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Davide GiudiciAndrea Monti Guarnieri, Daniele
Mapelli, Fabio Rocca
Generation and calibration of high resolution DEM from single baseline space-borne interferometry: the ‘split-
swath’ approach
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Outline
• Introduction: single pass Digital Elevation Models (DEMs) generation missions
• Urban and peri-urban DEMs
• A single-pass Ka-band interferometer concept
• Vertical accuracy performance model – the need of baseline calibration
• The split-swath approach for efficient calibration
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DEM generation and Single pass interferometry
• The generation of Digital Elevation Models (DEMs) through single pass SAR interferometry is a well known application
• It takes advantage of the almost null target de-correlation• SRTM and TANDEM-X missions are successful examples
• Is it possible (and useful?) to go beyond this accuracy with SAR DEMs?
kellylab.berkeley.edu
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Urban and peri-urban
• [Brunner, 2010]: “TerraSAR-X VHR data are not enough, horizontal resolution < 3 m and vertical < 1 m is needed to count floors”.
• [Cellier, 2006]: Incidence angle is critical: observations is limited by shadow: if layover is solved by polarimetry,
with 24°, urban roads are
invisible if L<0.88H
• [Allenbach 2010]: In urban areas, very high resolution optical sensors provide analogous results, especially if flood traces are represented by apparent water. SAR results in rural landscape are relevant; this pertinence is not observed in urban areas
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PS urban DEMs
• [Perssin 2008]: High 3D resolution can be achieved by repeat pass interferometry over PS (< 1 m from coarse resolution ERS)
• with possible layover separation due to tomography [Reale 2011]
• and polarimetry [Perissin 2007]
• PS + radargrammetry [Adam 2010]
• at very «high» density (100 000 PS/Km2, [Gernhart 2010])
Higher density can only be achieved with finer resolution and without temporal decorrelation
[Adam igarss 08]
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Single pass interferometer at Ka-band
Ka band – 2.5 inch from SANDIA Natl Labs
• We concentrate on a single-pass interferometer in Ka band (35 GHz)
• Goal single look resolution: < 1x1 m
• Boom length is paramount to maintain low height of ambiguity.
Need >20 m to have q2
< 60 m
Boom
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Approach to performance models definition
3D SAR location equations
1.The range equation:
2.The Doppler equation:
3.The interferometric equation:
11th May 2011
The following simplifications are introduced:
1. Ignore bistatic delay2. Small errors (linearization)3. Zero Doppler pointing : The problem
can be handled in a simplified 2D geometry
x
z
P(0, q)r
O y '
rP
SM
SS
By
B
Bz
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Vertical accuracy model
• The simplified interferometric equations are obtained:
• Linearization close to the optimal soultion leads to the 3D location error, due both to measures (x)
and geometry (θ)
Position covariance
2
2
2 sin4
n
q Br
1: error due to phase 2: term due to unknown geometry: parallel and normal baseline
2
2
2
2
sin
sin4
p
n
Bn
p
p
Bnn
BrB
B
Br
B
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Phase variance model
• Assuming that the SAR image has high resolution compared to the final DEM resolution.
• The phase variance is computed with the CRB formula, valid for high number of looks:
• With this formula, the phase variance depends on:1. The total coherence ()
•2. The total number of independent looks (NL)
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40 50 60 70 80 90 100 110 1200.9993
0.9994
0.9995
0.9996
0.9997
0.9998
0.9999
1
Heigth of ambiguity [m]
vol
[-]
Ext. coeff: 1.00e-001dB/KmExt. coeff: 2.00e-001dB/KmExt. coeff: 3.00e-001dB/KmExt. coeff: 4.00e-001dB/Km
• Five contributions are considered:- Thermal noise- Ambiguity- Volume- Coregistration error- Quantization error
Total coherence computation
Volumetric decorr,
-10 -8 -6 -4 -2 0 2 4 6 8 100.65
0.7
0.75
0.8
0.85
0.9
0.95
1
sigma0 [dB]
thc
lut [-
]
NESZ= -15 dB
SNCR: 10dBSNCR: 15dBSNCR: 20dB
-25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -150.93
0.94
0.95
0.96
0.97
0.98
0.99
1
RASR [dB]
am
b [-]
AASR: -15dBAASR: -20dBAASR: -25dB
Thermal noise decorr,
Ambiguity decorr,
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Target urban DEMs
11
UoM Initial value(SOW)
Single-pass interferometry
“HRTI+”
Single-pass interferometry
“HRTI++”Remarks
Wavelength m 0.0084 0.0084 0.0084 Corresponding to 35.75 GHz
Acquisition mode - High resolution mode TOPSAR 2-swaths Stripmap
Output DEM resolution m x m 12 x 12 6x 6 4 x 4 >HRTI-3
Output DEM height accuracy 1 m 0.86 0.75 0.7 >HRTI-3
Orbit altitude Km 500-800 500 500 Average orbit altitude
Look angle deg 25-45 35 25 HRTI+: average caseHRTI++: analysis from Polimi
Terrain slope deg 0 5 5 Assumed as margin (Impact on spectral shift)
Topography extent m <9000 9000 9000 Assumed as margin
Calibration DEM H-resolution m 90 90 90 SRTM DEM
Calibration DEM V-res 1 m 5 5 5 SRTM; DEM
In the following analysis, two target-DEM cases have been considered, corresponding to two single pass interferometry systems (Stripmap and TOPSAR).
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Height accuracy with perfect geometry
12
20 40 60 80 100 120 140 160
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
X: 144Y: 0.4429
Total number of Looks
DE
M re
triev
al e
rror 1
[m
]Total Coherence: 0.7Total Coherence: 0.8Total Coherence: 0.9
HRTI3: q =0.86m
NL=144: DEM resolution 12x12 m2
Interf. resolution: 1 m2
NL=36: DEM resolution 6x6 m2
Interf. resolution: 1 m2
NL=36: DEM resolution 12x12 m2
Interf. resolution: 4 m2
This is the contribution to overall height retrieval accuracy that cannot be compensated through calibration
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Height accuracy with geometry errors
13
0 50 100 150 2000
10
20
30
40
50
60
70
80
90
100
Normal baseline calibration error 1 [ m]
Par
alle
l bas
elin
e ca
libra
tion
erro
r 1
[ m
]
DEM retrieval error 1 due to Bp and Bn [m]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.86/20.6 m
2
2
2
2
sin
sin4
p
n
Bn
p
p
Bnn
BrB
B
Br
B
The normal and parallel baselines have to be known with an accuracy in the order of 10-5 m
100001
80008.0
Be
n
Bn
Parallel baseline: - error increasing with distance («DEM rotation»), - independent on the elevation:
Bpn
q Br sin
2
Normal baseline:
- Error proportional to the elevation:
Calibration needed !
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Baseline calibration methods
• Baselines can be calibrated considering known topography control points:
- Reference DEM (e.g. SRTM)- A flat surface (the sea level)
- A least squares method is considered to compute the calibrated baseline
- Two calibration scenarios are considered:
18 km
18 km
75 km
“Continuous swath” “Split swath”
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Baseline calibration accuracy comparison
15
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
120
140
X: 20Y: 23.52
Azimuth length [Km]
Par
alle
l bas
elin
e ca
libra
tion
erro
r 1
[ m
]
X: 10.5Y: 22.95
Sub-swath size: 10 KmSub-swath size: 15 KmSub-swath size: 20 Km
2 4 6 8 10 12 14 16 18 200
10
20
30
40
50
60
70
80
90
100
Azimuth length [Km]
Nor
mal
bas
elin
e ca
libra
tion
erro
r 1
[ m
]
Sub-swath size: 10 KmSub-swath size: 15 KmSub-swath size: 20 Km
Single swath (dashed line)
Split swath (solid line)
Single swath (dashed line)
Split swath (solid line)
Parallel Baseline Normal Baseline
Split swath allows calibration within a length of 5 Km
With continuous swath more than 20 Km are needed: it is not the preferred solution
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Calibration methods comparison
Calibration
method PRO CONS
Continuous swath -Wider continuous swath- Smaller beam elevation angle
- A long observation is needed to calibrate and models for vinbration
Split swath - Allows doing the calibration in short length: large low- frequency boom errors are tolerated
-No wide continuous swath-High beam elevation capability required
In the table the two calibration methods are compared, identifying the first pros and cons.
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DEM retrieval accuracy budget summary (HRTI+)
17
Item UoM value
Wavelength m 0.0084
Output DEM resolution mxm 6 x 6
Slant range Km 620
Look angle deg 35
Terrain slope deg 5
Topography extent m 9000
Volume depth m 0.9
Extintion coefficient dB/m 0.2
Reference DEM resolution m 90
Reference DEM 1 m 5
SNCR dB 30
NESZ dB -16
Sigma0 dB -4 *
AASR dB -20
RASR dB -20
SQNR dB 20
Image size across track Km 18
Azimuth calibration length Km 5
Normal baseline m 22
Range bandwidth MHz 500
Azimuth resolution m 2
Heigth of ambiguity m 59.18
Coregistration error m 0.001
Item UoM value
Coherence clutt+thermal - 0.9397
Coherence volume - 0.9996
Coherence coreg. - 0.9999
Coherence ambiguity - 0.980
Coherence quantization - 0.99
Total coherence - 0.91
Interferogram gr.rg.resolution
m 0.6
Number of looks - 29.89
Phase variance rad^2 0.00334
Height error std with perfect geometry
m 0.675
Parallel baseline std after cal
m 16
Normal baseline std after cal
m 1.0
Height error std due to geometry only
m 0.34
Total height error std m 0.76
*Ulaby F.; Moore R.; Fung A., Microwave Remote Sensing, Active andP i V l III
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DEM retrieval accuracy budget summary (HRTI++)
18
Item UoM value
Wavelength m 0.0084
Output DEM resolution mxm 4 x 4
Slant range Km 556
Look angle deg 25
Terrain slope deg 5
Topography extent m 9000
Volume depth m 0.9
Extintion coefficient dB/m 0.2
Reference DEM resolution m 90
Reference DEM 1 m 5
SNCR dB 30
NESZ dB -16
Sigma0 dB -4 *
AASR dB -22
RASR dB -22
SQNR dB 20
Image size across track Km 9
Azimuth calibration length Km 5
Normal baseline m 22
Range bandwidth MHz 500
Azimuth resolution m 1
Heigth of ambiguity m 36.3
Coregistration error m 0.001
Item UoM value
Coherence clutt+thermal - 0.9397
Coherence volume - 0.9989
Coherence coreg. - 0.99998
Coherence ambiguity - 0.9875
Coherence quantization - 0.99
Total coherence - 0.9178
Interferogram gr.rg.resolution
m 0.88
Number of looks - 18
Phase variance rad^2 0.0052
Height error std with perfect geometry
m 0.58
Parallel baseline std after cal
m 16
Normal baseline std after cal
m 1.0
Height error std due to geometry only
m 0.34
Total height error std m 0.68
*Ulaby F.; Moore R.; Fung A., Microwave Remote Sensing, Active andP i V l III
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Conclusions
• The preliminary models to assess vertical accuracy for a single-pass, high resolution, Ka-band interferometer have been studied.
• Modeling method is based on small error assumption (linearization)
• It results that the vertical accuracy is the sum of two main contributions:A. Error due to phase variance non-calibrableB. Error due to unknown geometry calibration NEEDED
• Accuracies better than HRTI3 can be obtained• With the split swath calibration technique, sufficient
accuracy on the baseline calibration can be achieved in less than 1s