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Detection of Obscured Targets: Signal Processing
James McClellan and Waymond R. Scott, Jr. School of Electrical and Computer Engineering
Georgia Institute of TechnologyAtlanta, GA 30332-0250
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 2
Outline
Introduction
Location with Acoustic/Seismic ArraysManeuvering Array (3x10)
Cumulative Array strategy for imaging
GPR and QuadtreeRegion Elimination
Accomplishments/Plans
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 3
Three Sensor ExperimentSensor Adjustments and Features
Adjustable Parameters for all three sensors
Frequency rangeFrequency ResolutionSpatial ResolutionIntegration time/bandwidthHeight above ground
Location
Possible Features for sensorsEMI
Relaxation frequencyRelaxation strengthRelaxation shapeSpatial response
GPRPrimary ReflectionsMultiple ReflectionsDepthSpatial Response
SeismicResonanceReflectionsDispersionSpatial response
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 4
Multi-Resolution Processing
GPR
EMI
Seismic
Imaging
SigProc
Imaging
Features
Features
Features
DecisionProcess
ExploitCorrelation
Training
Detect
Classify
ID
Quadtree Imaging@ increasingResolution(Eliminate Areas)
Target Localization@ specific sites
Ad-HocArray
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 5
Outline
Introduction
Location with Acoustic/Seismic ArraysManeuvering Array (3x10)
Cumulative Array strategy for imaging
GPR and QuadtreeRegion Elimination
Accomplishments/Plans
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 6
Seismic Sensor
Radar:R.F. Source,Demodulator, andSignal Processsing
Signal Generator
Elastic WaveTransducer
ElasticSurfaceWave
Mine
E.M. Waves
AirSoil
S N S
Wav
egui
de
Displacements
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 7
Ground Contacting Seismic Sensor Array Deployed on a Small Robotic Platform
Source Platform
Sensor Platforms
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 8
Home in on a Target
Problem Statement:Use a small number of source & receiver positions to locate targets, i.e., landmines
Minimize the number of measurements
Three phases1. Probe phase: use a small 2-D array (rectangle or cross)
Find general target area by imaging with reflected waves
2. Adaptive placement of additional sensorsManeuver receiver(s) to increase resolution
Use “Theory of Optimal Experiments”
3. On-top of the targetEnd-game: Verify the resonance
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 9
Adaptive Sensor Placement
Probe ArrayProbe Array findsgeneral target area
1
2
3Additional sensors are added to the “cumulative array”
Target
Source
On-top forresonance
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 10
Probe PhasePick five sensors in a cross patternApply Imaging algorithm and plot the surface over a search grid
Maneuver PhaseAdd one more sensor depending upon which direction to moveIncrease aperture of triangulationSpatial resolution increases which narrows down the area in which to search for target
Review from January
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 11
TS-50 (1cm)
Source at(-20,50)
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 12
1
2
3
Next Measurement
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 13
Want to formulate an optimal maneuvering strategy
Instead of adding One Sensor, move the Whole Array to the next optimal position
Append the array data at the new position with previous data
Estimate the target location
Find the “best” next sensor position
Repeat this until target is localized
Choose Next Sensor Position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 14
Steps in Optimal Maneuver
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 15
Wave Separation by Prony
Imaging algorithm
- Data Model
- ML solution for target position estimates
- Performance bounds for position estimates
Next optimal Array Position
- D-optimal Design
- Constrained Optimization
Steps in Optimal Maneuver
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 16
P-element array with position of every sensor is given in terms of array center Seismic wave penetration depth depends on frequency, hence a band of frequencies is used in processingK near-field wideband targetsIn the DFT, select ‘L’ Frequency components
Goal: estimate location (p) of the targets from measured array data
Data Model
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 17
Data Model
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 18
Target Position Estimate
The Cramer-Rao lower bound (CRLB) provides a lower bound for the variances of the unbiased estimators
CRLB requires the inverse of the Fisher information matrix
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 19
Fisher Information Matrix for Position Estimate
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 20
The theory of optimal experiments uses various measures of the Fisher information matrix to produce decision rules
Determinant
Trace
Maximum value along the diagonal
D-optimal Design uses the determinant
X. Liao and L. Carin, “Application of the Theory of Optimal Experiments to Adaptive Electromagnetic-Induction Sensing of Buried Targets,'' IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 26 , no.8, pp. 961−972, August 2004.
Theory of Optimal Experiments
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 21
Next Optimal Position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 22
Target position is estimated from reflected seismic energy
Source is nearbyNeed separation between forward and reverse waves
Array position has to be between source and targets always
Landmines reflections are not “omni-directional”
Next array position has to be Constrained“Between” source and estimated target positionTwo ways to implement constrained optimization
Circle constraint, or Penalty Function
Unique Problems for Seismic
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 23
Constrained optimization for next array position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 24
Single TS-50 landmine is buried at 1cmReflected waves are separated at each position by using a line array of 15 sensors (3cm apart)
Actual receiver is a single sensor (Synthetic Array)Measurements are grouped into line arrays
From each line array, three sensors at equal distance positions are chosen
With three line arrays, an array of nine sensors is available for 2-D imaging
Inverse of the cost function is plotted for imaging algorithm
Experimental Data Setup
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 25
Seismic Detection of VS-1.6 AT Landmine Buried 5cm Deep in Experimental Model
Landmine (22.2 cm diameter) buried 110 cm from first measurement location in 171 cm linear scan.
5 measurements with center line of sensor array along a line over the burial location.
Compressional, Rayleigh Surface, and ReflectedWaves.
Resonance of Landmine-Soil System.
Interactions of incident waves with buried landmine evident in measured data.
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 26
12
34
Wave Separation at each iteration: along top-most line array
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 27
All wave types
Only the reflected waveAfter Prony processing
Data Movies
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 28
ACTUAL TARGET : (135,135) ± 5ESTIMATE (102,120)
First Iteration
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 29
Circle constraintR=30cm Movement Penalty
Next Array Position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 30
Values calculated on half circle
Next array position values calculated on half circle of radius=30cm
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 31
ALONE CUMULATIVE
ACTUAL TARGET : (135,135) ± 5ESTIMATE: ALONE (100,127), CUM(112,127)
Second Iteration
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 32
Values calculated on half circle
Next Array Position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 33
ALONE CUMULATIVE
ACTUAL TARGET : (135,135) ± 5ESTIMATE: ALONE (143,138), CUM(127,133)
Third Iteration
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 34
ALONE CUMULATIVE
ACTUAL TARGET : (135,135) ± 5ESTIMATE: ALONE (124,144), CUM(146,139)
Fourth Iteration
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 35
All Four Iterations: Imaging with one array at a time
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 36
Four Iterations: Cumulative Imaging
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 37
2D array (3 X 10): Three lines having 10 sensors each
Sensors are ground contacting accelerometers
LabView is used to control the movement of array and seismic source firing and interface with MATLAB
Processing algorithms are implemented in MATLAB
Target is a VS1.6 mine buried at 5cm
Implementation
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 38
Experimental Setup of Seismic Landmine Detection Measurements
3 by 10 Element Array of Ground-
Contacting Sensors
Seismic Source
VS-1.6 AT Landmine (5cm deep)
50 Tons of Damp, Compacted Sand
Scan Region of 2m by 2m
45 cm
174 cm
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 39
Target is localized in four iterationsEach iteration takes 10 secs. for processing and 30 secs. for data acquisitionTotal time for four iterations is 2 minutesTypical raster scan takes a few hours to locate the target with a large number of measurements
EXPERIMENTAL SETUP
Demo in Sandbox
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 40
Four Iterations
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 41
Four Iterations: another run
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 42
We can further scan in line with the last estimated target positionExtract the reverse wave and try to locate the exact location of resonanceMovies shown the extracted wave with the line array of 30 sensors, which is moved toward the target with 1cm incrementTarget center is (50,50) and the starting location and position of target is shown
End-game Detection
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 43
Extracted reverse wave as array moves near and above the target
Movie: VS-1.6 (5cm)
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 44
Extracted reverse wave as array moves near and above the target
Movie: TS-50 (1cm)
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 45
Outline
Introduction
Location with Acoustic/Seismic ArraysManeuvering Array (3x10)
Cumulative Array strategy for imaging
GPR and QuadtreeRegion Elimination
Accomplishments/Plans
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 46
Detecting non-target areas by GPRΘ : Beamwidth of the transmitter and receiver antennas
dtr : Transmitter – Receiver Distance
h : Antenna Height
If there is no detection at this location
Shaded region does not contain targets
Instead of one step size.
Move transmitter by trdh −θtan2
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 47
Results from the GPR Air Measurements
Shotput in Air; Measured Data
10 20 30 40 50 60 70 80 90
100
200
300
400
500
600
700
800
900-200
-180
-160
-140
-120
-100
-80
-1 -0.5 0 0.5 1
x 10-9
-0.05
0
0.05
0.1
0.15
time(seconds)
Double Differentiated Gaussian Pulse
)(12FAPQ−=′ εσγ• Threshold :
• PFA is a user defined parameter
• σ2 is estimated from the data
Measured Data Theoretical Reference Signal
• Correlate with a delayed and scaled version of the transmitted signal
• Estimate the variance by taking average energy of the signals from non-target areas
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 48
Detection Test
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
0
2
4
6
8
10
12x 10
-8
Signal Correlation
Threshold
0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
0
2
4
6
8
10
12x 10
-8 Detection Test at X = -72cm
Signal Correlation
Threshold
0 200 400 600 800 1000 1200 1400 1600 1800 2000-1
-0.5
0
0.5
1
1.5x 10
-7 Detection Test at X = -54cm
Signal Correlation
Threshold
No detection, movetrdh −θtan2
Detection Test for first measurement point
Target Detected !
Apply time delay difference to find the apex of the hyperbola.
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 49
Monostatic Antenna in Homogeneous Medium
tα+1 Δ tα
z0
22
221
22202
21
2201
2202
2220
)12(4
))12()((4
))1((2
))((4
)(2
Δ+=−⇒
Δ++Δ+=⇒Δ++=
Δ+=⇒Δ+=
+
++
α
ααα
αα
αα
αα
αα
ctt
zc
tzc
t
zc
tzc
t
Does not depend on target depth!
Find α which indicates how many step size the antenna is away from the target position
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 50
Target Position Found
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3
4x 10
-5 Reading at X = -54
0 100 200 300 400 500 600 700 800 900 1000-3
-2
-1
0
1
2
3
4
5x 10
-5 Reading at X = -52
TDD
tα
tα+1
α = 26 is found and the antenna is moved to target position which is X = 0
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 51
AccomplishmentsDeveloped three sensor experiment to study multimodal processing
Developed new metal detector and a radarInvestigated three burial scenariosShowed responses for all the sensors over a variety of targetsDemonstrated possible feature for multimodal/cooperative processingDeveloped new 3D quadtree strategy for GPR data
Developed seismic experiments, models, and processing Developed optimal maneuver algorithm to locate targets with a seismic array Demonstrated reverse-time focusing and corresponding enhancement of mine signatureDemonstrated imaging on numerical and experimental data from a clean and a cluttered environmentModified time-reverse imaging algorithms to include near field DOA and range estimates. The algorithms are verified for both numerical and experimental data with and without clutter.Modified wideband RELAX and CLEAN algorithms for the case of passive buried targets. The algorithms are verified for both numerical and experimental data with and without clutter. Developed a vector signal modeling algorithm based on IQML (Iterative Quadratic maximum Likelihood) to estimate the two-dimensional ω-k spectrum for multi-channel seismic data.
Developed multi-static radarDemonstrated radar operation with and without clutter objects for four scenariosInvestigated pre-stack migration imaging of multi-static data
Buried structuresDeveloped numerical model for a buried structureDemonstrated two possible configurations for a sensorMade measurement using multi-static radar
MURI Review 3-Aug-05 Scott/McClellan, Georgia Tech 52
PlansThree sensor experiment (Landmine)
Incorporate reverse-time focusing and imagingIncorporate multi-static radarMore burial scenarios based on inputs from the signal processorsLook for more connections between the sensor responses that can be exploited for multimodal/cooperative imaging/inversion/detection algorithms
Imaging/inversion/detection algorithmsUse reverse-time ideas to characterize the inhomogeneity of the groundInvestigate the time reverse imaging algorithm for multi-static GPR data.Investigate the CLEAN and RELAX algorithms for target imaging from reflected data in the presence of forward waves with limited number of receivers.Develop elimination and end-game strategies for seismic detection with a maneuvering arrayInvestigate joint imaging algorithms for GPR and seismic data.
Buried Structures & TunnelsExperiments with multi-static radarDevelop joint seismic/radar experimentSignal Processing