kei suwa, toshio wakayama, masafumi iwamoto mitsubishi electric co
DESCRIPTION
A Study on The Resolution Limit of Polarimetric Radar and The Performance of Polarimetric Bandwidth Extrapolation Technique. Kei Suwa, Toshio Wakayama, Masafumi Iwamoto Mitsubishi Electric Co. Information Technology R&D Center. Outline. - PowerPoint PPT PresentationTRANSCRIPT
A Study on The Resolution Limit of Polarimetric Radar
and The Performance of Polarimetric Bandwidth Extrapolation
Technique
Kei Suwa, Toshio Wakayama, Masafumi Iwamoto
Mitsubishi Electric Co. Information Technology R&D Center
Outline
• Background -- SAR resolution, PRF, and Polarimetry --
• Polarimetric Bandwidth Extrapolation (PBWE)• The Signal Model• Statistical Resolution Limit (SRL)• The Cramér-Rao Bound (CRB)• SRL and The Performance of PBWE• Conclusion
Range resolution is determined by the signal bandwidth.
Azimuth resolution is determined by the synthetic aperture length.
Background -- SAR resolution, PRF, and Polarimetry --
Range resolution : signal bandwidth / Azimuth resolution : synthetic aperture lengthRange resolution : signal bandwidth / Azimuth resolution : synthetic aperture length
orbit
freq. range
cr =2B
FT
2 2
Ra
L
L
R
Strip map mode
D
222
DDa
DHigher resolution with smaller aperture size .
Spotlight mode
: Signal Bandwidth
: Speed of light
c
B
rB
: wave length
: Synthetic Aperture length
LR : Range
Background -- SAR resolution, PRF, and Polarimetry
orbit
BeamIlluminationarea
Platform trajectory
Doppler Freq.
TimePRF
Due to PRF limitation, Polarimetric SAR often give up the resolution.Due to PRF limitation, Polarimetric SAR often give up the resolution.
Conditions of the PRF PRF must be higher than the signal
Doppler bandwidth, which is determined by the azimuth beam width.
PRF must be low enough so that the range ambiguity is sufficiently low.
The problem with Polarimetry Polarimetry requires sending H-polarization
pulse and V-polarization pulse. PRF gets lower for each polarization
channel, so polarimetric SAR often need to give up the resolution.
It would be nice if polarization information helps enhancing
the resolution
Background -- SAR resolution, PRF, and Polarimetry
Dr. Mihai Datcu “Semantic Content Extraction from High Resolution Earth Observation Images”
Background -- SAR resolution, PRF, and Polarimetry
… resolution refers to separate two or more nearby targets, i.e., to determine that there are two instead of one.
~Radar Handbook (1970) 4-2~
… resolution refers to separate two or more nearby targets, i.e., to determine that there are two instead of one.
~Radar Handbook (1970) 4-2~
What is “resolution”?
Background -- SAR resolution, PRF, and Polarimetry
range
1. Flat plate and dihedral corner reflector case
2. Two flat plates case
Polarizationvector
range
HH
VV
HH
VV
Flat plateDihedral corner reflector
101
10
-1
polarization vectors
Shh
Shv
Svv
=
Two vectors are orthogonal to each other.
Polarization information would not help
It seems to be possible that polarization information helps improving the “resolution”.It seems to be possible that polarization information helps improving the “resolution”.
Polarimetric Bandwidth Extrapolation (PBWE)
FFT
IFFT
Polarimetric Linear Prediction Model Estimation
range
range
i ii
iii
ivv
2B
c
2B’
c
freq.HH
HVVV
B
freq.
B’
HHHV
VV
HHHV
VV
HHHV
VV
• A polarimetric linear prediction model is fitted to the spectral data. • Then the HH,HV,VV spectral data is extrapolated up to B’.
• A polarimetric linear prediction model is fitted to the spectral data. • Then the HH,HV,VV spectral data is extrapolated up to B’.
Polarimetric Bandwidth Extrapolation (PBWE)
http://www.emi.dtu.dk/research/DCRS/Emisar/emisar.html
EMISAR : dual frequency (L- and C-band) polarimetric Synthetic Aperture Radar (SAR) system developed at Technical University of Denmark.
Storebaelt : the great belt
range
azimuth
We have empirically shown that Polarization information does contribute tothe resolution enhancement
We have empirically shown that Polarization information does contribute tothe resolution enhancement
Resolution
“Nominal” Resolution does not reflect polarization properties
Fourier analysis would give the nominal resolution. Parametric spectrum analysis would achieve higher resolution.
--- e.g. PBWE, MUSIC, ESPRIT, MVM, MEM, etc
cr =2B
2 2
Ra
L
Quantitative analysis on the influence of polarization information onthe resolution is provided in this presentation.
Quantitative analysis on the influence of polarization information onthe resolution is provided in this presentation.
range azimuth
We are interested in the resolution achievable by “polarimetric” parametric spectrum analysis method such as PBWE.
We are interested in the resolution achievable by “polarimetric” parametric spectrum analysis method such as PBWE.
Statistical Resolution Limit (SRL)
• “Statistical Resolution” : Δd
• “Statistical Resolution Limit” : min(Δd)
[1] S.T.Smith, “Statistical Resolution Limits and the Complexified Cramér-Rao Bound,” IEEE Trans. Signal Process., vol. 53, no. 5, pp1597—1609, May 2005
The estimate of target separation contains error due to noise. If the expected error is sufficiently small compared to the real separation, we can claim that these targets are resolvable.
true target separation = d
d̂
d̂
d
2
ˆ ˆˆs.t. , where
d dd d d d d E d d
2
ˆ ˆˆmin s.t. min , where
d dd d d d d E d d
SRL is a simple metric that provides the highest resolution achievableby any unbiased parametric spectral estimator.
SRL is a simple metric that provides the highest resolution achievableby any unbiased parametric spectral estimator.
The Signal Model
clutter
range
target
HH
HV
VV
power
scene
Polarization property
Polarimetricchannels
The signal at each resolution cell is represented by a polarization vector.The signal at each resolution cell is represented by a polarization vector.
The Signal Model
denotes the long column vector formed by concatenating the columns of X.
:z Va n
HE nn R I
11, exp : :
H
Nf z a z Va R z Va
R
n: Gaussian noiseV: matrix of steering vectorsa: complex amplitudes of
the targetsN: the number of samples
The probability density function of the data z is:
"X : "
1 1jj
a ae e
1
2
1
2
1
1
Nj
Nj
e
V
e
freq.
B
ranged
VVHH
11a
HHVV
target #2target #1
12a21a
22a
Two closely located point targets signal model is considered.Two closely located point targets signal model is considered.
The Cramér-Rao Bound (CRB)
2; ; log | ,a aG E f z a
1
|| | aVar a CRB a G
ˆ |2d
Nd CRB a
11, exp : :
H
Nf z a z Va R z Va
R
The CRB for the parameters are derived.The CRB for the parameters are derived.
• Likelihood function of the parameters
• Fisher Information Matrix
• Cramér-Rao Bound on the covariance of the estimator of the parameters
• Convert the CRB to the lower bound of the target separation d
The Cramér-Rao Bound (CRB)
The CRB for 2 polarimetric channels case is derived.The CRB for 2 polarimetric channels case is derived.
• The lower bound for the target separation
(Polarimetric / 2 channels / White Gaussian noise)
• cf) when ∆φ →large (two targets are far away)
0
2 2 20 1
[ ]2 cos / 2G
dNStd d Tr D D FRC
a d d
2
0 2 2
2
1 2 2
(0) '( )"(0)
(0) ( )
( ) '( )"( )
(0) ( )
s sd s
s s
s sd s
s s
sin2
( )1
sin2
N
s
1
2 "(0)
NStd d
a s
0 1"(0), 0d s d
SRL and the Performance of PBWE
The PBWE achieves CRL and SRL fairly well.The PBWE achieves CRL and SRL fairly well.
(a) ∆Ψ = 0 (b) ∆Ψ = π/6
Δd=0.4Δd=0.1
5
ranged
jaea jaea
HH
VV
• Monte Carlo iteration 1,000 times.• N=50 / SNR=40dB / order of the linear prediction filter = 6• If the polarization properties of the two targets are the same
polarization information does not help (a).
SRL and the Performance of PBWE
The SRL is minimum when the polarization properties of the two targets are orthogonalThe SRL is minimum when the polarization properties of the two targets are orthogonal
ranged
jaea jaea
HH
VV
(c) ∆Ψ = π/2 (d) ∆Ψ = π• The SRL is improved to ¼ by using polarization information,
when the polarization properties of the two targets are orthogonal (d).
• (d) corresponds to a case where two targets are trihedral and dihedral corner reflectors.
Conclusion
• The SRL of polarimetric radar is derived and compared with that of single polarization radar
• It has been shown analytically that the polarization information helps improving the resolution when the polarization properties of the two closely located targets are different, and thus on the average, the polarimetric radar outperforms single polarization radar. – e.g. If the polarization properties of the two closely located
targets are orthogonal to each other, the SRL is improved to ¼ by using polarization information.
• It has been shown that the resolution of the PBWE previously proposed by the authors almost achieves the SRL.