND ESTIMATION OF ITS MAGNETIC MOMENT Genetic algorithms provide an effective wa to solve problems such as traveling salesman (the shortest route to visit a list of cities [9]. In this work we focus on GA as a search method to find the maimum of an obect function, also called fitness function. The GA mimics the evolutionar principle b emploing three main operators: selection, crossover, and mutation. 8

10 . GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS As a first step we build a chromosome, which has the genotpe of the desired solution. In the case of localiation of a magnetic dipole the chromosome has the form of (. Each element of the chromosome is called gene and ma take onl restricted values that were defined previousl b range and resolution as is eplained in the former eample. Implementing the evolutionar principle obligates a collection of L chromosomes, which is entitled as population. At first, random values are set for each chromosome of the population. A fitness value is calculated for each chromosome b substituting for the chromosome into the fitness function. The chromosomes can be arranged in a list from the fittest chromosome (with the largest fitness result to the least fit one. Then the selection operator is applied, selecting onl the K fittest chromosomes from the list. There are several was to perform the selection, which would not be described here. After selection, the crossover operator is utilied resembling a natural breeding action. Onl the K fittest chromosomes of the list are allowed to breed amongst themselves b the following mathematical operation, X = λx + ( λ X new i Chromosomes X i, X are randoml chosen from the list of the K fittest chromosomes. λ is a crossover parameter (usuall.5, and X new is a newborn chromosome. The process is repeated until a population of K newborn chromosomes is reached. Afterward mutation operator is implemented b randoml selecting a chromosome from the newborn population, and changing a random gene to a random permitted value. The randomness propert enables the GA to overcome local minima. After mutation is applied, fitness evaluation is performed on the mutated newborn population. The process of fitness evaluation-selection-crossovermutation is repeated for a predetermined number of generations or until the fittest chromosome reaches a predefined fitness value. The convergence of the GA is epressed b increase in the average fitness of the population from generation to generation. The chromosome with the largest fitness value is chosen as the solution, according to survival of the fittest principle. Defining an appropriate fitness function is an important step in utiliing GA. We have proposed the following fitness function for magnetic dipole localiation b a - ais magnetometer (without considering noise characteristics: ( n ( X N Fitness (X = (6 n= ( n (5 9

11 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 where (n represents the n-th measurement sample while (X is the calculated magnetic field produced b chromosome X. Note that the fittest chromosome fitness value is closest to ero. In order to investigate magnetic dipole localiation b Genetic Algorithm, we performed numerous computer simulations. To illustrate here some of simulation results we have chosen magnetic dipole with M =.7 A m, M =.5 A m, M =.8 A m located at the origin of coordinate sstem (,,. The samples were taken ever. m from -7.m to +7.m along the -ais (south-north at a constant -ais coordinate of 6.7 m (see Fig. and a constant height of. m. so that a CPA distance R is of about 7 m. Random noise was added to the magnetic dipole signal to ensure SNR value of. (Fig. a.the GA was set to a population of chromosomes and a stop condition of, generations. The mutation probabilit was set to 5% and the crossover probabilit to %. Statistical processing of the simulation results after eecutions leads to the following results. a. Moment estimation Total magnetic moment of the target dipole is A m. Estimated magnetic moment averaged over eecutions of GA algorithm was. A m relative biased estimate value of %. Statistical distribution of the obtained moment values is shown in Fig. 5. Figure 5. Distribution of magnetic moments obtained as a result of GA eecutions. b. Target localiation Estimated target location averaged over eecutions of GA algorithm was (-.6m, -.5m,.7m so that absolute biased estimate length was.5m which makes up less than

12 . GINZURG ET., AL., INVESTIGATION OF ADVANCED DATA PROCESSING TECHNIQUE IN MAGNETIC ANOMALY DETECTION SYSTEMS % error relative to CPA distance. Spatial distribution of the obtained target locations is shown in Fig. 6. Track of the sensors platform Figure 6. Spatial distribution of target locations obtained as a result of GA eecutions. VII. CONCLUSION In the present work we have investigated two approaches to the data processing of the MAD signals. Our first approach to MAD signal processing relies on the decomposition of the MAD signal in the space of speciall constructed orthonormalied functions. It turns out the signals of flugate sensor tpe can be presented as a linear combination of three orthonormal functions while the search coil signals need four orthonormal functions for correct representation. The dipole energ signal is introduced in the basis chosen and is found to be a useful function for the data processing algorithm based upon the results of the modeling. It is important to underline this method works equall well for various orientations of target moment relative to eternal Earth s magnetic field and direction of surve line. The aforementioned processing procedure provides a considerable improvement of the SNR thus enabling reliable target detection even with low values of SNR. To proceed with target parameters estimation we proposed and tested another approach to MAD signal processing based on Genetic Algorithm. Tpical parameters of GA included: population of chromosomes; stop condition of, generations; mutation probabilit 5%; crossover probabilit %. Statistical processing of the simulation results after eecutions shows good algorithm convergence and acceptable (<% relative errors of main target parameters estimation even with rather low signal-to-noise ratio in raw magnetometer

13 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL., NO., MARCH 8 signal. Further investigation addresses a comparison of the GA to other global optimiation methods such as the simulated annealing (SA for magnetic target localiation and magnetic moment estimation []. REFERENCES [] M. Hirota, T. Furuse, K. Ebana, H. Kubo, K. Tsushima, T. Inaba, A. Shima, M. Fuinuma and N. Too, Magnetic detection of a surface ship b an airborne LTS SQUID MAD, IEEE Trans. Appl. Supercond. ( [] W.M. Winn, in: C. E. aum (Ed., Detection and Identification of Visuall Obscured Targets, Talor and Francis, Philadelphia, PA, 999, Chapter, [] H. Zafrir, N. Salomonski, Y. regman,. Ginburg, Z. Zalevsk, M. aram, Marine magnetic sstem for high resolution and real time detection and mapping of ferrous submerged UXO, sunken vessels, and aircraft, in: Proc. UXO/Countermine Forum, New Orleans, LA, 9- April. [] R..Semevsk, V. V. Averkiev, V. V. Yarotsk, Special Magnetometr,, Nauka, pp.8, St.-Petersburg, (in Russian [5] G.A. Korn and T.M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw Hill, New York, second ed., 968, p. 9. [6] Y. D. Dolinsk, Vlianie osobennostei signala na strukturu optimalnogo priemnika pri obnaruhenii namagnichennkh tel, Geofiicheskaa Apparatura, 97 ( (in Russian. [7]. Ginburg, L. Frumkis and.z. Kaplan, Processing of magnetic scalar magnetometer signals using orthonormal functions, Sens. Actuators A ( [8] H. C. Seran, P. Fergeau, "An optimied low-frequenc three-ais search coil magnetometer for space research", Review of Sci. Instr., 76, pp 5-5- (5. [9] F. O. Karra, C. DeSilva Soft Computing and Intelligent Sstems Design Theor, Tools and Applications, Addison Wesle, England, (. [] A. Sheinker,. Lerner, N. Salomonski,. Ginburg, L. Frumkis and.-z. Kaplan, Localiation and magnetic moment estimation of a ferromagnetic target b simulated annealing, Measurement Science and Technolog, Vol. 8, pp 5-57, (7.