The Center for Signal & Image Processing
Georgia Institute of Technology
Localization of Subsurface Targets using Optimal Maneuvers of Seismic Sensors
J. H. McClellan, W. R. Scott Jr., and M. Alam
New Experimental Setup
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Sensors will be on a small mobile robotic platform
Outline
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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
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Two types of seismic waves Body Waves
Primary (P) waves Shear (S) waves
Seismic waves due to point source on a free surface*
Surface Waves
Rayleigh 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
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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
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Spectrum Analysis (land mine case) TS-50 (1cm)
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VS-1.6 (5cm)
30 Sensors are used in processing Experimental Data
Extract Individual Mode Signals
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Extract individual modes in the ( k , ω ) domain e.g., Obtain the reflected signal alone
Inverse transform to reconstruct the time domain signals:
Waves Extraction for VS-1.6
Reflected Wave
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Forward Wave
VS1.6 (5cm) 30 sensors are used in processing
VS-1.6 at 5 cm Raw collected Data
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Extracted forward wave
Extracted reflected wave
Applications
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Dispersion Curves : To identify different waves modes To 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
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Spectrum Analysis of Surface Waves Seismic waves New Prony based spectrum analysis technique Experimental results and applications
Locating Buried Targets (landmines) by using Seismic Waves Prototype seismic landmine system Existing imaging algorithm Proposed algorithm Waves separation and identification by Prony Imaging algorithm Optimal maneuvering Experimental results for different scenarios
Summary and Contributions
Prototype Seismic Mine Detection System
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Interaction 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
b
y c
d x
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New Experimental Setup
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Sensors will be on a small mobile robotic platform
Search-Mode Algorithm: 3 steps
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1) Waves separation and identification Isolate the reflected waves
2) Imaging algorithm for target position estimate Maximum Likelihood solution for target position estimate Small array has poor resolution
3) Optimal maneuvering of array
Fisher Information Matrix Algorithm is based on D-optimal design
Array Data Model
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Data model is given by (K targets, P sensors)
The elements of steering matrix A are given by
where is array center position and position in 2-D space
Target Position Estimate
is target
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The 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
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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 EMI Sensing of Buried Targets,'' IEEE Trans. PAMI, vol:26 , Aug. 2004
Next Optimal Array Position
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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
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Array=+, Position Estimate=■, Actual Mine Positions=o
Next Array Position Circle constraint, R=30cm
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Penalty Function
Values calculated on half circle of radius 30 cm Array=+, Position Estimate=■, Actual Mine Position=o
Four Iterations
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Array=+, Position Estimate=■, Actual Mine Position=o
Total # of Measurements = 180
Implementation
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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 mode
Probe Phase (2 or 3 fixed positions w.r.t source are used)
Search mode: 3 steps
Optimal maneuvering
Detection/Confirmation mode
On top of target (isolate the resonance)
Different Scenarios
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Single target Case Multi-target Case Strategy for multi-target cases
Performance in the presence of clutter (rock) Drunken waves case
“Real-Time” System (movie)
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VS-1.6 at 5 cm (AT mine)
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Total Measurements = 150 Processing time = 4.5 minutes
After last move
Probe Phase
Array=+, Position Estimate=◊, Actual Mine Position=o
Two Target Case (Two AT mines, 5cm)
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Penalty Function
Probe Phase
1.12
Values on a Circle
1.1 1.08 1.06 1.04 1.02 1 0.98 0.96 −100
−50
0
Degree
Circle constraint, R = 25 cm
50
100
Next Optimal Moves After first optimal move
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After last optimal move
Array=+, Position Estimate=◊, Actual Mine Positions=o
Use the CLEAN Algorithm
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“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)
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Find rock
Find mine
Array=+, Position Estimate=◊, Actual Mine and Rock Position=o
Clutter Case (rocks) TS50 at 1 cm
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VS2.2 at 5 cm
Array=+, Position Estimate=◊, Actual Mine Position=o, Rock Position=■
Apply CLEAN and Find Next
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TS50 at 1 cm surrounded by 4 rocks
Array=+, Position Estimate=◊, Actual Mine Position=o, Rock Position=■
General Strategy for Multi-Target Cases
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Assume one target: locate this strongest target Apply CLEAN and find next strongest target Stopping criterion: z
z z
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
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L∞ Lf
Stop when the LF norm gets within +- 15 % of the calibrated value
L1
Converging to same value after all the strong targets are located and removed
Drunken Waves (TS50 at 1 cm)
a
b
Y c
d
X
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Area= 2 m by 1.5 m
Processing Results After three optimal moves
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Extracted reflected wave
Array=+, Position Estimate=◊, Actual Mine Position=o
Start and Detection/Confirmation mode
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Start (Probe) mode 2 or 3 fixed positions with respect to source are used Goal 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 position Waves are separated by using Prony Energy-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
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Separate the forward and reflected waves by using a window of M sensors, move Δx at each step Reconstruct waves at the middle position z Estimate group velocity (Vg) from Prony z
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
z
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
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Extracted forward wave
Product of reflected and forward
Energy Calculation
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Forming a window of length L at each x position
Energy at each x position
Confirmation Phase: (TS-50 & 4 rocks)
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TS50 Energy Calculation on top of the target
Rock
Only extracted reflected wave is used
Summary
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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
