Magnetic anomaly detection systems target based and noise based approach

Transcription

1 Magnetic anomaly detection systems target based and noise based approach International Scientific CNRS Fall School High Sensitivity Magnetometers "Sensors & Applications" 4 th Edition, Monday - Friday 6 October Branville, Normandy, FRANCE Dr. Boris Ginzbrg, NRC SOREQ, 88 Yavne, Israel

2 Magnetized body prodces magnetic anomaly S Sensor platform a) N T h s R CPA (closest proximity approach) distance M Target M Target b) h R CPA Typical magnetic anomaly detection scenario: s Sensors a) search system b) warning system.

3 MAD Goals Target detection real time Target localization & characterization Target tracking Applications Search systems Sbmarine detection Ships wreck detection Mine detection UXO detection Bried drms detection

4 MSU Ch A C E G I L Bat Det B D F H K M Err CU Period Goals Target detection Target localization & characterization Target tracking Virtal Fence Radio link m LOS Antennas Radio link 4 Km NLOS Relay Unit - F High gain antenna Relay station Battery TS 4 Radio C 4 I Control Unit Magnetic Sensor Units Undergrond Installation Applications Search systems Sbmarine detection Ships wreck detection Mine detection UXO detection Bried drms detection Warning systems Intrder detection Virtal fence Facilities protection Perimeter protection Access control Passage access control Entry points monitoring Medical applications Indstrial control Geophysics EQ prediction 4

5 Goals Target detection Target localization & characterization Target tracking Applications Search systems Sbmarine detection Ships wreck detection Mine detection UXO detection Bried drms detection Warning systems Intrder detection Virtal fence Facilities protection Perimeter protection Access control Passage access control Entry points monitoring Medical applications Indstrial control Geophysics EQ prediction 5

6 Approach to MAD data processing.. Target based Analytic soltion. a) One single-axis magnetic sensor or single total field sensor. b) Differential three-axis magnetometer. Nmerical soltion by means of PCA. Generalization of the method. Three-axis gradiometer. Detrended signal. Other than straight line relative sensor-target movement. Noise based Entropy detector High-order crossing detector 6

7 Target based approach certain mtal target-sensor movement pattern is assmed Z S Sensor platform X Y N R CPA (Closest Proximity Approach) Target B Earth M Different target magnetic moment directions reslt in variety of signal crve shapes 7

8 Dipole signal Target based approach certain mtal target-sensor movement pattern is assmed w Magnetic dipole signals for N-S srvey line with 45 magnetic inclination angle and s>>h. w = x/r - nondimensional coordinate along srvey line - - M x =, M y =, M z = - - M x =.5, M y =.8, M z = M x = -, M y =, M z = - Target signal crve can take variety of shapes Accepted approach to signal processing: decomposition of the acqired signal in the orthonormal basis fnction (OBF) space where each dipole signal can be expressed as a linear combination of basis fnctions 8

9 One single-axis magnetic sensor or single total field sensor. Analytic soltion. 5 4 ), ( r m r r r m m r B t R t v R d ) ( j j j f a B t t t f t t t f 5. 8 t t t f ) ( ) ( dw w f w f j i ) ( dw w f j i, j =,, 9 Wronskian W(f,f,f ) Gram-Schmidt orthogonalization - characteristic time

10 Algorithm of MAD data processing a ~ i wm ) Fi ( w wm ) B ( w) ( dw i=,, Raw signal S r (w i ) i =..m+k =? Observation window.7 w m-k w m w m+k -.7 f (w). w -k f (w). w -k w w w -k f (w) w w k w k w k Convoltions of the raw signal of the sensor with appropriate basic fnctions for each acqired sample a (m) a (m) a (m) j Target fnction for j a ( m) E(m) Threshold vale Threshold comparison detection algorithm energy in OBF space Mlti-channel scheme of magnetic anomaly detection the gess vale of target characteristic time Raw signal S r (w i ) i =..m+k Ch = Ch = ChS = s E (m) E (m) E s (m)

11 Energy Dipole signal w Dipole signals for varios directions of magnetic moment vector Corresponding energy signals w

12 Example of algorithm implementation - b) c) - d) fn READPRN"c:/data/Flx/nfltr.dat" ( ) w w w Raw data - signal Hz(w) with niform noise. Reslt of data processing. The reslt of bandpass filtration of the raw signal.

13 How many channels do we need? Range of possible target vales

14 Differential three-axis magnetometer. Analytic soltion. 4 A three-axis referenced magnetometer detects a ferromagnetic target that moves along a straight line track with a constant velocity Target track Ferromagnetic target R Three-axis magnetometer Reference three-axis magnetometer = > < CPA x y z 5 4 ), ( r m r r r m m r B y R x R r ˆ ˆ z m R y m m m R x m m m R B z y y x x y x ˆ 4 ˆ 4 ˆ 4 ) ( ) ( m m m m m m m m R B z y x y x z y x ,.455,.899 g g g

15 The set of orthonormal fnctions: g, g, g for presentation of target field Magnetic target detection scheme sing OBFs. 5

16 In practice, pre target signals are sally accompanied with nonrandom bias and temporal trends Linear fnction is not orthogonal to OBF and therefore data are to be detrended before mapping onto OBF sbspace Signal distortion as a reslt of detrend procedre. a) pre target signal; b) b) the same signal after detrending. Universal method of obtaining orthonormal basis appropriate for any specific processing techniqe and path-time pattern of relative sensor target movement is needed 6

17 Nmerical soltion by means of PCA. Generalization of the method. X Gradiometer comprising a cople of three-axis magnetometers detects a ferromagnetic target that moves along a straight line track with a constant velocity Upper sensor Target path d Y Lower sensor Z Algorithm stages a) windowing of the sampled signals; b) calclation of gradiometer signals for each axis G i =B ipper - B ilower, i=x, y, z; c) detrending of each gradiometer signal component G i (G_detrend) I ; d) calclation of gradient norm; e) mapping of gradient norm G onto the space of appropriate OBF; f) smmation of sqared coordinates in OBF space for getting decision index; g) comparison of index obtained in f) with predetermined threshold. 7

18 X s h Detection scheme Upper sensor d CPA p Y Target path Warning Or Lower sensor Z a M Threshold fast Threshold slow Sx Sy Sz Sx Sy Sz Sx Sy Sz Sx Sy Sz Window fast fast slow Window slow Difference Sx-Sx Sy-Sy Sz-Sz B&T redction ( i ) fast slow Dot prodct Basic fnctions Difference B&T redction ( i ) Dot prodct (a i ) (a i ) 8

19 Finding of OBF space with the help of PCA (Principal Component Analysis). Bild data matrix B( m, r) 4 mr 5 r r m r Window Difference B&T redction ( i ) a =, 5 8 =, 5. Mean redction G g g g 5 g g g g g g 5 Z d s Y h X a M N G[ k, n] N n B G - nit vector. Find covariance matrix C N B T B 4. Find eigenvectors and eigenvales C e j e j j 9

20 Three first eigenvales sed as OBF for representation of gradiometer norm signals. Window length is taken eqal to. =.6; =.; =.6; 4 =.8; 5 =.4;

21 Expansion coefficients for variety of target moment directions G j a j f j ( ) a =, 5 8 =, 5 As it is formlated by PCA theory, the eigenvector with the largest eigenvale corresponds to the dimension having the strongest correlation in the data set.

22 Relative expansion coefficients for variety of target moment directions a/a a =,.5, 8 =, 5, 55 G j a j f j ( ) a/a a4/a Contribtion of f j for j> is insignificant

23 Real-world data acqisition Fast target movement Slow target movement

24 PCA method provides an niversal way for finding OBF basis Other than straight line relative sensor-target movement e(n) e(n) e(n) n [samples] The orthonormal basis fnctions (OBFs) which are associated with the three largest eigenvales in case of a parabolic track. 4

25 Noise based approach. No tentative assmption concerning mtal target-sensor movement can be made. Approach - Statistical analysis of acqired magnetometer noise LEMI-9 single-axis flxgate magnetometer Freqency range -. 5 Hz, Intrinsic noise - less than 5 pt/ Hz. Sampling period -. s. Probability density fnction f M mean x M i i x exp i i, M M i x variance x. i px f x dx. px f x x. i x x x i i i i i x. - qantization level i B [nt] The normalized histogram of h data acqisition of magnetometer noise. 5

26 Entropy [nats] B [nt] Adaptive minimm entropy detector I i x px lg px. i n n nil The entropy filter calclates the entropy in a moving window of L samples Several parallel channels with different window length shold be sed to cover possible detection scenarios.5 Target samples samples Target signal, contaminated by real-world magnetic noise (top). The target moved along a straight line toward the sensor and then retrned, reaching a CPA of m. The target signal is clearly detected by the entropy filter. 6

27 A posteriori probabilities of both noise and target after filtering. 6 x Target Magnetic noise Entropy [nats] The target with a magnetic moment of.6 Am aligned with the Earth magnetic field was moved along a Soth-North track with CPA of m, reslting in SNR of -5 db. target passes within randomly chosen windows With threshold vale of.9 nats, a false alarm rate is 4%, detection probability is 94%. 7

28 Estimated freqency Adaptive magnetic anomaly detector based on the high order crossings (HOC) Sampled time series First difference series k-th difference series Example xn xn xn n=,..n xn xn k x k n x n Zero crossings cont N D H( xn) H( xn) n Dk.n.4cos.5 n.cos.7 n.8cos.8 D( k xn) n =,, HOC order 8

29 HOC rate differences HOC rate HOC mean rate and STD for a recorded real-world magnetic backgrond HOC order k R R k R R k, k, k N Magnetic backgrond Target signal with magnetic backgrond A moving window of 4 samples was sed to calclate the HOC rate differences for the recorded real-world magnetic backgrond, and the target signal bried in the magnetic backgrond HOC order 9

30 n Adaptive detector decision index K k k Rwindow k Rbackgrond k Rbackgrond

31 Conclsion. Target-based approach MAD signal decomposition in the space of OBF. PCA techniqe - any specific path-time pattern of target-sensor movement. A few principal components corresponding to maximal eigenvales make p the OBF space. Signal norm in this space is sed to constrct an efficient detector. Noise-based approach No tentative assmption concerning mtal target-sensor movement can be made Statistical evalation of the magnetometer noise is implemented in a moving window. Adaptive minimm 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