Atmospheric Phase Screen in Ground Based Radar: Statistics ... · Atmospheric Phase Screen in...

Atmospheric Phase Screen in Ground Based Radar:

Statistics and Compensation

Andrea Monti Guarnieri, Lorenzo IanniniDipartimento di Elettronica e informazione, Politecnico di Milano

Davide GiudiciAresys s.r.l.

Contents

Ground‐based interferometry

Atmospheric delay

APS compensation techniques

Novel Model‐based approach

Conclusions

L. Iannini, A. Monti Guarnieri, D. Giudici Fringe 09 Workshop 30 /11/2009

Ground Based Interferometry


Antenna Axis

Range

Echo Amplitude

Sensor Module

Range Bin

Real aperture radar

Range resolution

Time sampling

m 5.0=Δρ

msec 10=Δt

IBIS‐S (*)

(*) IDS (Ingegneria dei Sistemi) S.p.A



Synthetic aperture radar

Amplitude

Resolution Pixel

Range Direction

Cross‐Range Direction

Focused Imageexample

(*) IDS (Ingegneria dei Sistemi) S.p.A

IBIS‐L (*) Max Cross‐Range resolution

Time sampling

mrad 5.4=Δϑ

min 5=Δt


Synthetic aperture radarI1

I2

Displacement

( ) 12*21 4

arg4 −Δ=⋅=Δ φ

πλ

πλ IId


Interf.

Model differential phase in time:

Effects of APS on a single target (example):

Atmospheric delay is the major responsible for target decorrelation

APS effects on data

( ) ndatm +Δ+Δ=Δ ρλπφ 4 Effects of clutter, thermal noise and

other minor decorrelation sources

Target displacement Atmospheric delay


x

y

0 500 1000 1500-2

-1

0

1

2

3

4

5

6

Image Nr.

Dis

plac

emen

t [m

m]

APS phase screen on individual target

Target displacement + noiseDisplacement introduced by APS

Target is not moving

Atmospheric Delay Model

Delay (in m) is produced by non‐zero refractivity index N

N is a function of pressure, temperature and humidity and is modeled in literature as the sum of dry and wet components

)1(10

)(10

6

6

−⋅=

= ∫−

nN

dllNdL

atm

( )( )HTNN

TPNN

NNHTPN

wetwet

dhydhyd

wethydd

,

,

),,(

=

=

+=


Pd Dry pressureT temperatureH Humidity

Delay StatisticsFrom radar acquisitions


Days

APS Variogram (Mountain)

[mm

2 ]

104

103

102

101

100

10-110-3 10-2 10-1 100 101

APS Variogram (stable targets)

10-1

[mm

2 ]

100

10-3

10-2

10-1 102101100 10310-2

10 ms 16.6 min

Urban (Milano)

Mountain

Seconds

Short‐time statistics

Longer‐time statistics10 days ‐> 10 cm2

Target Range 1200 m

Target Range 1200 m

PS (Permanent Scatterers) technique– Separation of long‐term independent APS

fluctuations from target’s almost linear displacement

DownsideNot suitable for short time intervals, APS cannot be separated from target displacement

GCP (Ground Control Point) technique1. Exploits a‐priori information on targets not

affected by motion (GCP)

2. Extraction from GCP of a first or second order delay model with respect to range

APS CompensationCurrent Techniques


GCP

PS

BolzanoSynthetic aperture radar

Complex scenario

A meteo station is placed nearby the radar: • Pressure

• Temperature

• Humidity

(*) courtesy of: Paolo Mazzanti, Università di Roma, “Sapienza”

Campaign

data available (*)

Bolzano


Milano

Top part of the cliff

Reflective rocks

Reflective Buildings

CampaignPicture from the instrument view


GCP‐Based CompensationEstimated Velocity


Top part of the cliff

Reflective rocks

Reflective Buildings

Goes Farther1 mm/day

Gets Closer1 mm/day

Point V

elocity

[m

m/day]

GCP‐Based CompensationTarget Displacement


Stable point

12:00 00:00 12:00 00:00 12:00 00:00 12:00 00:00 12:00-3

-2

-1

0

1

2

3Target displacement

Acquisition time [hh:mm]

[mm

]

20-May 21-May 22-May

PSpo-3824

Point affected by motion

12:00 00:00 12:00 00:00 12:00 00:00 12:00 00:00 12:00-4

-3

-2

-1

0

1

2

3

4Target displacement

Acquisition time [hh:mm]

[mm

]

20-May 21-May 22-May

PSgr-1919

• GCP technique limitations– The technique relies on the presence of GCPs

– In troublesome scenarios GCPs near the area of interest cannot be identified

• Model‐Based technique– Compensation through a suitable APS model by means of

available meteo data

Novel Approach

Novel approach


APS Model‐based Compensation

IdeaExploit the pressure, temperature and humidity data gathered by the meteo station placed nearby the acquisition site

ImplementationAtmosphere modeled as a uniform medium. The delay (refered to p‐th target) is:

Compensation (for p‐th target)

( ) ( )idi patmp ,6104~⋅⋅= −

λπφ

( )tpφ

( )tpε

( )( ) residualphase

phase wrapped observed

t

t

p

p

ε

φ

( ) ( )( ) ( ) pL

patm iNdlilrNidp

ρ66, 10,10 −− == ∫

r


Model‐based compensationPhase Residuals

-5

0

5

10

15

20

Phas

e [ra

d]

Range 570 mDataModelResidual

8.5 mm

7 days

12:00 00:0016/06/08

00:0017/06/08

00:00

18/06/0800:00

19/06/0800:00

20/06/0800:00

21/06/0800:00

22/06/0812:0012:0012:00 12:00 12:00 12:00 12:0000:00

15/06/08-4

-2

0

2

4

6

8

10

12

Phas

e [ra

d]


8.5 mm

4π = 1.7 cm


Model Refinement

Current model limitations:– Homogenous troposphere

– Meteo station calibration

Observation:– Residual phases show high

semblance with humidity

Solution

Calibration process through proper humidity tuning inside the delay model

30

40

50

60

70

80

90

100

Relative H

umidity [%

]

15/06/0816/06/08 17/06/08 18/06/0819/06/08 20/06/0821/06/08 22/06/08-1.5

-1

-0.5

0

0.5

1

1.5

2

Phas

e [ra

d]

Phase Residual for PS 327mHumidity


( ) ( ) βα +⋅= iHiHcal

Model‐based compensationPhase Residuals

-5

0

5

10

15

20

Phas

e [ra

d]


8.5 mm

7 days

12:00 00:0016/06/08

00:0017/06/08

00:00

18/06/0800:00

19/06/0800:00

20/06/0800:00

21/06/0800:00

22/06/0812:0012:0012:00 12:00 12:00 12:00 12:0000:00

15/06/08-4

-2

0

2

4

6

8

10

12

Phas

e [ra

d]


8.5 mm

4π = 1.7 cm


Without calibration

Without calibration

With calibration

With calibration

Humidity CalibrationPhase Residuals Considerations

-5

0

5

10

15

20 Far buildings - Range 570 m

Phas

e [ra

d]

DataModel with calib.Residual w/out calib.Residual with calib.

12:00 00:0016/06/08

00:0017/06/08

00:0018/06/08

00:0019/06/08

00:0020/06/08

00:0021/06/08

00:0022/06/08

12:0012:0012:00 12:00 12:00 12:00 12:0000:0015/06/08

7 days

15/06/08 16/06/08 17/06/08 18/06/08 19/06/08 20/06/08 21/06/08 22/06/08-4

-2

0

2

4

6

8

10

12

Pha

se [r

ad]

Near Buildings - Range 327 mDataModel with cal.Residual w/out cal.Residual with cal.

7 days

Most critical intervals occur at central hours of the dayTemperature registers the greatest fluctuations and reaches the highest values. In this situations even small inaccuracies in humidity produce significant errors in refractivity

30

40

50

60

70

80

90

100

Hum

idity

[%]

15/06/08 16/06/08 17/06/08 18/06/08 19/06/08 20/06/08 21/06/08 22/06/0810

15

20

25

30

35

40

Tem

pera

ture

[°C

]


Humidity CalibrationCoherences

7‐DAYS COHERENCE

200 400 600 800 10000

0.2

0.4

0.6

0.8

1

Range [m]

Coh

eren

ce

W/out compensationCompensation w/out calibrationCompensation with calibration


Conclusions


Different techniques for APS compensation on GB‐SAR data have been presented.

The model‐based approach led to significant improvements on near range targets, leaving a residual error in the order of 2 mm, starting from centimeters.

The proposed model tuning by means of humidity calibration reduced displacement fluctuations to less than 2 mm, for targets up to 500 m.

Still large errors exist in presence of turbulent APS, mainly near noon.• The prediction of these turbulences seems feasible from meteo measures• Its achievement is a key element for the selection of the acquisitions to

process.

The APS compensation at far ranges is still critical, the use of more than one meteo measure is under investigations.


Thank you

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