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Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Radar Signal Processing: Opportunities for SSPers
Randy Moses
Dept. of Electrical and Computer Engineering The Ohio State University
This research was supported by AFOSR, AFRL, and DARPA
TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Context
n Advances in digital processing are enabling revolutionary opportunities for radar signal processing
n Opportunities for Statistical Signal Processing – Persistent sensing over space and time – More sophisticated radar image/volume reconstructions – Multi-function radars that can simultaneously perform imaging,
detection, moving object tracking and recognition, … – Uncertainty analysis and estimation bounds
n Challenges – Traditional models for radar backscattering may not apply over
wide angles – Large data, processing, and communications tasks
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Persistent, Wide-Angle Radar
Persistent Sensing enables: • High resolution, volumetric imaging of stationary objects and
scenes • Continuous tracking of moving objects
UAV UAV
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
SAR Data Collection
Frequency Space!
θ
φ
• • • • •
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
SAR Image Formation
n Traditional approach: tomography
n Tomographic image I(x,y) is a matched filter for an isotropic point scatterer at location (x,y). [Rossi+Willsky]
I(x,y)
2D IFFT
E(f,φ)→E(fx,fy)
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
3D Reconstruction
n Large data size and processing requirements
n Filled aperture is difficult to collect
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
9
X-Band Radar 3° aperture 1ft x 1ft res
Example: Ohio Stadium
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
10
SAR Image Detail
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Persistent, Wide-Angle SAR
Persistent Sensing enables: • High resolution, volumetric imaging of stationary objects • Continuous tracking of moving objects
UAV UAV
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
AFRL Gotcha Radar
5 Km
15.25 Km
Data Storage: 90 G samples/circle
Image formation: 45 Tflops/sec
Communications: 190 M samples/sec
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Wide Angle Scattering Behavior
n At high frequencies, radar backscatter is well-modeled as a sum of responses from canonical scattering terms.
n EM scattering theory provides a rich characterization of backscatter behavior as a function of object shape – Azimuth, elevation, frequency dependence – Polarization dependence – Phase response - range
n Most backscatter does NOT behave like a point scatterer over wide angles – Standard imaging is not statistically (close to) optimal
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Scattering Model
Jackson & RLM: 2009
Frequency!Dependence"
Location!Dependence!
"
Aspect!Dependence"
Polarization!Dependence!
f 2 [9.7, 10.3] GHz
�m = 3�
⇡ c2�fx
⇡ c2�fy
S(f,�, ✓) =
AHH AHV
AVH AV V
� ⇣jffc
⌘�
M(�, ✓) ej4⇡ffc
�R(x,y,z;a)
⇥ =
2
6666664
p0p0p0
p1 � p0...
pn�1 � p0
3
7777775
F⇥ =
2
6666664
F0 Fp0
p0p0
p1 � p0...
pn�1 � p0
3
7777775
~pk p0, p0
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Wide-Angle Data Collections
When the radar measurement extent is ≤ scattering persistence, the isotropic assumption is ~satisfied, and tomographic imaging is ~a matched filter.
azimuth
Sc. Ctr Responses
φc φc
α α
Radar measurements
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Wide-Angle Data Collections
For wide-angle measurements the isotropic scattering assumption breaks down.
– Tomography is no longer a matched filter
azimuth
Sc. Ctr Responses
φc φc
α α
Radar measurements
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
φc=−40°
φc =−20°
φc =0°
φc=20°
φc=40°
Frequency Support Image
φc=−40°
φc =−20°
φc =0°
φc=20°
φc=40°
Frequency Support Image
Scattering Aspect Dependence
Most scattering centers have limited response persistence 20° or less [Dudgeon et al, 1994]
Image response is no longer characterized by a single impulse response shape.
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Coherent wide-angle SAR Images
Coherent wide-angle image is not well-matched to limited persistence scattering behavior!
500 MHz Bandwidth 110 degrees az
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
GLRT Image Formation GLRT Image: Image I(x,y) is GLRT output at (x,y) to a limited-
persistence scattering center with center φc and width α."
αφαφ
αφαφ
width, center withimage std cc
c
yxR
yxRyxIc
=
=
),,,(
),,,(maxarg),(,
GLRT Image: !
Approximation: fix width α; quantize φc. !!Then the GLRT image is approximately
max over sub-aperture images.!
azimuth φc
α
RLM, Potter, Cetin: 2004
azimuth
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
GRLT Imaging
max
Frequency Data
GLRT Image
Generalizes Rossi+Willsky matched filter result to wide-angle imaging with limited-persistence scattering
RLM, Potter, Cetin: 2004
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Coherent and GLRT Image
110° Coherent Image 110° GLRT Image
4 GHz bandwidth
RLM, Potter, Cetin: 2004
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Sparse 3D Radar Reconstruction
n 3D radar reconstruction necessarily will use (very) sparse measurements
n Is the radar reconstruction sufficiently sparse to overcome measurement sparsity?
k-space
AFRL Backhoe Data Dome, with sparse “squiggle path” shown
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Polarization
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Squiggle Path 3D Tomographic Reconstruction
Largest
Smallest
Voxe
l mag
nitu
de Squiggle
PSF
Top 25 dB voxels shown
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Parametric: Canonical Scattering Model
Frequency!Dependence"
Location!Dependence!
"
Aspect!Dependence"
Polarization!Dependence!
Jackson & RLM: 2009
f 2 [9.7, 10.3] GHz
�m = 3�
⇡ c2�f
x
⇡ c2�f
y
S(f,�, ✓) =
AHH AHV
AVH AV V
� ⇣jffc
⌘�
M(�, ✓) ej4⇡ff
c
�R(x,y,z;a)
⇥ =
2
66666664
p0p0p0
p1 � p0...
pn�1 � p0
3
77777775
F⇥ =
2
66666664
F0 Fp0
p0p0
p1 � p0...
pn�1 � p0
3
77777775
~pk p0, p0
S(f,�, ✓) =
KX
k=1
AHH AHV
AVH AV V
�
k
✓jf
fc
◆�k
Mk(�, ✓) ej 4⇡f
f
c
�R(xk
,yk
,zk
;ak
)
Θ
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Sparsity – Measurements y (M £ 1) : sparse sampling of full (f,az,el) radar
measurement space – Reconstruction: x (N £ 1): sparse set of (x,y,z) locations with significant
radar scattering energy
Sparse reconstruction:
Nonparametric: lp Regularized Least-Squares
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Algorithmic Challenges
n For large scale problems, the algorithm can become very memory and computationally expensive. – E.g. for backhoe squiggle problem:
l M ≈ 105
l N ≈ 107
n A is structured and may not satisfy RIP for reconstruction samplings of interest. – Recent advances [e.g Austin, Fannjiang] incorporate structure in x to
allow high coherence in A.
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Squiggle Path Collection: lp Regularized LS Reconstruction
Top 30 dB voxels shown; p=1
Austin, Ertin, RLM, 2011
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Backhoe Squiggle Image
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Gotcha Vehicle Data
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Gotcha lp Reconstructions: Camry
Austin, Ertin, RLM, 2011
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Vehicle Classification
Camry
Maxima Prism Taurus
Malibu Sentra
• Six sedans from a 10-class problem • Spatially-varying signatures across
large scene
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Vehicle Classification; Attributed Point Sets
0
5
10
0
5
100
100
200
300
x(m)
Camry q=0.3, θv=0, pose=0°
y(m)0
5
10
0
5
100
100
200
300
x(m)
Camry q=0.0, θv=0, pose=0°
y(m) 0
5
10
0
5
100
100
200
300
x(m)
Camry q=0.4, θv=0, pose=216°
y(m)
>95% correct classification
PHD, dij
Squared Euclidian Distance Matrix
MDS
x
y
φ
Dungan and Potter, 2011
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Outline
n Radar 101 n Revisit modeling assumptions for wide angle radar n How can sparsity play a role?
– Parametric Modeling – Sparse Reconstruction
n Feature-Based Classification n Transmit adaptation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Joint Communication and Radar Sensing
Can adaptive transmit waveforms be used to simultaneously sense a scene and communicate sensed data to a receiver?
AFRL Gotcha Radar Communications:
190 M samples/sec
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
OSU Software Defined Radar
n Compact n Wide Bandwidth (125 MHz) n Real-time (DSP + FPGA)
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Joint Sensing-Comm Experiment
n Self-adaptive joint radar/communication system – PN transmit signal waveform
n Measured and communicated range-Doppler maps – nth range-Doppler map used to adapt (n+1)st waveform set.
Doppler Range
Measured Communicated Rossler, Ertin, RLM: 2011
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Take-Home Points
n Advances in sampling and digital processing are moving radar systems more firmly in the digital realm.
n Persistence and wide-angle sensing motivate rethinking the models and algorithms for radar processing.
n Effective 3D reconstruction from sparse apertures is possible – Surprising fidelity – Huge issues in computation, communication remain
n Huge opportunities for SSPers – Modeling; tractable algorithms; adaptation; persistent tracking;
classification; performance estimation
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Data Resources
n AFRL Sensor Data Management System – https://www.sdms.afrl.af.mil – Backhoe Volumetric Data (synthetic) – Civilian Vehicle Data Domes (synthetic) – Gotcha data (measured) – SAR-GMTI Challenge Problem
Presented at: the 2012 Statistical Signal Processing Workshop, Ann Arbor
Thank you!