IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 4, APRIL 2012
1095
Magnetic Anomaly Detection Using High-Order Crossing Method Arie Sheinker, Member, IEEE, Boris Ginzburg, Nizan Salomonski, Member, IEEE, Phineas A. Dickstein, Lev Frumkis, and Ben-Zion Kaplan, Life Senior Member, IEEE
Abstract—Magnetic anomaly detection (MAD) is a passive method used to detect visually obscured ferromagnetic objects by revealing the anomalies in the ambient Earth magnetic field. In this paper, we propose a method for MAD employing the high-order crossing (HOC) approach, which relies on the magnetic background nature. HOC is an alternative method for spectral analysis using zero-crossing count, also enabling signal discrimination. Tests with real-world recorded magnetic signals show high detection probability even for low signal-to-noise ratio. The high detection probability, together with a simple implementation and low power consumption, makes the HOC method attractive for real-time MAD applications such as intruder detection and for research on an earthquake magnetic precursor. Index Terms—Adaptive filtering, high-order crossing (HOC), magnetic anomaly detection (MAD), remote sensing.
I. I NTRODUCTION
D
ETECTION of a needle in a haystack is quite an ancient problem. It became a figure of speech, referring to something that is difficult to locate in a much larger space, usually filled with clutter. There are many types of sensors which exploit various physical phenomena such as light and acoustics that can be applied in order to find the needle. In fact, employing a magnetic sensor seems as one of the most effective tools for detection of a steel needle. A ferromagnetic object such as a which, far enough steel needle generates a magnetic field B from the object, can be considered as a magnetic dipole field µ0 −5 m, 3(m · r)r − m| r |2 . (1) |r| B( r) = 4π Here, m is the object magnetic moment, and r is the vector from the object to the measurement point. In this paper, we focus on field measurements where the field generated by the object is in superposition with the Earth magnetic field. For remote sensing applications, where the object magnetic field is much smaller than the Earth magnetic field, the generated field is considered as an anomaly in the ambient Earth magnetic Manuscript received October 11, 2010; revised April 28, 2011; accepted July 31, 2011. Date of publication September 15, 2011; date of current version March 28, 2012. A. Sheinker, B. Ginzburg, and N. Salomonski are with SOREQ Nuclear Research Center, Yavne 81800, Israel (e-mail:
[email protected];
[email protected];
[email protected]). P. A. Dickstein is with SOREQ Nuclear Research Center, Yavne 81800, Israel, and also with the Israel Atomic Energy Commission, Tel Aviv 61070, Israel (e-mail:
[email protected]). L. Frumkis and B.-Z. Kaplan are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/TGRS.2011.2164086
field. From (1), it is seen that the magnetic field decreases with the cube of the distance, which may result in a limited detection range. In the case of low signal-to-noise ratio (SNR), magnetic anomaly detection (MAD) methods are adopted in order to reveal the anomaly buried in the magnetic background. MAD approach benefits from the fact that air, water, foliage, and many sorts of soils are practically transparent to static magnetic field. Moreover, MAD systems have the advantage of not being directly influenced by bad weather or bad vision conditions. Since animals do not usually carry any ferromagnetic materials, they do not produce magnetic anomalies. Hence, intruder detection systems based on MAD do not suffer from false alarms caused by animals. On the other hand, human intruders usually carry objects that may include ferromagnetic materials, such as cellular phones, keys, coins, and belt buckles, just to mention a few. In particular, weapons are made of steel, which can be detected using MAD, even when concealed. These are significant advantages of intruder detection systems based on MAD over other intruder detection systems. Another important advantage is that MAD is a passive technique, allowing the searcher to stay unexposed. Traditional military applications of MAD include airborne magnetometers for antisubmarine warfare [2], and vehicle tracking [3]. Recent developments in sensor technology and real-time data processing have led to scope expansion, including today’s “Green” attitude applications such as mine detection and unexploded ordnance disposal [4]–[7], mapping of contaminated sediment distribution [8], survey for and solid buried waste [9], just to mention a few. Attempts to predict earthquakes by sensing changes in the Earth magnetic field [10] seem as one of the challenging objectives in the near future. We divide MAD methods into two major categories. One category includes methods, such as the orthonormal basis function (OBF) decomposition method, that are based on analyzing target signal typical patterns [11]. Those methods are found to be very effective, although in order to work optimally, they require several assumptions regarding the target. The second category includes methods such as the minimum entropy detector (MED) that reveals changes in the magnetic background nature [12], assuming that the changes are caused by the presence of a ferromagnetic target. Detectors such as MED are adaptive to the magnetic background, and since the magnetic background is not generally a stationary process, they should adapt periodically. The adaptive methods benefit from the fact that no a priori assumptions regarding the target are required, which may result in a simpler implementation, leading to reduced power consumption. In many cases, the adaptive methods can be used to trigger a more profound inquiry, which
0196-2892/$26.00 © 2011 IEEE
1096
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 4, APRIL 2012
Fig. 1. Typical recorded magnetic background at Amram Geophysical Observatory using a SUPERGRAD total-field magnetometer with a sampling rate of 20 samples/s.
may include algorithms for target localization and magnetic moment estimation [13]. In this paper, we propose an adaptive MAD method based on employing the high-order crossing (HOC) approach [14]. HOC is an alternative method for spectral analysis based on zero-crossing counts. The HOC approach was applied successfully to discriminate between signals, such as in the case of nondestructive testing [15], and the identification of changes in the entropy of seismic signals [16]. Here, we exploit the fact that HOC counts in the presence of a magnetic target signal differ from HOC counts of the magnetic background. Using HOC counts enables the construction of an effective detection method. Obviously, this method relies on the nature of the magnetic background, making the a priori assumptions regarding the target unnecessary. Being a part of adaptive methods, the proposed method benefits from a simple implementation and low power consumption. In this paper, we have tested the proposed method with real-world data, showing high detection probability even at low SNR. The aforementioned advantages make the HOC method attractive for many real-time remote sensing applications. II. BACKGROUND A. Magnetic Background In order to construct an effective HOC detector, it is important to understand the role of the magnetic background. Fig. 1 shows a segment of a typical recording of the magnetic background, measured in a relatively quiet surrounding, with a sampling period Ts of 0.05 s. The measurement was taken in the Amram Geophysical Observatory, located in the vicinity of the Dead Sea rift. The observatory is equipped with instruments for earthquake research, including three total-field SUPERGRAD magnetometers, operating in the principle of optical pumping in potassium. The SUPERGRAD is a highly sensitive magnetometer system, designed for earthquake prediction research, √ featuring an intrinsic noise of about 0.05 pT/ Hz at a frequency of 1 Hz [17].
Fig. 2.
PSD of a typical recorded magnetic background after detrending.
Fig. 3. Normalized histogram of the recorded magnetic background after detrending resembles a pdf of a Gaussian distribution with zero mean and STD of about 0.016 nT.
Fig. 2 shows the power spectral density (PSD) of a typical recorded magnetic background after detrending, i.e., bias and trend removal. The magnetic background is mainly influenced by processes in ionosphere and magnetosphere, as well as other interferences. Fig. 3 shows the normalized histogram of the recordings after detrending. The normalized histogram resembles a probability density function (pdf) of a Gaussian distribution with zero mean and standard deviation (STD) of about σ = 0.016 nT. B. Magnetic Target Signal Model In this paper, we focus on the case of a static magnetometer sensing a moving ferromagnetic target. However, addressing the opposite scenario, where the target is static and the sensor moves, is quite similar. In order to model the target signal, we use several assumptions regarding the target. In contrast to the OBF detection method, where the assumptions are essential for detector construction, here, the assumptions are being made just for analyzing detector performance. We assume that the target
SHEINKER et al.: MAGNETIC ANOMALY DETECTION USING HIGH-ORDER CROSSING METHOD
Fig. 4. Magnetic target signal can be expressed as a linear combination of three OBFs.
moves along a straight line track with a constant velocity ν and that the target magnetic moment m is constant in magnitude and orientation. Under these assumptions, the target signal s(n) can be decomposed into a set of three OBFs gk (n), where k = 1, 2, 3 [11], [18]. Therefore, a linear combination of the OBFs with coefficients ck can be used for the discrete representation s(n) =
3
ck gk (n),
n = −0.5N + 1, . . . , 0.5N.
(2)
k=1
An observation window of N -sample length is used in (2) in order to construct the target signal. The window length affects the calculation of (2), in a way that a short window may loose much of the target signal energy, whereas too long a window tends to pick up extra noise. In many cases, a window length of about 3τ /Ts samples may be a good choice for OBF analysis, where τ is the characteristic time, defined by τ≡
CP A . ν
(3)
The closest proximity approach (CPA) is the shortest distance between the target and the sensor. The OBF is obtained by exploiting the aforementioned assumptions together with (1) and then performing the Gramm–Schmidt procedure [11] 24 1 − 53 (nTs /τ )2 g1 (n) = 5π [1 + (nTs /τ )2 ]2.5 128 nTs /τ g2 (n) = 5π [1 + (nTs /τ )2 ]2.5 (nTs /τ )2 128 g3 (n) = . (4) 3π [1 + (nTs /τ )2 ]2.5 The target position along the track relative to CPA can be expressed using a single dimensionless variable y, given by y = nTs /τ . Fig. 4 shows the OBF as a function of y. It is
1097
obvious from (4) that larger values of τ correspond to wider target signals. To explain the HOC method response to the target signal, let us analyze the spectral contents of the target signal. According to (2), the spectral contents of the OBF reflect the target signal spectrum. It turns out that most of the target signal energy is concentrated at low frequencies. Hence, we define the boundary frequency fc as the frequency where 95% of the signal energy is concentrated in the frequency band (0, fc ]. In practice, for many typical targets, the boundary frequency is less than 1 Hz. From (4), it is clear that larger values of τ result in a lower boundary frequency. Thus, keeping velocity constant, the farther the target, the wider is its temporal signal, and the lower is its boundary frequency. The target signal representation in (2) is helpful for detector construction. From (2), we learn that, under the aforementioned assumptions, any target signal contains the components in (4), and therefore, revealing the OBF leads to the detection of target presence. Notice that coefficients c1 , c2 , and c3 reflect the intensities of the OBFs g1 , g2 , and g3 , respectively. From (2), we see that correlating s(n) with g1 (n) yields c1 . In the same manner, correlating s(n) with g2 (n) and g3 (n) yields c2 and c3 , respectively. Hence, an OBF detector is constructed by correlating the measured signal inside a moving window with each OBF separately. Afterward, an energy index is calculated by the squared sum of the correlators outputs. Detection occurs whenever the energy index rises above a predetermined threshold. Although the target signal shape depends strongly on the direction of the target magnetic moment, it turns out that the energy index is stable for various magnetic moment orientations [11]. Therefore, from a practical point of view, relying on the energy index for detection is found to be very efficient for many applications, eliminating the need for a more complicated parallel detection schemes. Notice that the characteristic time is an argument of the OBF in (4). Since we do not know a priori the characteristic time, we can adopt a multichannel approach, where each channel is associated with a different characteristic time. Detection occurs whenever one or more channel outputs rise above the threshold. III. HOCs The HOC method is an advanced approach which can be used very effectively for spectrum analysis. Here, we present briefly the theory behind the method [14] and its application to MAD. A. HOCs From Differences Assume a sampled time series x(n), where n = 1, . . . , N . The clip operator outcome is one whenever the input is larger than zero; otherwise, the outcome is zero. Applying the clip operator to the series x(n) results in a clipped series q(n) defined by 1, x(n) > 0 q(n) = (5) 0, x(n) ≤ 0.
1098
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 4, APRIL 2012
A zero-crossing count is evaluated using D=
N
[q(n) − q(n − 1)]2 .
(6)
n=2
Obviously, D takes values between 0 and N − 1, and hence, the zero-crossing rate is defined by R≡
D . N −1
(7)
Now, we can extend the zero-crossing count to higher order zero crossings by introducing the difference operator defined by ∇x(n) ≡ x(n) − x(n − 1).
(8)
The difference operator of the kth order ∇k is obtained by differentiating the series x(n) for k times. Hence, in a recursive manner (9) ∇k x(n) = ∇ ∇k−1 x(n) . Notice that the length of x(n) is N samples, whereas the length of ∇1 x(n) is N − 1 samples, and the length of ∇k x(n) is N − k samples only. We denote by Dk the zero-crossing count for the series ∇k−1 x(n). Accordingly, we denote Rk as the zero-crossing rate of the series ∇k−1 x(n), expressed as Rk = Dk /(N − 1 − k).
Fig. 5. Estimated frequencies by HOC for the deterministic signal u(n) = 0.8 cos(0.1n + θ1 ) + 0.4 cos(0.5n + θ2 )+0.1 cos(0.7n + θ3 ) with random phases θ1 , θ2 , and θ3 .
of zero crossings yields D2 = 159, and thus, R2 = 0.1593. Estimating the frequency yields πR2 = 0.5005, which is a good estimate for 0.5, the second harmonic of (11). The estimation of the second harmonic works, since counting the second-order zero crossings is based on (9), which is a recursive form of (8). Notice that (8) is, in practice, a high-pass filter (HPF), with an impulse response of h(n) = {1, −1} and a transfer function given by
B. HOCs of a Deterministic Signal In many cases, HOC can be used as an alternative way for spectral analysis. It is understood intuitively that the number of crossings is related to the frequency of the signal. This argument is exemplified in the simple case of a single tone with a frequency of f1 , sampled with a period of Ts . The single tone is expressed as cos(λ1 n), where λ1 = 2πTs f1 . It is expected to cross zero level twice in a period of 1/f1 . Thus, for N samples, where N is large enough, the expected number of zero crossings D1 is 2Ts N f1 or N λ1 /π. Estimating the frequency using the number of zero crossings yields D1 ∼ R 1 fˆ1 = = 2Ts N 2Ts
ˆ 1 = πD1 ∼ λ = πR1 . N
(10)
We demonstrate the use of (10) on a deterministic discrete signal u(n) constructed of three different frequencies, with random phases θ1 , θ2 , and θ3 in the range of [0, 2π] u(n) = 0.8 cos(0.1n + θ1 ) + 0.4 cos(0.5n + θ2 ) + 0.1 cos(0.7n + θ3 ).
H(λ) = 1 − e−iλ .
(12)
The gain of (12) is given by |H(λ)|2 = 2(1 − cos λ), and it is monotonically increasing in the range of [0, π], as should be in the case of an HPF. Thus, applying (8) to the signal in (11) really emphasizes the second harmonic, and therefore, the second harmonic determines the number of second-order zero crossings. Using (9), which is similar to applying (8) successively, results in emphasis of higher and higher frequencies, and in fact, higher and higher frequencies will determine the zerocrossing counts. Fig. 5 shows the estimated frequencies from HOC for (11), where, after several iterations, it tends to “land” on R9 = 0.223, which corresponds to λ = 0.223π = 0.7006. This is a good estimate for 0.7, the third and last harmonic of (11). The “landing” on the highest harmonic is one of HOC features.
C. HOCs of a Random Signal (11)
This example was chosen in light of the fact that any periodic signal can be expressed by a Fourier series as a linear combination of sine waves. We examine the zero-crossing count of u(n) in the interval n = 1, . . . , 1000. Counting the zero crossings yields D1 = 32, and thus, the rate of crossings is R1 = 0.032. Estimating the frequency yields πR1 = 0.1006, which is a good estimate for 0.1, the first harmonic of (11). Applying (9) to (11) in order to calculate the second order
In many cases, the magnetic background can be modeled using an autoregressive (AR) process [18]. An AR process is defined as a random process where the current value is a linear combination of previous values and an additive white noise. Let us explore the first-order AR process, denoted by AR(1), for the recorded magnetic background. We denote by z(n) an AR(1) process z(n) = a1 z(n − 1) + w(n).
(13)
SHEINKER et al.: MAGNETIC ANOMALY DETECTION USING HIGH-ORDER CROSSING METHOD
Fig. 6. HOC mean rate and STD for a recorded real-world magnetic background.
Here, w(n) is a white Gaussian noise, with zero mean and STD of one. Using the Yule–Walker equation, we find that the coefficient a1 for the recorded magnetic background is about 0.93. A very important feature of HOC is the cosine formula that enables the estimation of a1 from the HOC rate [14] a1 = cos(πR1 ).
(14)
In the particular case of AR(1), given in (13), the autocorrelation is a1 . However, in fact, (14) can be used to estimate the autocorrelation of any random sequence. Calculating R1 for the recorded magnetic background, after removing the bias, yields R1 = 0.09, and thus, cos(πR1 ) = 0.96, which is close to the estimated value of a1 by the Yule–Walker equation. Using the aforementioned examples, we have demonstrated the ability of HOC to characterize a deterministic signal and also a random signal regarding the spectral contents. This suggests that HOC could be able to characterize the magnetic background and, thereby, to distinguish between it and a magnetic target signal. IV. HOC D ETECTOR FOR MAD A. HOC for Magnetic Signals and Noise We have applied the HOC method to the magnetic background measured at the Amram Geophysical Observatory. It is common in magnetic sensing to use gradiometeric measurements in order to cancel common interferences of far away origin. Thus, rather than readings of a single magnetometer, we have used differential readings of a couple of magnetometers. We have employed a moving window of 200-sample length, removing the bias from each window before the HOC method was applied. Fig. 6 shows the mean HOC rate and the STD. Other windows of lengths of 100 and 800 samples featured close results, indicating the robustness of the HOC method in characterizing the magnetic background in a quiet environment. We have also applied the HOC method to a magnetic target signal contaminated by a real-world magnetic background.
1099
Fig. 7. Moving window of 400 samples was used to calculate the HOC rate differences for the recorded real-world magnetic background and the target signal buried in the magnetic background.
Assume a target with a magnetic moment of 0.1 A · m2 , aligned with the Earth magnetic field, moving with a constant velocity of 1 m/s along a straight line track. The target passes by the magnetometer with a CPA of 7 m, resulting in an SNR of about 3.3 dB. The SNR was calculated by the ratio between signal power and mean noise power within the moving window. Tests were carried out using a simulated target signal added to the recorded magnetic background. In order to distinguish between the HOC rate sequence of magnetic background and the HOC rate sequence with the presence of a target, we use the HOC rate difference operator defined by R1 , k=1 (15) ∆k (R) ≡ 1 < k < N − 1. Rk − Rk−1 , For convenience, we chose to use the difference between HOC rates, although in many cases, the difference between HOC counts is employed. Using the differences of HOC counts is more power efficient for real-time implementation since normalizing by N is avoided. Fig. 7 shows ∆k (Rbackground ), which denotes the HOC rate differences for the recorded magnetic background, and ∆k (Rsignal ), which denotes the HOC rate differences for a target signal contaminated by the magnetic background. Here, ∆k (Rsignal ) was calculated within a moving window of real-world recorded magnetic background with an added simulated target signal. Notice that there is a difference between the sequence for the target signal and the sequence for the magnetic background. The difference is clear from the first and second components of the HOC rate difference sequences, where the components of the target signal are outside the error bar of the magnetic background. For HOC rate sequences, it is acceptable that two sequences are considered as different whenever even a single component of one sequence is outside of the error bar of the other sequence. This difference indicates that an effective detector can be constructed. In order to detect target presence, we are interested in comparing between ∆k (Rbackground ) with a HOC rate difference sequence of a fresh window of readings
1100
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 4, APRIL 2012
Fig. 9. Estimated pdfs of ψ 2 (background) and ψ 2 (signal + background) using a real-world recorded magnetic background. Fig. 8. Typical target signal buried in a real-world recorded magnetic background with SNR of about −2 dB. It is fed to (top) the HOC detector input and revealed at (bottom) the output.
∆k (Rwindow ). Hence, we use the following discrimination function as a detector [14]: ψ ≡ 2
K [∆k (Rwindow ) − ∆k (Rbackground )]2 k=1
∆k (Rbackground )
.
(16)
Here, K is the number of the HOC used for comparison between a target signal and the magnetic background. The use of rates in (16) as opposed to counts means just a division by N . Fig. 8 shows the detector response for a typical target signal contaminated by the recorded magnetic background. At the detector input, the target signal is deeply buried in the magnetic background and therefore barely noticed. However, at the detector output, the target signal is revealed. B. Detector Performance With Real-World Magnetic Background The first step for testing the detector performance with realworld magnetic background is to evaluate ∆k (Rbackground ). This is done using the first hour of the recorded magnetic background. The remaining 4 h of the recordings are used to evaluate ψ 2 (background), which is the detector response to the magnetic background, and ψ 2 (signal + background), which is the detector response to a target signal buried in the magnetic background. For calculating the detector response, a moving window was used, where, for each window, ∆k (Rwindow ) was evaluated and substituted into (16) to obtain ψ 2 (background). Afterward, we have added the simulated target signal to each moving window and evaluated ∆k (Rwindow ) for ψ 2 (signal + background). Fig. 9 shows the resulting pdfs of ψ 2 (background) and ψ 2 (signal + background), where a moving window of 400 samples was used to calculate ∆k (Rbackground ) and ∆k (Rwindow ). Using the Neyman–Pearson criterion, we calculate a threshold which guarantees that the false alarm rate (FAR) will stay
Fig. 10.
ROC of the magnetic anomaly detector based on the HOC method.
below a predetermined value [19]. For a reasonable FAR of 10−4 , the calculated threshold is 0.0813, resulting in a detection probability of about 99.7%. Although using K = 1 will result in a higher detection probability, we have used K = 2 in order to achieve more robustness. A more detailed description of the HOC detector performance is given in Fig. 10 by the receiver operation characteristics (ROCs). The ROC in Fig. 10 corresponds to the aforementioned scenario regarding target track and magnetic moment orientation. From OBF analysis, it is shown that the magnetic moment orientation governs the weights c1 , c2 , and c3 of the OBF in (2). Thus, we have tested the HOC method response to each OBF separately. For an SNR of about −3 dB, we have used a moving window of 800 samples and set the threshold value to obtain a FAR of 10−4 . The resulting detection probabilities for the OBFs g1 , g2 , and g3 were about 0.74, 0.76, and 0.82, respectively, indicating a difference of less than 10% in detection probability. Hence, from a practical point of view, we should expect a quite similar detector performance for any orientation of target magnetic moment.
SHEINKER et al.: MAGNETIC ANOMALY DETECTION USING HIGH-ORDER CROSSING METHOD
Fig. 11. Detection probability decreases with time. The detector was calculated using the recordings of the magnetic background of the first hour. Here, we have used a window length of 400 samples, and the threshold was calculated for a FAR of 10−3 at an SNR of 0 dB.
When designing a MAD detector based on HOC, one should take into account that the magnetic background might feature a somewhat nonstationary behavior. Fig. 11 shows the detection probability as a function of time passed for the real-world recorded magnetic background. Here, ∆k (Rbackground ) was calculated for the first hour of recording and was used to calculate the detection probability every half an hour. Notice the high detection probability during the first and second hours, whereas starting from the third hour, the detection probability decreases with time passed. Therefore, designed in an adaptive manner, ∆k (Rbackground ) should be updated from time to time, and accordingly, the threshold should be recalculated in order to keep FAR below limit. For real-time applications, it is recommended that the optimal period of updating should be determined after a long-term inspection of the magnetic background behavior. Usually, the target characteristic time τ is unknown a priori. The characteristic time governs the width of the target signal, as was discussed earlier. Hence, we have tested the influence of the chosen window length on the detection probability for various characteristic time values. Fig. 12 shows the results of the test for the real-world recorded magnetic background. Notice that the larger the characteristic time, the wider window is needed. However, the curves in Fig. 12 are wide enough, indicating that one window of a chosen length can be useful in detecting targets with a quite wide range of characteristic time values. Hence, a multichannel approach can be adopted, where each channel has a different window length and thus corresponds to a different range of characteristic time values. From a practical point of view, only a few channels are needed to cover the expected target characteristic time values. V. F URTHER R ESEARCH In this paper, we have used the data recorded in the Amram Geophysical Observatory to investigate the HOC method. We have demonstrated the HOC method to be efficient in MAD.
1101
Fig. 12. Detection probability as a function of window length for various characteristic time values.
We believe that the proposed method can be useful in searching for earthquake magnetic precursors.
VI. C ONCLUSION We have proposed a method for MAD based on higher order crossings. The proposed detector relies on the nature of the magnetic background and thereby does not require assumptions regarding the target signal. Hence, the proposed method is also applicable for detecting a target moving along a curved track with changing velocity and varying magnetic moment. Tests with real-world recorded magnetic background showed high detection probability even for low SNR values. The proposed method can be practically accomplished almost without any multiplication operation, which results in a simple implementation and low power consumption. The high detection probability, together with simple realization and low power consumption, makes the proposed method attractive for realtime applications such as intruder detection [20] and observatory monitoring of the Earth magnetic field. R EFERENCES [1] R. J. Blakely, Potential Theory in Gravity and Magnetic Applications. Cambridge, U.K.: Cambridge Univ. Press, 1996, pp. 75–79. [2] C. D. Hardwick, “Important design considerations for inboard airborne magnetic gradiometers,” Geophysics, vol. 49, no. 11, pp. 2004–2018, Nov. 1984. [3] R. J. Kozick and B. M. Sadler, “Algorithms for tracking with an array of magnetic sensors,” in Proc. 5th IEEE SAM Signal Process. Workshop, 2008, pp. 423–427. [4] M. Tchernychev and D. D. Snyder, “Open source magnetic inversion programming framework and its practical applications,” J. Appl. Geophys., vol. 61, no. 3/4, pp. 184–193, Mar. 2007. [5] E. Gelenbe and T. Kocak, “Area-based results for mine detection,” IEEE Trans. Geosci. Remote Sens., vol. 38, no. 1, pp. 12–24, Jan. 2000. [6] D. K. Butler, “Implications of magnetic backgrounds for unexploded ordnance detection,” J. Appl. Geophys., vol. 54, no. 1/2, pp. 111–125, Nov. 2003. [7] M. Munchy, D. Boulanger, P. Ulrich, and M. Bouiflane, “Magnetic mapping for detection and characterization of UXO: Use of multi-sensor fluxgate 3-axis magnetometers and methods of interpretation,” J. Appl. Geophys., vol. 61, no. 3/4, pp. 168–183, Mar. 2007.
1102
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 50, NO. 4, APRIL 2012
[8] M. R. Pozza, J. I. Boyce, and W. A. Morris, “Lake-based magnetic mapping of contaminated sediment distribution, Hamilton Harbour, Lake Ontario, Canada,” J. Appl. Geophys., vol. 57, no. 1, pp. 23–41, Dec. 2004. [9] M. Marchetti, L. Cafarella, D. D. Mauro, and A. Zirizzotti, “Ground magnetometric surveys and integrated geophysical methods for solid buried waste detection: A case study,” Ann. Geophys., vol. 45, no. 3/4, pp. 563– 573, Jun.–Aug. 2002. [10] L. Alperovich, V. Zheludev, and M. Hayakawa, “Application of wavelet technique for the detection of earthquake signatures in the geomagnetic field,” Nat. Hazards Earth Syst. Sci., vol. 1, no. 1/2, pp. 75–81, 2001. [11] B. Ginzburg, L. Frumkis, and B. Z. Kaplan, “Processing of magnetic scalar gradiometer signals using orthonormal functions,” Sens. Actuators A, Phys., vol. 102, no. 1/2, pp. 67–75, Dec. 2002. [12] A. Sheinker, N. Salomonski, B. Ginzburg, L. Frumkis, and B. Z. Kaplan, “Magnetic anomaly detection using entropy filter,” Meas. Sci. Technol., vol. 19, no. 4, p. 045 205, Apr. 2008. [13] A. Sheinker, N. Salomonski, B. Ginzburg, L. Frumkis, and B. Z. Kaplan, “Remote sensing of a magnetic target utilizing population based incremental learning,” Sens. Actuators A, Phys., vol. 143, no. 2, pp. 215–223, May 2008. [14] B. Kedem, Time Series Analysis by Higher Order Crossings. New York: Inst. Elect. Electron. Eng., Inc., 1994. [15] P. A. Dickstein, J. K. Spelt, and A. N. Sinclair, “Application of a higher order crossing feature to non-destructive evaluation: A sample demonstration of sensitivity to the condition of adhesive joints,” Ultrasonics, vol. 29, pp. 355–365, 1991. [16] P. A. Dickstein, “Identification of changes in the entropy of seismic signals preceding an event through higher order zero crossings analysis,” Seismol. Res. Lett., vol. 80, no. 3, pp. 473–478, May/Jun. 2009. [17] GEM Systems Advanced Magnetometers. [Online]. Available: www.gemsys.ca [18] A. Sheinker, A. Shkalim, N. Salomonski, B. Ginzburg, L. Frumkis, and B. Z. Kaplan, “Processing of a scalar magnetometer signal contaminated by 1/f α noise,” Sens. Actuators A, Phys., vol. 138, no. 1, pp. 105–111, Jul. 2007. [19] S. M. Kay, Fundamentals of Statistical Signal Processing Detection Theory. Englewood Cliffs, NJ: Prentice-Hall, 1998, pp. 61–75. [20] A. Sheinker, N. Salomonski, B. Ginzburg, A. Shkalim, L. Frumkis, and B. Z. Kaplan, “Network of remote sensors for magnetic detection,” in Proc. 4th Int. Conf. ITRE, Tel Aviv, Israel, 2006, pp. 56–60.
Arie Sheinker (M’06) was born in Czernowitz, Ukraine, in 1971. He received the B.Sc., M.Sc., and Ph.D. degrees from the Ben-Gurion University of the Negev, Beer-Sheva, Israel, in 1992, 2003, and 2009, respectively. In 1993–1999, he was a Communications Systems Engineering Officer with the Israeli Air Force. He is currently with SOREQ Nuclear Research Center, Yavne, Israel. His current research is in the fields of magnetic anomaly detection, methods for localization and magnetic moment estimation, remote magnetic sensing, and magnetic signal processing.
Boris Ginzburg was born in St. Petersburg, Russia, in 1951. He received the M.Sc. degree in radio physics and electronics from the Technical University of St. Petersburg, St. Petersburg, in 1974 and the Ph.D. degree in physics and mathematics from the Ioffe Physical–Technical Institute, Russian Academy of Sciences, St. Petersburg, in 1986. In 1974–1996, he was a Research Scientist with the Geophysical Research Institute, St. Petersburg. During this period, he was engaged in R&D of optical pumping magnetometers for precise measurements of the Earth’s magnetic field. His experimental investigation of optical pumping phenomena in alkalis and helium resulted in the design of new Rb–He and K–He magnetometers with very high metrological features. He headed a research group concerned with the elaboration of technological processes for precise magnetic sensor production. He is currently the Head of a research group in SOREQ Nuclear Research Center, Yavne, Israel. His main scientific interests are in the fields of precise measurements of the Earth’s magnetic field and various magnetic search and detection applications.
Nizan Salomonski (M’09) was born in Haifa, Israel, in 1963. He received the B.Sc., M.Sc., and Ph.D. degrees in mechanical engineering from Technion–Israel Institute of Technology, Haifa, in 1991, 1994, and 1999, respectively. In 1991–1994, he was an Assistant Scientist with the Robotics Laboratory, Technion–Israel Institute of Technology. During this period, he was engaged in R&D of flexible inflatable articulated robots and control algorithms related to tool trajectory. In 1994–1999, he was a Scientist with the Center for Manufacturing Systems and Robotics, Technion–Israel Institute of Technology. During this period, he was engaged in R&D of nonparametric algorithms for adaptive disassembly processes and planning mechanisms. Since 1999, he has been a Researcher with SOREQ Nuclear Research Center, Yavne, Israel, where he has been the Head of the R&D Integrated Systems Group since 2001. His main scientific interests are nonparametric algorithms for prediction, detection and localization, and their application for various magnetic anomaly detection systems. Dr. Salomonski has been a member of the American Society for Mechanical Engineering since 1998.
Phineas A. Dickstein was born in Montevideo, Uruguay, in 1954. He received the B.Sc. degree in electrical engineering and the M.Sc. and D.Sc. degrees in nuclear engineering from the Technion–Israel Institute of Technology, Haifa, Israel, in 1976, 1983, and 1987, respectively, and the B.A. degree in history from The Open University, Israel. He was a Postdoctoral Fellow and then a Research Scientist with the University of Toronto, Toronto, ON, Canada, between 1988 and 1992. Since 1993, he has been with the Israel Atomic Energy Commission, Tel Aviv, Israel, and in the last seven years, he has been the Head of the Safety Division, SOREQ Nuclear Research Center, Yavne, Israel. He has also been an Adjunct Professor at the Technion–Israel Institute of Technology. His main scientific interests are in the fields of signal analysis and nondestructive testing.
Lev Frumkis was born in Barnaul, Russia, in 1938. He received the M.Sc. degree in radio physics and electronics, the D.Phil. degree in radio physics, and the D.Sc. degree in radio physics from Tomsk State University, Tomsk, Russia, in 1961, 1967, and 1989, respectively. From 1961 to 1990, he was a Scientist with the Siberian Physics and Technology Institute, Tomsk, where he worked on various electromagnetic problems. He immigrated to Israel in 1991. From 1991 to 1993, he was an Engineer with the Israel aircraft industry. Since 1994, he has been with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel, where he is currently a Research Fellow who is financed by the Ministry of Absorption Grant. His present research activity is mainly in the fields of magnetic shielding and magnetometry.
SHEINKER et al.: MAGNETIC ANOMALY DETECTION USING HIGH-ORDER CROSSING METHOD
Ben-Zion Kaplan (M’76–SM’82–LSM’07) was born in Tel Aviv, Israel, in 1936. He received the B.Sc. (cum laude) and M.Sc. degrees from the Technion–Israel Institute of Technology, Haifa, Israel, in 1958 and 1964, respectively, and the D.Phil. degree in electrical engineering from the University of Sussex, Brighton, U.K., in 1971. From 1961 to 1968, he was a Research Engineer with the Electronics Department (presently the Department of Physics of Complex Systems), Weizmann Institute of Science, Rehovot, Israel. From 1968 to 1971, he was with the Inter University Institute of Engineering Control, School of Applied Sciences, University of Sussex. Since 1972, he has been with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel, where he was a Professor from 1985 and has been a Professor Emeritus since October 2006. He established the laboratory for magnetic and electronic systems. He was the incumbent of the Chinita and Conrad Abrahams–Curiel Chair in Electronic Instrumentation from 1988 to 2006. In 1992, he was on a sabbatical leave in the Department of Physics, University of Otago, Dunedin, New Zealand. He has published more than 130 articles in refereed scientific journals. His main current interests are magnetic and electronic instrumentation, electromechanical devices including magnetic levitators and synchronous machines, nonlinear phenomena in electronic networks and magnetic devices, nonlinear and chaotic oscillations, coupled oscillator systems, multiphase oscillators, magnetometry and its relationship to extremely low frequency phenomena, and magnetic- and electricfield sensors for dc and ultralow frequency. Dr. Kaplan is a member of the Israeli Committee of Union Radio Scientifique Internationale and a member of its Metrology Subcommittee. He was a recipient of a prize in the field of applied electronics donated by the Polish–Jewish Ex-Servicemen’s Association–London in 1993. The prize was due to his achievements in nonlinear electronics and magnetics.
1103
