Advancements on interferometric radar: studies and applications

Coordinatore: Prof. Carlo Atzeni

Tutor: Prof. Massimiliano Pieraccini

Candidato: Andrea Barucci

CorsodiDottorato

in IngegneriadeiSistemiElettronici

XXIII ciclo

Introduction

Applicationofadvancedmonitoringtechniquesto the monitoring and

characterizationofquarriesfor the profit optimization and for the

safety and environmentalprotectionof the quarrymining

CWSF Ground BasedSynthetic Aperture Interferometric radar

CentralFrequency 16.75 GHz

Banwidth 400 MHz

Tx Power 26 dBm EIRP

SAR scan length 2 m

SAR acquisition time 4 min (minimum)

Power consumption < 40 W

Radar installation

Powersupply system

Wide angle SAR

Start 16 feb 2009

End 25 mar 2009

Days of measurement 39

N. Radar acquisitions about 600 (1 every 2 hours)

Measurementcampaign

RCS SAR image

Range

resolution

0.5 m

Cross

range

resolution

5mrad

Interferograms in scarp area

(m) (m) (m)

(m)(m)(m)

(m)

(m)

(m)

(m)

(m)

(m)

Eachinterferogramrelatesto a timelapseoftwohours

Interferometricanalysisin the wallarea

1. PSsselection

DispersionIndex

2.

Atmosphericmeanphasescreen

removal3. Calculationofdisplacements

About 50.000 PSsselected in

all the area

Interferometricanalysis in the wallarea

cum

ula

ted

dis

pla

cem

ent

Timeperiod: 23 days

Selectionof 50 pixels in the wall

Interferometricanalysis in the wallarea

cum

ula

ted

dis

pla

cem

ent

Timeperiod: 3days

Selectionof 50 pixels in the wall

Validationof the methodby a corner reflector

Distance: 800 m

Actual

(mm)

Measured

(mm)

Error

(mm)

2.0 2.05 0.05

1.0 0.89 0.11

0.5 0.53 0.03

Interferometric DEM of the quarry

Radar

Laser

Conclusions• A ground based Synthetic Aperture Interferometer was

successfully tested for the first time in a quarry.

• The system showed an accuracy of few tenths of a millimeterin displacement’s measurement, over a long period and at800 meters of distance.

• In short term measurements a simulation showed anaccuracy in measurement of displacements of the order of atenth of a millimeter.

• DEM reconstruction showed some limitations especially inhigh slopes.

S. T. Bramwell, P. C.W. Holdsworth, and J.-F. Pinton,

Universality of rare fluctuations in turbulence and critical

phenomena, Nature 396, 1998

Physical Review Letters [2000, 2005, 2008]

• Long term atmospheric artifacts on GB-SAR are known

• Radar signal propagation through tropospheric turbulence is a new

research topic

Data

Analysis

Classic:Fluctuations of signal

as a function of

turbulence

Modern:Correlated systems,

Gumbel statistics

Experiment

Universal fluctuations in tropospheric radar measurements

Introduction

Firenzuola scenario

Scenario and raw-data

CR distance

Ultrasonic Anemometer / Weather sensor

Radar sampling freq Range Resolution

Observational time

65 m 4/1Hz About 50 Hz 1 m 6 h

Detrending – High-pass filter

• Turbulent phenomena occur

at the micro scale,

corresponding to distances

shorter than 1 km, which are

the usual working distances for

a GB-SAR.

• We use a moving average to

remove the fluctuations on

temporal scales greater than 30

minutes

Time series data analysis

We use overlapping

temporal windows, with

length of about 30

minutes:

- About 10^5 points ->

rare fluctuations & good

statistics

- Constant Reynolds

number

Turbulent Kinetic

Energy (TKE) is a

measure of the

turbulence

Wind fluctuations dependency

R = 0.98 R = 0.89

Radar signal statistics & Correlated Systems

Correlated

Systems

Turbulence

Ising& 2D XY

Forest fires,

etc.

River water

level

Radar signal through a

turbulent atmosphere

Global quantity

Generalized

Gumbel PDF

Radar Data

statistics?

Generalized Gumbel

• Generalized Gumbel describes the fluctuations in Correlated Systems, its

shape depends on a real parameter a

• As a varies, the shape of the distribution varies from a completely

asymmetric, negatively skewed, distribution to a symmetric one quite similar

to a Gaussian function

• The parameter a has been proposed to be inversely related to the correlation

length of the system

Data distribution

• Fit of the data with the GG(a)

• Amplitude statistic appears to fit with the GG

• Phase statistic doesn’t show the same behaviour

• The radar data distributions calculated over the analysis windows show different means and standard deviations new method from Nature

Amplitude

Phase

• a is determined by the turbulence strength

• In hard windy conditions, a is nearly equal to pi/2 which is the value

for which GGa is approximately the Bramwell-Holdsworth-Pinton

distribution observed in turbulence and critical systems

Andrea Barucci

Conclusions

• The radar signal statistic:

– It is influenced by the turbulence

– It is a global quantity able to measure the “correlation of the

atmosphere” at the micro-scale

• We confirm the adequacy of the Gumbel statistic to describe

highly correlated complex systems

• SAR images - turbulence: work in progress• Paper published by Europhysics Letters: A. Barucci, G. Macaluso, D. Mecatti, L. Noferini, D. Fanelli, A.

Facchini, M. Materassi, M. Pieraccini and C. Atzeni, Universal fluctuations in tropospheric radar

measurements, EPL, 89 (2010) 20006, DOI 10.1209/0295-5075/89/20006