localization of subsurface targets using optimal maneuvers of...

The Center for Signal & Image ProcessingThe Center for Signal & Image Processing Georgia Institute of TechnologyGeorgia Institute of Technology

Localization of Subsurface Targets using Optimal Maneuvers of Seismic Sensors

J. H. McClellan, W. R. Scott Jr., and M. Alam

2The Center for Signal & Image ProcessingThe Center for Signal & Image Processing

New Experimental Setup

Sensors will be on a small mobile robotic platform


Outline

Spectrum Analysis of Surface Waves

Seismic waves

Wave separation via Prony-based spectrum analysis technique

Processing results and applications

Locating Buried Targets (landmines) with Seismic Waves

Prototype seismic landmine system

Existing imaging algorithm

Maneuver algorithm

Waves separation and identification by Prony (IQML)

Imaging algorithm

Optimal sensor placement

Experimental results for different scenarios


Seismic Waves

Seismic waves due to point source on a free surface*

Two types of seismic wavesBody Waves

Primary (P) waves

Shear (S) waves

Surface WavesRayleigh Waves

First step is to identify Rayleigh wave and estimate its dispersion curves (Phase velocity vs. Frequency)

* C. T. Schroder, On the Interaction of Elastic Waves with Buried Landmines: An Investigation Using the Finite-Difference Time-Domain Method, Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA, 2001.


Parametric Model for Single Channel

Take 1-D Fourier transform over time

ARMA modeling is done across x to derive (k ,ω) model

Estimate ap(ω) and kp(ω) by IQML

( Steiglitz-McBride/ Prony)


VS-1.6 (AT land mine) at 5 cm

Raw collected Data


Spectrum Analysis (land mine case)

30 Sensors are used in processing

Experimental Data

TS-50 (1cm) VS-1.6 (5cm)


Extract Individual Mode Signals

Extract individual modes in the ( k , ω ) domaine.g., Obtain the reflected signal alone

Inverse transform to reconstruct the time domain signals:


Waves Extraction for VS-1.6

VS1.6 (5cm)

30 sensors are used in processing

Reflected Wave Forward Wave


VS-1.6 at 5 cm

Raw collected Data

Extracted

reflected wave

Extracted forward wave


Applications

Dispersion Curves :

To identify different waves modesTo estimate Green’s function To provide frequency range

In-situ estimation of various wave velocities like phase, group and effective phase velocity

Identify and separate individual waves reflected from buried targets


Outline

Spectrum Analysis of Surface Waves

Seismic wavesNew Prony based spectrum analysis techniqueExperimental results and applications

Locating Buried Targets (landmines) by using Seismic WavesPrototype seismic landmine systemExisting imaging algorithmProposed algorithm

Waves separation and identification by PronyImaging algorithmOptimal maneuveringExperimental results for different scenarios

Summary and Contributions


Prototype Seismic Mine Detection SystemInteraction of Rayleigh wave with mines can be used for detection and localization of mines

W. R. Scott Jr., J. S. Martin, and G. D. Larson, “Experimental model for a seismic landmine detection system,” IEEE Trans. Geoscience and Remote Sensing, vol. 39, pp. 1155–1164, June 2001.


Raw Data (TS-50 at 1cm, Area=(1.8 x 1.8)m)

a

dc

b

x

y


New Experimental Setup

Sensors will be on a small mobile robotic platform


Search-Mode Algorithm: 3 steps

1) Waves separation and identificationIsolate the reflected waves

2) Imaging algorithm for target position estimateMaximum Likelihood solution for target position estimate

Small array has poor resolution

3) Optimal maneuvering of arrayFisher Information Matrix

Algorithm is based on D-optimal design


Array Data ModelData model is given by (K targets, P sensors)

The elements of steering matrix A are given by

where is array center position and is target position in 2-D space


Target Position EstimateThe Maximum Likelihood estimate can be reduced to a cost function that depends on target position only

The best choice for target position z is

Fisher Information Matrix

1. Y. Zhou, P.C. Yip, and H. Leung, “Tracking the direction-of-arrival of multiple moving targets by passive arrays: Algorithm,” IEEE Trans. on Signal Processing, vol. 47, no. 10, pp. 2655–2666, October 1999

2. V. Cevher and J. H. McClellan, “Acoustic node calibration using a moving source,” IEEE Trans. on AES 2005


Theory of Optimal Experiments

Uses various measures of Fisher information matrix to produce decision rules

The various measures are Determinant, Trace and Maximum value along the diagonal

D-optimal design uses the Determinant

Select the next array position that reduces the uncertainty of the location estimate by maximizing the determinant of FIM

X. Liao and L. Carin “Application of the Theory of Optimal Experiments to Adaptive EMISensing of Buried Targets,'' IEEE Trans. PAMI, vol:26 , Aug. 2004


Next Optimal Array Position

To achieve the maximum information gain, the next optimal array position is obtained from

Constrained optimization to keep array between source and target

Circle Constraint: Next optimal position is located on (half) circle of radius ‘r’ from previous array center position

Radius ‘r’ can be made fixed or adaptive

Penalty Function: Penalize the main cost function as we move away from previous array center


Example: Starting position

Array=+, Position Estimate=■, Actual Mine Positions=o


Next Array Position

Values calculated on half circle of radius 30 cm

Circle constraint, R=30cm Penalty Function

Array=+, Position Estimate=■, Actual Mine Position=o


Four Iterations

Total # of Measurements = 180

Array=+, Position Estimate=■, Actual Mine Position=o


Implementation

A 2-D array (3 X 10)Three lines having 10 sensors each

Sensors are ground contacting accelerometers

To make the system robust for realistic situations, a multi-mode algorithm is proposed:

Start modeProbe Phase (2 or 3 fixed positions w.r.t source are used)

Search mode: 3 stepsOptimal maneuvering

Detection/Confirmation modeOn top of target (isolate the resonance)


Different Scenarios

Single target Case

Multi-target CaseStrategy for multi-target cases

Performance in the presence of clutter (rock)

Drunken waves case


“Real-Time” System (movie)


VS-1.6 at 5 cm (AT mine)

Probe Phase

Total Measurements = 150

Processing time = 4.5 minutes

Array=+, Position Estimate=◊, Actual Mine Position=o

After last move


Two Target Case (Two AT mines, 5cm)

−100 −50 0 50 1000.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

Degree

Val

ues

on

a C

ircl

e

Circle constraint, R = 25 cm

Penalty FunctionProbe Phase

30The Center for Signal & Image ProcessingThe Center for Signal & Image ProcessingNext Optimal Moves

After first optimal move After last optimal move

Array=+, Position Estimate=◊, Actual Mine Positions=o


Use the CLEAN Algorithm

“CLEAN” the effect of all targets except mth

Probe Phase After last optimal move

Array=+, Position Estimate=◊, Actual Mine Positions=o


Rock and Land Mine Case (@ 6.5 cm)

Find rock

Find mine

Array=+, Position Estimate=◊, Actual Mine and Rock Position=o


Clutter Case (rocks)TS50 at 1 cm VS2.2 at 5 cm

Array=+, Position Estimate=◊, Actual Mine Position=o, Rock Position=■


Apply CLEAN and Find Next

TS50 at 1 cm surrounded by 4 rocks

Array=+, Position Estimate=◊, Actual Mine Position=o, Rock Position=■


General Strategy for Multi-Target Cases

Assume one target: locate this strongest target

Apply CLEAN and find next strongest target

Stopping criterion:A power distribution (PD) is calculated at each Probe stage (Matched Field, Time-Reversal)

L1, L∞, LF , Matrix norms are also calculated for this PD

As we remove the strongest target, there is decrease in the power and norm values

Compare LF to “empty region” value for stopping criterion


Matrix Norms for Power Distribution

Converging to same value after all the strong targets are located and removed

Stop when the LF norm gets within

+- 15 % of the calibrated value L1

Lf

L∞


Drunken Waves (TS50 at 1 cm)

a b

dc

Area= 2 m by 1.5 mX

Y

38The Center for Signal & Image ProcessingThe Center for Signal & Image ProcessingProcessing Results

After three optimal moves Extracted reflected wave

Array=+, Position Estimate=◊, Actual Mine Position=o


Start and Detection/Confirmation mode

Start (Probe) mode2 or 3 fixed positions with respect to source are usedGoal is to have an initial estimate of target position

Detection/Confirmation mode *

A linear scan is done on a line connecting the source to the estimated target positionWaves are separated by using PronyEnergy-based imaging algorithm is used

* Imaging and detector framework for seismic landmine detection

Mubashir Alam and James McClellan, in SAM-2006


Energy based Imaging Algorithm

Separate the forward and reflected waves by using a window of M sensors, move Δx at each step

Reconstruct waves at the middle positionEstimate group velocity (Vg) from Prony

Calculate the time the wave takes to travel from source to a point x

Calculate the energy at point x by using a window of length L

where y is the product of the extracted reflected and forward waves, or the reflected wave alone.


VS-1.6 at 5 cm

Raw collected Data

Extracted reflected wave Product of reflected and forward

Extracted forward wave


Energy Calculation

Forming a window of length L

at each x positionEnergy at each x position


Confirmation Phase: (TS-50 & 4 rocks)

TS50

Only extracted reflected wave is used

Rock

Energy Calculation on top of the target


Summary

Spectrum analysis technique for surface waves identification and extraction

Data model and imaging algorithms for seismic detection of near surface buried targets (Landmines)

Algorithm for optimal maneuvering of array

Implemented the real-time version to simulate a mobile robotic sensor platform capable of sensing the environment on its own

Tested the algorithms for a variety of scenarios

Multi-target and Confirmation Phase

localization of subsurface targets using optimal maneuvers of...

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