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

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

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

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

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]

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

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

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

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)

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,

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).

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

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

qq

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 !

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”

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

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.

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

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

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