17 2012 Magn Anomaly Detection Boris Ginzburg

8/12/2019 17 2012 Magn Anomaly Detection Boris Ginzburg

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International Scienti f ic CNRS Fall School 2012High Sensitivity Magnetometers

"Sensors & Applications"

4thEdit ion ,

Monday 22 - Friday 26 Octob er2012

Branv i l le, Normandy, FRANCE

Magnetic anomaly detection systems

target based and noise based approach

Dr. Boris Ginzburg, NRC SOREQ, 81800 Yavne, Israel


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Magnetized body produces

magnetic anomaly

Typical magnetic anomaly detection scenario:

a) search system

h

s

R0CPA

TargetM

Sensors

b)

R0CPA (closest proximityapproach) distance

a)

Sensor

platform

h

s

N

S

Target

M

T

2b) warning system.


3/31

Search systemsSubmarine d etect ionShips wreck detection

Mine detect ion

UXO detect ion

Bur ied drums detect ion

ApplicationsMAD GoalsTarget detectio nTarget local izat ion & character izat ion

Target tracking

3

real time


4/31

Search systems

Warning systemsIntru der detect ion

Virtual fence

Faci l i t ies protect ion

Per imeter protect ion

Access con t ro lPassage access contro l

Entry po in ts m oni to r ing

Submarine d etect ionShips wreck detection

Mine detect ion

UXO detect ion


Applications

Medical appl icat ion s

Indu str ial c ontro l

Geophysics EQ predict io n

GoalsTarget detectio nTarget local izat ion & character izat ion

Target tracking

AB

CD

EF

GH

IK

LM

PeriodErr

Det

CU

Bat

MSU

Ch

Virtual Fence Magnetic Sensor UnitsUnderground Installation

BatteryRelay Unit - F

Antennas

High gain antenna

TS 4000

Radio

Control Unit

Radio link

100 m LOS

Radio link

4 Km NLOS

Relay station

C4I

4


5/31

Search systems

Warning systemsIntrud er detect ion

Virtual fence

Faci l i t ies protect ion

Per imeter pro tect ion

Access con t ro lPassage access con trol

Ent ry po in ts mo ni to r ing

Submarine d etect ionShips wreck detection

Mine detect ion

UXO detect ion


Applications

Medical appl icat ion s

Indu str ial c ontro l

Geophysics EQ predict io n

GoalsTarget detectio nTarget local izat ion & character izat ion

Target tracking

5


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Approach to MAD data processing.

1. Target based

Analytic solution.a) One single-axis magnetic sensor or single total field sensor.

b) Differential three-axis magnetometer.

Numerical solution by means of PCA. Generalization of the

method.

Three-axis gradiometer. Detrended signal.Other than straight line relative sensor-target movement

2. Noise based

Entropy detector

High-order crossing detector

6


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Sensor

platform

N

S

Target

M

BEarth

R0 CPA (Closest Proximity Approach)

Z

X Y

7

Target based approachcertain mutual target-sensor movement pattern is assumed

Different target magnetic moment directions result in variety of signal curve shapes


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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

3

2

1Dipolesignal

w

Magnetic dipole signals for N-S survey line with 45magnetic inclinationangle and s>>h. w = x/R0 - nondimensional coordinate along survey line-1 - Mx = 0, My = 0, Mz = - 12 - Mx = 0.5, My = 0.8, Mz = - 0.35

3 - Mx = - 1, My = 0, Mz = - 0

Accepted approach to signal processing:

decomposition of the acquired signal in the orthonormal basis function (OBF) spacewhere each dipole signal can be expressed as a linear combination of basis functions 8

Target signal curve

can take variety of

shapes

Target based approachcertain mutual target-sensor movement pattern is assumed


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One single-axis magnetic sensor or single total field sensor.

Analytic solution.

35

0 3

4

),(

r

m

r

rrmrmB

t

R

tv

R

du

00

3

1

)(j

jj ufauB

5.22

2

1

1

3

51

5

24

t

t

tf

5.222 15128

t

ttf

5.222

3

13

128

t

ttf

0)()(

dwwfwf ji

1)(2 dwwfj

i, j = 1, 2, 3 9

Wronskian W(f1,f2,f3)0

Gram-Schmidt orthogonalization

- characteristic time


10/31

10

Target function for

detection algorithmenergy in OBF space

dwwBwwFwa mimi )(~

)()( i=1, 2, 3Convolutions of the raw signal of the sensor

with appropriate basic functions for each

acquired sample0.7

1(m)

f1

(w)

Raw signal

S1r(wi)i = 0..m+k

3(m)

Observation

window

wm-k wm wm+k

0

0

0-0.7

0.0w-k

w

-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.03.54.0

0.00

w

-1.2-0.8-0.40.00.4

0.81.2

w

wk

w-k wk

f2(w)

f3(w)

wkw-k

2(m) E(m)3

1

2)(

j

j mThreshold

comparison

Threshold

value= ?

Algorithm of MAD data processing

Multi-channel scheme of magneticanomaly detection

0the guess value of targetcharacteristic time

E1(m)

Ch1 0= 01Ch2 0= 02

ChS 0=

0s

Raw signal

S1r(wi)i = 0..m+k

E2(m)

Es(m)


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-5 -4 -3 -2 -1 0 1 2 3 4 5

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

3

2

1-1

+1

0

Dipolesig

nal

w

Dipole signals forvarious directions

of magnetic

moment vector

Correspondingenergy signals

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

321

Ene

rgy

w

11


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12

30 20 10 0 10 20 30

1

-1

b)w

Raw data - signal Hz(w)with uniform noise.

30 20 10 0 10 20 30

1

0

c)w

Result of dataprocessing.

: .

30 20 10 0 10 20 30

1

-1

d)w

The result of band-pass filtration of the

raw signal.

Example of algorithm implementation


13/31


14/31

Differential three-axis magnetometer. Analytic solution.

14

A three-axis referenced magnetometer detects a ferromagnetic target

that moves along a straight line track with a constant velocity

Target track

Ferromagnetictarget

R0

Three-axismagnetometer

Referencethree-axis

magnetometer

u=0

u>0

u


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The set of orthonormal functions:g1, g2, g3for presentation of target field

Magnetic target detection scheme using OBFs. 15


16/31

Signal distortion as a result of

detrend procedure.

a) pure target signal;

b) b) the same signal after

detrending.

16

In practice, pure target signals are usually accompanied with nonrandom

bias and temporal trends

Linear function is not orthogonal to OBF and therefore data are to be

detrended before mapping onto OBF subspace

Universal method of obtaining orthonormal basis appropriate for any specific

processing technique and path-time pattern of relative sensortargetmovement is needed


17/31

Numerical solution by means of PCA. Generalization of the method.

Lower sensor

d

U er sensor

Target path

X

Z

Y

Gradiometer comprising a couple of

three-axis magnetometers detects a

ferromagnetic target that moves along a

straight line track with a constant velocity

17

Algorithm stages

a) windowing of the sampled signals;b) calculation of gradiometer signals for each axis Gi=Biupper- Bilower, i=x, y, z;

c) detrending of each gradiometer signal component Gi(G_detrend)I ;d) calculation of gradient norm;

e) mapping of gradient norm Gonto the space of appropriate OBF;f) summation of squared coordinates in OBF space for getting decision index;

g) comparison of index obtained in f) with predetermined threshold.


18/31

S1x

S1y

S1z

S2x

S2y

S2z

S1x

S1y

S1z

S2x

S2y

S2z

Detection scheme

a

M

Y

Z

sh

Target path

Upper sensor

Lower sensor

d

X

CPA up

Window

slow

Window

fast

fastslow

Difference

S1x-S2xS1y-S2y

S1z-S2z

B&T reduction (i)2Dot

product

Basic functions

fast

slow

Difference B&T reduction (i)2 Dotproduct

(ai)2

Threshold

fast

(ai)2

Threshold

slow

Or

Warning

18


19/31

Finding of OBF space with the help of PCA (Principal Component Analysis)

1. Build data matrix

Window Difference B&T reduction

(i)2

35

0 3

4

),(

r

m

r

rrmrmB

50

1332

49

1332

50

1332

50

2

49

2

50

2

50

1

49

1

50

1

...

............

...

...

ggg

ggg

ggg

G

a= 0, 5180= 0, 10350

2. Mean reduction

N

n

nkGN 1

],[1 uGB u - unit vector

3. Find covariance matrix

T

BBN

C 1

4. Find eigenvectors and eigenvalues

jjj eeC

a

M

Y

Z

h

d

X

s

19


20/31

Three first eigenvalues used as OBF for representation of

gradiometer norm signals. Window length is taken equal to 30.

20

1= 22.6; 2= 2.1; 3 = 0.6; 4 =0.08; 5= 0.04;


21/31

21

3

1

)(j

jj ufauG

a= 0, 5180= 0, 10350

Expansion coefficients for variety of target moment directions

As it is formulated by PCA theory, the eigenvector with the largest eigenvalue

corresponds to the dimension having the strongest correlation in the data set.


22/31

22

a= 0, 2.5,180= 0, 5,355

Contribution of fj forj>3is

insignificant

Relative expansion coefficients for variety of target moment directions

1

)(j

jj ufauG

a2/a1

a3/a1

a4/a1


23/31

Real-world data acquisition

Fast target movement Slow target movement 23


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-100 -80 -60 -40 -20 0 20 40 60 80 100

-0.1

-0.05

0

0.05

0.1

0.15

n [samples]

e1(n)

e2(n)

e3(n)

The orthonormal basis functions (OBFs) which are associated with

the three largest eigenvalues in case of a parabolic track.

Other than straight line relative sensor-target movement

24

PCA method provides an universal way for finding OBF basis


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Noise based approach.

No tentative assumption concerning mutual target-sensor movement can be made.

Approach - Statistical analysis of acquired magnetometer noise

25

LEMI-019 single-axis fluxgate magnetometer

Frequency range - 0.025 Hz,Intrinsic noise - less than 15 pT/Hz @1 Hz.Sampling period -0.1 s.

The normalized histogram of 12 h data

acquisition of magnetometer noise.

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

B [nT]

2

2

2 2exp

2

1

i

i

xxf

.1,11

22

1 M

i

i

M

i

i xM

xM

Probability density function

mean variance

.

xx

x

iii

i

i

dxxfxp .xxfxp ii

.x - quantization level


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Adaptive minimum entropy detector

.lg1

i

Linnni

xpxpxI

Several parallel channels with different window length should be used to cover

possible detection scenarios

26

0 100 200 300 400 500 600 700 800 900 1000

-0.5

0

0.5

samples

100 200 300 400 500 600 700 800 900 1000

0

5

samples

Target

Entropy[nats]

B[

nT]

Target signal, contaminated by real-world magnetic noise (top). The target moved along a

straight line toward the sensor and then returned, reaching a CPA of 3 m. The target

signal is clearly detected by the entropy filter.

The entropy filter calculates the entropy in a

moving window of L samples


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0 1 2 3 4 5 6 70

1

2

3

4

5

6x 10

-3

Entropy [nats]

Target Magnetic

noise

A posteriori probabilities of both noise and target after filtering.

The target with a magnetic moment of 0.06 Am2 aligned with the Earth magnetic fieldwas moved along a South-North track with CPA of 3 m, resulting in SNR of -5 dB.

10000 target passes within randomly chosen windows

27With threshold value of 2.9 nats, a false alarm rate is 4%, detection probability is 94%.


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Adaptive magnetic anomaly detector based on the high

order crossings (HOC)

28

N

nnxHnxHD

2

)1()(nx n= 1, ..NSampled time series

Zero crossings count

1 nxnxnxFirst difference series

nxk

nxk 1k-th difference series )1( nx

kDkD

37.0cos1.025.0cos4.011.0cos8.0 nnnnx n= 1,,1000.Example

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

HOC order

Estimatedfrequency


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K

k backgroundRk

backgroundRkwindowRkn

1

22

30

Adaptive detector decision index


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Target-based approach

MAD signal decomposition in the space of OBF.

PCA technique - any specific path-time pattern of target-sensor movement.

A few principal components corresponding to maximal eigenvalues make up

the OBF space.

Signal norm in this space is used to construct an efficient detector.

Noise-based approach

No tentative assumption concerning mutual target-sensor movement can be

made

Statistical evaluation of the magnetometer noise is implemented in a moving

window.

Adaptive minimum entropy detector (MED), which detects any change in the

magnetic noise pattern.

Adaptive High Order Crossing (HOC) detector sensitive to the change of noise

statistics

Conclusion.

17 2012 Magn Anomaly Detection Boris Ginzburg

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