Estimation of the Temporal Evolution of the Deformation Using Airborne Differential SAR Interferometry
ABSTRACT This paper presents airborne differential synthetic aperture radar (SAR) interferometry results using a stack of 14 images, which were acquired by the Experimental SAR system of the German Aerospace Center (DLR) during a time span of 2.5 h. An advanced differential technique is used to retrieve the error in the digital elevation model and the temporal evolution of the deformation for every coherent pixel in the image. The two main limitations in airborne SAR processing are analyzed, namely, the existence of residual motion errors (RMEs) (inaccuracies in the navigation system on the order of 1-5 cm) and the accommodation of the topography and the aperture dependence on motion errors during the processing. The coupling between them is also addressed, showing that the estimation of the differential RME, i.e., baseline error, can be biased when using techniques based on the coregistration between interferometric looks. The SAR focusing chain to process the data is also presented together with the modifications in the differential interferometry processor to deal with the remaining baseline error. The detected motion of a corner reflector and the measured deformation in several agricultural fields allows one to validate the proposed techniques.
- SourceAvailable from: Alessandro Ferretti[show abstract] [hide abstract]
ABSTRACT: Discrete and temporarily stable natural reflectors or permanent scatterers (PS) can be identified from long temporal series of interferometric SAR images even with baselines larger than the so-called critical baseline. This subset of image pixels can be exploited successfully for high accuracy differential measurements. The authors discuss the use of PS in urban areas, like Pomona, CA, showing subsidence and absidence effects. A new approach to the estimation of the atmospheric phase contributions, and the local displacement field is proposed based on simple statistical assumptions. New solutions are presented in order to cope with nonlinear motion of the targetsIEEE Transactions on Geoscience and Remote Sensing 10/2000; · 3.47 Impact Factor
Conference Proceeding: Analysis of Permanent Scatterers in SAR interferometry[show abstract] [hide abstract]
ABSTRACT: In previous papers, it has been shown that stable and pointwise targets (Permanent Scatterers) can be identified from long temporal series of ERS SAR images. On the PS grid, all data can be exploited for displacement estimation, regardless of their temporal and geometrical baselines. In this paper, it will be shown how a first selection of PS (a key step in the PS technique) can be carried out by means of a statistical analysis of the amplitude time series, after radiometric correction. An example of this incoherent approach to PS candidates selection will be illustrated and discussed. The authors then present the results of a statistical analysis carried out on three different test sites (Milan, Paris and Los Angeles). More than 170 ERS acquisitions have been processed to get an estimation of the PS density as a function of phase noise. Results show that, in urban areas, about 100 PS/km<sup>2</sup> can be identified and exploited for terrain deformation monitoring with millimetric accuracyGeoscience and Remote Sensing Symposium, 2000. Proceedings. IGARSS 2000. IEEE 2000 International; 02/2000
- [show abstract] [hide abstract]
ABSTRACT: We present a new differential synthetic aperture radar (SAR) interferometry algorithm for monitoring the temporal evolution of surface deformations. The presented technique is based on an appropriate combination of differential interferograms produced by data pairs characterized by a small orbital separation (baseline) in order to limit the spatial decorrelation phenomena. The application of the singular value decomposition method allows us to easily "link" independent SAR acquisition datasets, separated by large baselines, thus increasing the observation temporal sampling rate. The availability of both spatial and temporal information in the processed data is used to identify and filter out atmospheric phase artifacts. We present results obtained on the data acquired from 1992 to 2000 by the European Remote Sensing satellites and relative to the Campi Flegrei caldera and to the city of Naples, Italy, that demonstrate the capability of the proposed approach to follow the dynamics of the detected deformations.IEEE Transactions on Geoscience and Remote Sensing 12/2002; · 3.47 Impact Factor
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 20081065
Estimation of the Temporal Evolution of the
Deformation Using Airborne Differential
Pau Prats, Member, IEEE, Andreas Reigber, Member, IEEE, Jordi J. Mallorquí, Member, IEEE,
Rolf Scheiber, and Alberto Moreira, Fellow, IEEE
Abstract—This paper presents airborne differential synthetic
aperture radar (SAR) interferometry results using a stack of 14
images, which were acquired by the Experimental SAR system
of the German Aerospace Center (DLR) during a time span of
2.5 h. An advanced differential technique is used to retrieve the
error in the digital elevation model and the temporal evolution of
the deformation for every coherent pixel in the image. The two
the existence of residual motion errors (RMEs) (inaccuracies in
the navigation system on the order of 1–5 cm) and the accom-
modation of the topography and the aperture dependence on
motion errors during the processing. The coupling between them
is also addressed, showing that the estimation of the differential
RME, i.e., baseline error, can be biased when using techniques
based on the coregistration between interferometric looks. The
SAR focusing chain to process the data is also presented together
with the modifications in the differential interferometry processor
to deal with the remaining baseline error. The detected motion
of a corner reflector and the measured deformation in several
agricultural fields allows one to validate the proposed techniques.
Index Terms—Differential interferometry, interferometry, mo-
tion compensation (MoCo), SAR processing, synthetic aperture
formation phenomena at a large scale –. Very high
accuracy, on the order of a fraction of the wavelength, can
be attained by exploiting the coherent nature of SAR systems.
The first differential results were published by Gabriel et al.
in 1989 , where changes in some agricultural fields on
IFFERENTIAL synthetic aperture radar interferometry
(DInSAR) has become a powerful tool to measure de-
Manuscript received June 20, 2007; revised August 23, 2007. This work was
supported in part by the Spanish Ministerio de Ciencia y Tecnologia and Fondo
Europeo de Desarrollo Regional Funds under Project TEC2005-06863-C02-01.
P. Prats was with the Remote Sensing Laboratory, Universitat Politècnica de
Catalunya, 08034 Barcelona, Spain. He is now with the Microwaves and Radar
A. Reigber is with the Computer Vision and Remote Sensing Laboratories,
Berlin University of Technology, 10587 Berlin, Germany (e-mail: anderl@
J. J. Mallorquí is with the Remote Sensing Laboratory, Signal Theory
and Communications Department, Universitat Politècnica de Catalunya, 08034
Barcelona, Spain (e-mail: firstname.lastname@example.org).
R. Scheiber and A. Moreira are with the Microwaves and Radar Institute,
German Aerospace Center (DLR), 82234 Oberpfaffenhofen, Germany (e-mail:
Digital Object Identifier 10.1109/TGRS.2008.915758
the order of some centimeters over approximately one month
were detected with Seasat L-band data. By comparing the
areas experiencing the detected surface elevation changes with
depth of the electromagnetic waves due to an increase of
soil moisture. Later on, Massonnet et al.  detected and
validated in 1993 an earthquake signature using ERS-1 data.
Since these breakthrough results, differential interferometry
techniques have evolved to become more reliable and accurate.
Indeed, DInSAR using a spaceborne platform is already an
established technique. The ideal stable trajectory of a satellite
ensures that the SAR processor will be able to properly focus
the data without introducing undesired artifacts. In addition,
the fact that a large stack of images is available has been of
great help to develop several advanced DInSAR (ADInSAR)
techniques –. However, the airborne data processing rep-
resents a further challenge, since it is subject to the limitations
imposed by motion compensation (MoCo). The fact that the
platform is not following an ideally rectilinear trajectory causes
several errors that must be compensated for achieving the
accuracy required for DInSAR.
However, the advantages an airborne platform can offer are
quite appealing: flexibility in the sense of spatial resolution,
used wavelength, and data acquisition (short revisit time). For
example, the radar frequency plays an important role regarding
temporal coherence and ground penetration, since lower fre-
quency bands (L, P) tend to have a better long-term coherence
and higher ground penetration than higher frequency bands.
This required flexibility is provided by several airborne sys-
tems, given that they can operate at different frequency bands
–. In addition, the flexibility of the data acquisition is a
major asset, since the aircraft can be used to acquire the images
with the desired time intervals and geometries, without having
to wait, as it happens in the orbital case, for the satellite to
illuminate the same area with a similar look angle.
There are mainly two limitations in airborne repeat-pass
interferometry. The first limitation, addressed in Section II-A,
is the fact that a constant reference height for the whole image
must be assumed during MoCo if fast Fourier-based processors
are to be used. However, several efficient algorithms have been
recently developed that precisely take into account topography
–. The second, and most important, limitation is the
presence of residual motion errors (RMEs), i.e., inaccuracies
0196-2892/$25.00 © 2008 IEEE
1066IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
in the measurements of the real antenna position on the order
of 1–5 cm. Several algorithms have been developed to estimate
and correct RME, either the baseline error in an interferometric
pair – or the individual error in an image , .
Section II-C addresses this topic.
Up to now, just a few publications related to airborne differ-
ential interferometry exist. In 1993, Gray and Farris-Manning
 were able to measure the movement of a corner reflector
with a precision on the order of some millimeters but measuring
with respect to the field surrounding the corner. It was not
until ten years later that the first airborne differential SAR
interferogram of a large area was presented by Reigber and
Scheiber , using a classical three-image DInSAR approach
. They measured some displacements in agricultural fields
waves due to a different soil moisture and also obtained indica-
tion of water-level change in a swamp area. In 2004, de Macedo
and Scheiber  presented some controlled experiments with
three corner reflectors measured at both L- and C-band. In this
case, relative and absolute measurements were shown, where
the latter had an accuracy that was better than 1 cm. In 2004,
Groot  reported the deformation of a dike after calibrating
using the phase of several corner reflectors deployed in the
scene. In addition, in 2004, Fornaro et al.  presented an
X-band differential interferogram, where the images had been
acquired with a temporal baseline of only a few minutes, so
that no displacements were expected. In 2005, de Macedo et al.
presented some preliminary results of a landslide . Re-
cently, Perna et al.  presented differential interferograms
at X-band where the displacement of a corner reflector is
This paper aims to describe, for the first time, the com-
plete methodology and algorithms for processing a stack of
images acquired by an airborne platform in order to retrieve
the temporal evolution of the deformation in the observed
scene. The processing chain to focus the data is described in
Section II-E, where a detailed description is given in order to
deal with the commented limitations. Section III starts revis-
iting the ADInSAR algorithm proposed by Berardino et al.
, which has been used to obtain the deformation maps. In
addition, the modifications needed in the ADInSAR processing
to consider RME are expounded. Finally, Section IV presents
results with data acquired by the Experimental SAR (E-SAR)
system of the German Aerospace Center (DLR). Data were
acquired the same day for 2.5 h. However, results show de-
formation in several agricultural fields, probably due to a
change in soil moisture. The motion of one corner reflector
that was moved intentionally during the experiment is also
II. MOTION COMPENSATION
The real challenge inairborne repeat-pass InSAR processing,
and particularly in DInSAR, is the accuracy of the MoCo. To
reach millimeter accuracy at L-band, the phase accuracy must
be better than 3◦. This implies that a very accurate MoCo
scheme must be used to properly deal with the nonlinear tra-
jectory of the platform. Hence, one must consider the following
under observation and the existence of RME.
Section II-A introduces several algorithms. The so-called
extended chirp scaling (ECS) algorithm with integrated MoCo
 is used for the efficient focusing of the raw data. However,
in order to properly focus airborne SAR data, MoCo must
consider topographic variations, as well as the dependence of
the correction with the azimuth angle. Hence, there is a need
for Topography- and Aperture-Dependent (TAD) MoCo algo-
rithms. Three of such efficient algorithms are commented: the
Sub-Aperture Topography- and Aperture-dependent (SATA) al-
gorithm , the Precise Topography- and Aperture-dependent
(PTA) algorithm , and the Frequency Division (FD) algo-
Concerning the algorithms to estimate RMEs, Section II-C
on the spectral diversity or split-spectrum technique  ap-
plied in the azimuthal dimension. In this way, RMEs are
estimated based on the azimuth coregistration offsets between
two looks of an interferometric pair. In particular, the multi-
squint technique  uses several looks instead of only two as
compared with the other approaches, resulting in an enhanced
performance. Phase tracking of isolated or pointlike scatters
techniques ,  are an alternative to interferometric ap-
proaches, but they need a sufficient number of such targets to
obtain reliable estimations.
A. TAD Motion Compensation
In order to properly focus a SAR image, the SAR processor
. Under ideal conditions, i.e., when the platform follows a
linear trajectory with a constant velocity, efficient processing
considering the inherent space-variant effects of SAR imaging
can be carried out in the spectral domain , –. Such
conditions are met in a spaceborne scenario but not in an
airborne one. The movement of the platform due to atmospheric
turbulence introduces motion errors in the received raw data. If
this movement is not considered, the final focused image will
be severely degraded –.
In order to take into account the motion of the platform,
each target should be focused with a different 2-D reference
function, increasing in this way the computation burden. As-
suming that the motion of the aircraft has been recorded,
commonly through differential global positioning (GPS) and
inertial navigation systems , a MoCo approach within an
efficient SAR processor is usually carried out , . The
main challenge is that the needed correction depends on the
relative 3-D position between the target (topography) and the
platform at every time instant (aperture), i.e., the phase history
of the target and the location of the target information in the
raw data are no longer hyperbolic. Therefore, exact focusing
will be achieved, provided that the height of the target is known.
This problem, coupled with the fact that the processing is space
variant, has given raise to several TAD algorithms: SATA ,
PTA , and FD . These algorithms rely on the two-
step MoCo integrated in the ECS algorithm . In this way,
the two-step MoCo partially considers the space variance of
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR 1067
the impulse response, allowing accurate range cell migration
correction. TAD algorithms deal with the remaining space-
variant effects due to the topography and aperture by means
of an azimuth block-processing approach, so that an accurately
focused image can be obtained.
The image quality can be degraded if no TAD algorithm
is used. The amount of degradation depends mainly on the
topographic variations within the scene and the magnitude of
the platform deviations . The main effects are phase errors
and the azimuth shift of the impulse response function (IRF).
For large topographic variations and/or large track deviations,
defocusing can also occur. Hence, these effects are just the
result of constant, linear, and quadratic errors in the phase
history of the target. Such errors will also result in a degraded
where track deviations are not correlated. Therefore, in order
to minimize phase and azimuth coregistration errors, a TAD
algorithm should be used. These algorithms use an external
digital elevation model (DEM), which must be back-geocoded
to the slant range geometry, in order to properly consider the
topography. The larger the error in the DEM, the larger the in-
troduced phase and image distortions. In addition, the accuracy
of each TAD algorithm should be considered (a comparison is
presented in ). The selected algorithm to process the data of
Section IV is SATA , since the external DEM used during
MoCo has a low spatial resolution as compared to the azimuthal
spatial resolution accommodation of SATA.
B. Interferometric Phase Content
An important key point is the information content of an
interferogram after processing master and slave images with a
TAD algorithm. The fact that MoCo is carried out using the
external DEM implies that this information is introduced in the
interferometric phase. However, interest lies in the unknown
information, e.g., DEM errors or deformation. Consequently,
the first step is to remove the information of the external DEM.
This is carried out by subtracting the synthetic phase, which
is computed using the external DEM and the reference tracks,
from the generated interferogram. The remaining phase, called
residual phase, contains the DEM error plus other contributions
like deformation, atmospheric artifacts, and noise. It can be
shown that the contribution of the DEM error to the synthetic
phase is proportional to the real track deviations, so that, in the
absence of the other contributions, the residual phase can be
expressed as , 
φresidual(x,r) ≈ kreal
(x,r) = −4π
wavelength, r is the range distance, x is the azimuth distance,
and θ is the off-nadir look angle. Therefore, the subtraction
of the synthetic phase is needed in order to remove the in-
is the real perpendicular baseline, λ is the used
formation introduced during MoCo. Otherwise, the content of
the interferometric phase would be a mix between the external
DEM, which is sensitive to the reference baseline (reference
tracks), and the unknown topography, which is sensitive to
the real baseline (real tracks). Equation (1) is important in
differential interferometry, since it allows one to relate the
residual phase linearly with the DEM error. Although it is a
first-order approximation, it is quite accurate, as the DEM error
is usually small. Note also that the larger the baseline gets
with respect to the platform deviations, the more similar are
the reference and real baselines.
C. Residual Motion Errors
The absolute positioning accuracy of current navigation sys-
tems using intertial navigation systems and differential GPS
is about 1–5 cm. Therefore, the navigation data used during
MoCo can have RMEs, resulting mainly in phase errors and
azimuth impulse response shifts. Although such errors will not
degrade significantly the high azimuthal resolution capability,
some applications, like repeat-pass interferometry, differential
interferometry, or very high resolution processing , can
be strongly limited by them. Consequently, some procedure is
needed to estimate the remaining trajectory deviations. Several
algorithms have been proposed in the literature – of
which the multisquint technique  has been used to estimate
RME in the results of Section IV. This particular approach is
based on the estimation of the azimuth coregistration offsets
between multiple looks of an interferometric pair . The
coregistration offsets are related to the derivative of RME, so
that after a proper scaling and integration, the time-varying
baseline error can be retrieved. The estimated baseline error can
be used toupdate the tracks of the slave image to reprocess it,so
that afterward, both master and slave images will have the same
RME of the master image, hence, canceling out after inter-
ferogram generation. The defocusing induced by the unknown
RME of the master image can be neglected in interferometric
In the case of having a stack of several images, different
interferograms can be formed with the possibility of different
images being master. In such a case, a first possibility is to
select one of the images as master (from now on called I0)
so that the baseline error estimation using multisquint can
be carried out with every interferogram formed between I0
and each of the remaining images (slaves). Afterward, the
slave tracks are updated with the estimates, ensuring that any
combination between any image pair will result as RME-free,
as all of them will have the same RME as image I0. A second
possibility is to estimate the baseline error of each individual
interferogram, but this implies the reprocessing of each pair for
every interferogram, resulting in an increase of the computation
burden. Both approaches have been tested resulting in similar
results . The results of Section IV have been processed
using the former approach, as expounded in Section II-E.
Other approaches to estimate RME are possible. In partic-
ular, the estimation of the individual RME using autofocus
techniques by phase tracking of isolated or pointlike scatterers
,  can be particularly attractive, above all considering
1068IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
the LOS motion error, d and αmare the distance and the tilt angle, respectively,
between real and reference positions, ∆y is the horizontal displacement, ∆z is
the vertical displacement, and H the platform height above ground assumed
Simplified sketch of MoCo geometry. herris the DEM error, ∆rmis
the potential coupling between the unknown topography and
RME, as commented next.
D. Coupling Between Unknown Topography and RME
Up to now, the two main limitations, i.e., the unknown
topography during MoCo and the estimation of RME (or base-
line error), have been tackled separately. However, a coupling
between them exists due to the fact that both have similar
effects in the retrieved interferogram, mainly phase errors and
azimuth coregistration offsets. This can become a problem if
time-varying baseline error estimation techniques based on the
estimation of coregistration offsets are used, as it is the case
in the presented results. Therefore, it should be expected to
retrieve a biased baseline error.
An analytical approach to analyze the problem is possible.
Given the geometry of Fig. 1, the correction in line-of-sight
(LOS) can be approximated by 
∆rm≈ −d(t)sin(θ − αm(t))
where αm(t) is the tilt angle between real and refer-
ence positions, θ is the off-nadir look angle, and d(t) =
∆z(t) is the vertical one. In order to retrieve the error as a
function of the DEM error herr, a first-order approximation
y(t) + ∆2
z(t), where ∆y(t) is the horizontal deviation and
∆rm,herr(t) = −d(t)cos(θ − αm(t))
A constant value of d⊥ induces a phase offset through the
phase history of the target, which, when combined with the
slave image, results in (1), i.e., it results in the measurement
of the unknown topography from the real antenna positions.
However, a linear variation of d⊥through the synthetic aperture
introduces an undesired azimuth shift of the impulse response.
displacements along the synthetic aperture due to unknown topography for a
target at midrange.
Induced azimuth shift in the IRF for different total linear horizontal
MAIN SYSTEM AND PROCESSING PARAMETERS
Effectively, a linear phase error introduces the following shift
in the IRF :
where r0is the closest approach distance of the target and v is
the forward velocity of the platform. Fig. 2 shows the azimuth
shift in pixels as a function of the DEM error for three different
total linear horizontal displacements along the synthetic aper-
ture using the system parameters of Table I. Considering the
high sensitivity of multisquint to estimate coregistration errors
, the shift due to the unknown topography can reach critical
values that will bias the baseline error estimation. In the case
of multisquint, several spectral diversity phases are computed,
which are aligned to the beam center geometry and added in
order to reduce phase noise . Although this alignment tends
to cancel out the errors induced by the unknown topography,
it cannot be expected that they will be completely removed, as
the aircraft deviations are usually smooth through the synthetic
Fig. 3(a) shows the induced shift for a target at midrange all
along the data take for two different acquisitions of the data
of Section IV. A height error of 5 m has been assumed in both
cases. The analysis has been carried out by fitting a line through
∆rm(t) along the synthetic aperture length to retrieve ∆vm.
Instead of considering a bandwidth of 100 Hz to compute the
synthetic aperture length, a value of only 30 Hz has been used,
as this is the used bandwidth of the looks during multisquint in
the results of Section IV. The dashed line in Fig. 3 corresponds
to a track with small deviations (∆y < 6 m), while the solid
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR1069
a height error of 5 m and (b) corresponding bias introduced in RME after
integration (the phase error is computed at L-band). Track with (solid line) large
and (dashed line) small deviations.
(a) Induced azimuth shift in the IRF for a target at midrange and
one corresponds to a track with large deviations (∆y > 15 m).
The integration of these offsets given by 
leads to an error in the RME estimation ?bias
result in a bias when using multisquint. Fig. 3(b) shows this
RME error for the same two track deviations as before. For the
large track deviation, the induced error is almost ±2 cm, hence,
limiting the potential accuracy of airborne interferometry. The
standard deviation of the shift of the IRF for all tracks of
the data processed in Section IV is 0.06 pixels at midrange,
assuming a height error of 5 m.
Concluding, the estimated baseline error might be biased
when using multisquint, since the unknown topography can
lead to an undesired shift of the IRF. Therefore, some proce-
dure is needed to remove the remaining baseline error. In the
presented case, this is done during the ADInSAR processing,
as commented in Section III-B.
rme(x,r), which will
E. Implemented SAR Processing Chain
The processing chain used to focus the data shown in
Section IV is shown in Fig. 4. The selected algorithms are
ECS  to focus the raw data, SATA  to accommodate
the topography and the aperture during MoCo, and multisquint
 to estimate the time-varying baseline error.
In this case, the idea is to generate M interferograms from
a set of N acquisitions. Instead of generating M0= N − 1
chirp scaling algorithm, while SATA stands for subaperture topography- and
aperture-dependent MoCo algorithm.
Block diagram of the used processing chain. ECS stands for extended
interferograms, i.e., all slaves with respect to a master image I0,
several interferograms can be generated as carried out in several
ADInSAR applications , ; for example, by selecting small
baselines to maximize the coherence, so that M is usually
greater than M0. The differential processor will later on retrieve
the deformation for each individual acquisition. Hence, the first
step is to compute the reference tracks using the navigation
data. By finding the best fit to all acquisition tracks, it is
ensured that the reference tracks will be parallel and with the
same azimuth image spacing , something that will ease
the forthcoming interferometric steps. With the reference tracks
and an external DEM, it is then possible to compute three
different products in the slant range plane: the topographic
height for the N images, M0coregistration error maps in range
for each slave image with respect to the master image I0, and
M synthetic phases (for each interferogram) in the geometry of
the master image I0. Once the SAR focusing is carried out for
each image using ECS and SATA, multisquint and the model-
based integration proposed in  are used to estimate the
baseline error for the first M0interferograms. Several iterations
are performed with multisquint to improve the estimation. After
the last iteration, constant and linear terms of the baseline
error, which cannot be estimated by means of multisquint, are
estimated using the external DEM, as also described in .
Note that, in order to carry out the multisquint estimation, it is
first necessary to coregister the images in the range dimension,
and also, the spectrum filtering can be applied if necessary.
After multisquint, the slave images are processed again after
updating their tracks with the full estimation of the baseline
error. At this point, all the images have the RME of image I0.
Consequently, any combination between them will result in an
RME-free interferogram, but note that, as already commented,
a remaining baseline error might be present due to the coupling
between the unknown topography and RME (see Section II-D).
It should be noted that the estimation of the baseline error
for each of the M interferograms might be of interest when
the temporal baseline or the geometric decorrelation increase
with respect to image I0. Doing so will yield a significant
increase in the computation burden, but results will be more
accurate in such scenarios. In the results to be presented, all
of 120 m with respect to the master image I0, so that the
1070 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
temporal coherence degradation is negligible, and spectrum
filtering approaches solve the problem of spectral decorrelation.
The interferometric processor carries out the typical steps:
range interpolation, spectrum filtering, interferogram genera-
tion, coherence estimation, phase unwrapping, and absolute
calibration using a corner reflector. In this case, the external
DEM has been used in some of these steps as follows.
1) Range coregistration: With the knowledge of the DEM
and the master and slave reference tracks, it is possible to
compute the coregistration offsets in range. Taking into
account that the reference tracks are computed to be par-
allel, the images will be aligned in azimuth, implying that
the time-consuming task of estimating the coregistration
offsets is avoided.
2) Spectrum filtering: As expounded in , an efficient
spectrum filtering can be carried out with the knowledge
of the topography. By subtracting the synthetic phase
computed with the DEM to the master and slave images,
the spectrum is basebanded, easing, in this way, the
filtering of the common part with a simple low-pass filter.
3) Coherence estimation: The bias introduced in the coher-
ence due to the topographic phase can be reduced by
subtracting again the synthetic phase to one of the images
prior to coherence computation.
4) Phase unwrapping: The reduction of fringes using the
synthetic phase is a standard procedure whenever a DEM
is available. However, in the described scheme, the sub-
traction of the synthetic phase is mandatory, as the valu-
able interferometric information is stored in the residual
Once the interferometric processing of all M interferograms
is finished, the data are prepared to be processed by the
III. ADVANCED AIRBORNE DInSAR
There are several techniques to retrieve the temporal evo-
lution of the deformation in a stack of images –. The
differential technique presented by Berardino et al.  has been
selected to process the data of Section IV. In the following,
this technique is briefly described for completeness, while the
modifications in order to deal with airborne data are detailed in
A. Small Baseline Technique (SBAS)
The SBAS  is based on the use of small baseline inter-
ferometric pairs to maximize the number of coherent points.
This technique is well suited to DInSAR when not only perma-
nent scatterers are being analyzed but also distributed targets
with enough coherence between the acquisitions. Therefore, a
multilook is generally carried out to the interferograms, with
a size equal to the coherence estimation window. Note that
high-resolution results can be obtained with additional steps,
as detailed in .
Prior to starting the algorithm, it is assumed that the residual
phases (from now on, called differential phases, as the external
DEM has been subtracted) have been unwrapped and calibrated
for singular-value decomposition, LS for least squares (estimation), and LP and
HP for low- and high-pass (filtering), respectively.
Block diagram of the implemented ADInSAR algorithm. SVD stands
with respect to one pixel whose deformation is known (usually,
a highly coherent pixel without deformation). This allows one
to make a pixel-by-pixel temporal analysis. The block diagram
of the implemented algorithm is shown in Fig. 5.
be the vector of the N − 1 unknown phase values associated
with the deformation of the considered pixel and
be the vector of the M known values of the computed differen-
tial interferograms. Two index vectors are defined
which correspond to the acquisition time indexes associated
with the image pairs used for the interferogram generation. It
is also assumed that the master (IE) and slave (IS) images are
chronologically ordered, i.e., ISj> IEj, ∀j = 1,...,M.1This
φdiff,j= φ(tIEj) − φ(tISj)
Given two SAR images with acquisition times tAand tB(tA<
tB), the differential phase after subtracting the external DEM is
∀j = 1,...,M.
φdiff,j=φ(tA,x,r) − φ(tB,x,r)
+ φerr(tA,x,r) − φerr(tB,x,r) + ∆nj
∀j = 1,...,M
· [dlos(tA,x,r) − dlos(tB,x,r)] + kreal
1Note that, in the original reference , they consider the opposite, i.e.,
IEj> ISj, ∀j = 1,...,M.
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR1071
where dlos(·) represents the displacement in LOS at every
time instant. Note that the real tracks are used to compute
, as commented in Section II-B. The herrterm accounts
for possible phase artifacts due to an error in the external
DEM. The third term in (11), represented by φerr(tA,x,r) −
φerr(tB,x,r), accounts for possible RMEs, which might have
not been properly estimated and corrected, and for atmospheric
artifacts (atmospheric phase component). Finally, the term ∆nj
represents the phase noise due to all sources of decorrelation.
The major difficulty in differential interferometry lies in the
unwrapping of the differential phases. Even if an external DEM
is used to remove the topographic component, errors in this
DEM, atmospheric artifacts, RMEs, or even the displacement
to estimate itself, can result in a wrapped differential phase.
The unwrapping operation is performed to each differential
interferogram, but only the pixels that have a mean coherence
higher than a certain threshold are used. Usually, in differential
applications, a sparse grid has to be unwrapped. Berardino et al.
 propose to use the approach presented in  to carry out
this phase unwrapping. Since the data presented in Section IV
were acquired in only one day and are very coherent, the con-
ventional region-growing algorithm with weighted least mean
squares has been used .
After phase unwrapping, the linear component of the de-
formation and any possible DEM error are estimated via a
least squares (LS) solution. Therefore, the following system of
equations can be formed for each pixel:
Ap = φdiff
∆tj= tISj− tIEj
∀j = 1,...,M
where ν is the mean deformation velocity. The LS solution is
p = (ATA)−1ATφdiff.
Once the DEM error herrand the mean deformation velocity
ν have been estimated, the DEM error is subtracted to each of
the differential interferograms modulo 2π, leading to a fringe-
rate reduction of the differential phase. All differential interfer-
ograms might be unwrapped again, but in the presented case,
this second phase-unwrapping step has been omitted, given the
good coherence of the whole data set. Indeed, in , both the
DEM error and the mean deformation velocity are subtracted,
so that the differential interferograms are unwrapped again, and
after phase unwrapping, ν is added. The next step is to find
the deformation for each image φ, which is solved via singular
value decomposition (SVD). As recommended in , the mean
phase velocity between time-adjacent acquisitions is used in the
SVD, instead of the individual phases. A final integration step
yields the desired solution φ(ti).
The problem with spaceborne data is that the esti-
mated displacements are affected by atmospheric artifacts.
Berardino et al.  propose to perform a filtering operation
to the estimated φ(ti), which is derived from the permanent
scatterers approach , . It is based on the fact that the
atmospheric signal phase component is characterized by a
high spatial correlation but exhibits a significantly low tempo-
ral correlation. Accordingly, the undesired atmospheric phase
component can be estimated after the SVD as follows. First, the
low-pass component of the deformation signal already esti-
mated via (16) is removed. Afterward, the atmospheric phase
component is detected as the result of the cascade of a low-
pass filtering step, performed in the 2-D spatial domain (i.e.,
azimuth and range), and a high-pass (HP) filtering operation
with respect to the time variable. Once the atmospheric phase
component has been evaluated, it is finally subtracted from the
estimated phase signal.
However, in the airborne case, one has to further deal with
the presence of RMEs, which might have not been properly
estimated. In the next section, a modified filtering approach to
remove them is proposed.
B. Modifications in the Airborne Case
Besides using the real baseline instead of the reference one,
the main difference arises due to the existence of RMEs. The
fact that RMEs might have not been properly estimated and
corrected (as noted in Section II-D) implies that some kind of
filtering should be carried out to remove them from the differ-
ential interferograms. Furthermore, the atmospheric component
should not be neglected, even at L-band .
This filtering can be carried out at the same point as when the
atmosphere is estimated in the spaceborne case, i.e., after the
SVD estimation and having subtracted the previously estimated
mean deformation velocity. In theory, only the nonlinear defor-
mation should remain, but the presence of baseline errors and
atmospheric artifacts must be considered. Their contribution
can be described as
· (?y(x)sinθ(r) − ?z(x)cosθ(r))
where the baseline error ?rmeis just the projection in LOS of the
individual unknown horizontal ?yand vertical ?zdisplacements
and N is the scaled-up refractivity equal to N = (n − 1) · 106,
where n is the refractive index of the medium. Note that the
slant atmospheric delay is inversely proportional to the cosine
of the look angle  and has a high spatial correlation. An
important approximation in (17) is that a 0◦squint angle is
1072 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
being assumed. In a squinted geometry, an azimuth phase ramp
would be present, which, depending on the coregistration error
due to the unknown topography, could introduce important
phase errors . However, the E-SAR system has a large
azimuth beamwidth at L-band (∼18◦), so that a 0◦processing
squint angle can be selected without a significant loss in the
signal-to-noise ratio. A further approximation is the assumption
that the nonlinear deformation is small enough not to bias the
refined estimation of the baseline error. Finally, it should be
stressed again that the error contribution of baseline errors and
atmosphere in each of the N − 1 images of the deformation
sequence is a differential error between the corresponding slave
image and master image I0.
A possible approach to estimate the two contributions would
be to first estimate the baseline error from each image of
the deformation sequence using an LS-estimation approach,
subtract them from the data, and then filter the atmospheric
component by means of a large low-pass filter. Therefore, an LS
estimation is performed for every azimuth position x to obtain
the remaining baseline error using all Nr samples in range.
Using the same model as in  yields
where δφ corresponds to the phase values at a given azimuth
position of an entire range line and θ1,...,θNrcorrespond
to the off-nadir look angle at every range bin. δφ contains
the projection in LOS of the baseline error, together with the
atmospheric component, the nonlinear motion of the defor-
mation, and noise. Therefore, the LS estimation obtains the
individual components ?y and ?z of the remaining baseline
error. Since all pixels are assumed to have an acceptable co-
herence level, no weighting is applied in the LS estimation.
After subtracting the remaining baseline error to the differential
interferogram, a large low-pass filtering can be carried out. In
the airborne geometry, the look angle changes considerably
along the scene (ca. 25◦–55◦). Therefore, in order to consider
the look-angle dependence, data should be first multiplied
by cosθ(r). Now, the large low-pass filter can be applied to
the image to retrieve the atmospheric component. Finally, the
estimated atmospheric component is subtracted from the data
after dividing it by cosθ(r). After the correction of baseline
errors and atmosphere, a further HP filtering in time reduces
the influence of these two effects, which are subtracted from
the deformation series in the last step of the algorithm.
The estimation of the DEM error herrand the mean velocity
ν via LS estimation performs better, the larger the number
of independent acquisitions. Since in the presented case only
Fig. 6.Baseline distribution for the selected interferograms.
N = 14 independent acquisitions are available, the estimated
herr and ν might be biased. If this biased ν is subtracted
before the refined estimation of the baseline error (as shown
in Fig. 5), then the refinement will not perform accurately.
Therefore, in a first iteration, ν should not be subtracted before
the LS estimation. Once the refinement has been performed, a
second iteration can be carried out, but, this time, correcting the
M interferograms with the refined estimates. The atmospheric
component might be also considered here, although, in the
presented results, only the baseline error has been taken into
account. The improvement in the results with the second iter-
ation is significant, as shown in next the section. Obviously,
here, it is assumed that the deformation will not bias this refined
estimation in the first iteration, something that is valid as long
as the deformation is located in a small area in range and is not
much larger than the baseline error.
IV. EXPERIMENTAL RESULTS
A total of 14 images were acquired at L-band by the E-SAR
system of DLR during a time span of 2.5 h (from 11 A.M.
until 1:24 P.M. with ∼11 min between each acquisition) in the
test site of Oberpfaffenhofen, Germany. The data acquisition
took place on May 11, 1998 in order to carry out the first
tomographic experiment with a SAR system . This same
data set has been used to analyze the performance and limi-
tations of ADInSAR techniques when working with airborne
data. With 14 images, up to 91 interferograms can be formed.
However, a maximum baseline of 50 m has been imposed in
order to keep a large number of coherent points without much
spectral filtering (better range resolution), resulting in a total
number of 27 interferograms (see the baseline distribution in
Fig. 6). Nevertheless, larger baselines lead to a similar result,
as reported in , where, in that case, 51 interferograms were
generated by imposing a maximum baseline of 90 m. Fig. 7
shows the reflectivity image of the observed scene, while Fig. 8
shows a detail with the location of the 11 corner reflectors.
The multilook applied to the interferograms and the window
for coherence estimation are of 4 pixels × 4 pixels, so that the
image spacing after the multilook is about 6 m × 6 m. Those
pixels having a coherence larger than 0.8 in at least 50% of
the interferograms have been selected. In addition, the mask
generated by the region-growing algorithm for each interfero-
gram has been used to discard pixels not properly unwrapped.
Fig. 9(a) shows the mean coherence of all 27 interferograms,
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR 1073
(azimuth × range). Image resolution: 1.3 × 1.9 m.
Reflectivity image of the observed scene. Scene dimensions: 7 × 2 km
Detail of the reflectivity image showing the location of the 11 corner
while Fig. 9(b) and (c) shows the two different DEMs used
during MoCo. The reason to use two different DEMs is to
validate the proposed processing chain, so that the retrieved de-
formation maps are the same independently of the used DEM.
The first DEM [a digital terrain model (DTM)] is provided
by MagicMaps GmbH as a commercial product and has a
nominal resolution of 50 × 50 m (http://www.magicmaps.de/).
The second is a C-band Shuttle Radar Topography Mission
(SRTM) DEM with a nominal resolution of 90 × 90 m
(http://www.jpl.nasa.gov/srtm/). It will be shown that, except
for the DEM error, the estimated deformation and baseline
errors are basically the same.
After subtracting the external DEM to each interferogram,
the differential interferograms have been unwrapped and cal-
ibrated using corner reflector #6 (see Fig. 8). Once the LS
estimation is applied to each selected pixel, the DEM er-
ror and the mean deformation velocity maps are obtained.
Fig. 10(a) and (b) shows the DEM error for the two DEMs,
where it can be noted that the height of some buildings has
been properly retrieved, as one of the interferograms with a
smaller baseline supported the phase unwrapping of the others.
Fig. 10(c) shows the refined DEM after adding the error to
the original DEM. The output for both refined DEMs is the
same, with a standard deviation in the height difference of only
12 cm after subtracting an azimuth and a range linear compo-
nent. The linear component in range was the larger one, with a
(b) MagicMaps and (c) SRTM used during the processing. Note that (b) is
indeed a DTM, while (c) includes the height of the vegetation.
(a) Mean coherence for all 27 interferograms, and DEMs from
icMaps GmbH and (b) SRTM and (c) refined DEM. Masked values in black.
Retrieved DEM error derived from the DEM provided by (a) Mag-
1074 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
reflectivity and (b) mean deformation velocity in LOS after a second iteration
using the refined correction of the baseline error.
Retrieved (a) mean deformation velocity in LOS with overlayed
variation in range of about ±1 m. In addition, a mean offset of
0.28 m was present. These linear and constant components
come from the difference in the original DEMs. Indeed, con-
stant and linear terms of the baseline error are estimated using
the external DEM, so that their accuracy depends mainly on the
accuracy of the external DEM. In order to test this hypothesis,
the data processed with the SRTM DEM were reprocessed with
the ADInSAR processor but using the constant and linear terms
of the baseline error estimated with the MagicMaps DEM. As
expected, linear trends disappeared, and only a mean offset of
9 cm remained, being the standard deviation between both
refined DEMs of 10 cm.
A third approach was carried out by applying MoCo, assum-
ing a constant reference height for the whole image, i.e., no
topography accommodation was applied during the focusing.
Since the scene under study has very low topography, the
focused images were not noticeably degraded. In this case,
constant and linear terms of the baseline error obtained with
MagicMaps DEM were used. The standard deviation in the
difference between the refined DEM, as compared to when the
processing is carried out with MagicMaps DEM, is 0.62 m,
with a mean of 0.13 m. It should be noted that, although in the
presented scenario not considering the topography results in a
fairly good estimation, in scenes with more topography, a TAD
algorithm becomes mandatory to reduce the coupling between
the unknown topography and RMEs and to improve the quality
of the interferogram.
Fig. 11(a) shows the mean deformation velocity map in LOS.
In order to improve the estimation of the mean deformation
map and the DEM error, a second iteration with the ADInSAR
processor was carried out. In this second case, the refined
estimation of the baseline error after the SVD was used as
commented in Section III-B. The refined result of the mean
deformation velocity is shown in Fig. 11(b).
Concerning the deformation results, some motion is mea-
sured in corner reflector #11, which was indeed moved in-
tentionally during the data take. The second mobile corner
sured by the meteorological station located inside DLR facilities at Oberp-
faffenhofen the day of the data take. The vertical dashed lines indicate the
beginning and the end of the data take.
(Solid thick line) Temperature and (solid thin line) humidity mea-
reflector (#10) also shows some movement, although it was
not moved during the experiment. Unexpectedly, several geo-
metrical shapes are observed all around the image, and they
do not seem to be a processing artifact. In fact, it can be
noted how these shapes correlate well with the shapes of the
agricultural fields. Hence, some deformation is indeed being
observed. Some fields show a raise and others a downfall of
the phase center. The most plausible explanation for these
effects is that the soil moisture content changed, similarly as
reported in , , and . In the case of a raise of the
phase center, the soil moisture might have increased during the
experiment due to dew, reducing, in this way, the penetration
depth of the electromagnetic waves, or maybe due to a raise
of the vegetation itself (note that irrigation is not usual in
the area under study). On the other hand, the downfall of the
phase center in some fields might occur due to evaporation
of water, reducing the soil moisture and, hence, increasing the
penetration depth. Fig. 12 shows the temperature and humidity
measured by the meteorological station located inside DLR
facilities at Oberpfaffenhofen the day of the data take. The
temperature raised from 22.1◦C at 11 A.M. to 25.6◦C at
1:24 P.M., while the humidity reduced from 59.6% to 45.4%.
After subtracting the DEM error herr, the SVD approach
is applied to obtain the time-sequence deformation of images.
Then, the filtering commented in Section III-B is carried out
to estimate the remaining baseline error and the atmosphere.
The estimated atmospheric component is very small in this
particular data set, with a standard deviation of only 0.7 mm
in all images. Fig. 13 shows the refined baseline estimation for
two different tracks and for both DEMs. It can be noted how
the estimations for the two DEMs differ, but the final refined
ones are fairly the same. The main difference is an offset,
which again is due to errors in the original DEMs. The standard
deviation in the baseline error difference between processing
with the two DEMs is about 1.1 mm.
Fig. 14(a) shows the deformation evolution for the corner
reflectors. Diamonds correspond to the corners next to the
runway (corners #5–#9), squares to the fixed ones on the left
(corners #1–#4), and stars to the mobile ones (corners #10 and
#11). The mobile corner reflector that shows a larger motion
corresponds to the one moved intentionally during the experi-
ment (corner #11). No filter in the time domain was applied in
this case to avoid filtering the nonlinear motion of the mobile
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR1075
after adding the previous two. Track with (top) large and (bottom) small deviations. For (a) MagicMaps DEM and (b) SRTM DEM.
Estimated baseline error in LOS with (solid line) multisquint, (dotted line) during the ADInSAR processing, and (dashed line) refined baseline error
filter in the time domain. The corners are as follows: (squares) corners #1–#4,
(diamonds) corners #5–#9, and (stars) corners #10 and #11. (b) Deformation in
two different fields: (diamonds) upraise and (stars) downfall of the phase center.
Their location is shown in Fig. 16.
(a) Deformation evolution in LOS for all corner reflectors without
corner reflector. Fig. 14(b) shows the deformation evolution of
two pixels located in two different fields. One is showing an
upraise of the phase center, while the second shows a downfall.
Unfortunately, none of these results can be validated, since no
in situ measurements are available.
Fig. 15 shows the deformation at some time instants (note
that the acquisition started at 11 A.M. and finished at 1:24 P.M.),
where the change in phase center of the fields can be clearly ob-
time of each image acquisition on the top-left corner. Acquisition started at
11 A.M. and finished at 1:24 P.M.
Three images of the deformation evolution in LOS, with the local
served. Fig. 16 shows the estimated mean deformation, where,
again, it can be noted how the detected deformation areas
correlate well with the shape of agricultural fields. The standard
deviation in the difference between the mean displacement
maps obtained when processing with the two different DEMs
1076IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
11 A.M. to 1:24 P.M.). The white circles indicate the location of the pixels
whose deformation is shown in Fig. 14(b).
Estimated mean deformation with overlayed reflectivity (from
is of 0.7 mm, but it reduces to 0.3 mm when using the same
estimation of constant and linear terms of the baseline error.
Finally, note that the magnitude of the measured deforma-
tions is around λ/20. Such good accuracy is possible due to the
short time span between acquisitions, allowing an exceptionally
good coherence between them.
This paper has shown the potential of airborne platforms to
retrieve differential interferometric products, presenting results
for the first time with a large stack of images and ADInSAR
techniques. The processing strategy to focus the data has been
expounded, emphasizing the limitations in airborne systems.
In this sense, RMEs are the main limitation. The multisquint
technique used to estimate the baseline error can lead to a
bias as a consequence of the undesired shift of the IRF due to
errors in the external DEM. Therefore, a solution is proposed
during the ADInSAR processing to estimate the remaining
baseline error. To test the proposed approach, two different
external DEMs have been used for the processing. The retrieved
deformation maps and refined baseline errors are basically the
same, and the minor differences are due to the accuracy of the
original DEMs. The use of an external DEM is necessary in
order to apply accurate MoCo, as well as being of great help in
several steps of the interferometric processing. Furthermore, it
is also used to estimate constant and linear terms of the baseline
error, as described in .
Besides the motion detection of a corner reflector that was
moved intentionally, it has been possible to detect some defor-
mation of just a few millimeters in several agricultural fields,
probably due to a change in soil moisture or vegetation vitality
during the data take. The high correlation between the shapes
of the deformation areas and the agricultural fields allows
one to validate the presented results. Unfortunately, no in situ
measurements are available. Ideally, a proper validation of the
proposed techniques should be carried out by performing a
campaign over a more controlled scenario.
Future work will address the use of approaches like  and
 to estimate RME in each individual image, instead of the
baseline error. In this way, the estimation is not affected by the
shift of the IRF due to the unknown topography during MoCo.
Consequently, the RME in the interferograms will be small,
increasing the reliability of the proposed approach. Finally,
the operational interferometric data processing chain of the
The authors would like to thank the anonymous reviewers for
their comments and suggestions.
 A. Ferretti, C. Prati, and F. Rocca, “Nonlinear subsidence rate estima-
tion using permanent scatterers in differential SAR interferometry,” IEEE
Trans. Geosci. Remote Sens., vol. 38, no. 5, pp. 2202–2212, Sep. 2000.
 A. Ferretti, C. Prati, and F. Rocca, “Permanent scatterers in SAR inter-
ferometry,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 1, pp. 8–30,
 R. F. Hanssen, Radar Interferometry. Data Interpretation and Error
Analysis. Dordrecht, The Netherlands: Kluwer, 2001.
 P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, “A new algorithm
for surface deformation monitoring based on small baseline differential
SAR interferograms,” IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11,
pp. 2375–2383, Nov. 2002.
 O. Mora, J. J. Mallorqui, and A. Broquetas, “Linear and nonlinear terrain
deformation maps from a reduced set of interferometric SAR images,”
IEEE Trans. Geosci. Remote Sens., vol. 41, no. 10, pp. 2243–2253,
 R. Lanari, O. Mora, M. Manunta, J. J. Mallorqui, P. Berardino, and
E. Sansosti, “A small-baseline approach for investigating deformations
on full-resolution differential SAR interferograms,” IEEE Trans. Geosci.
Remote Sens., vol. 42, no. 7, pp. 1377–1386, Jul. 2004.
 D. Perissin and F. Rocca, “High-accuracy urban DEM using permanent
scatterers,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 11, pp. 3338–
3347, Nov. 2006.
 D. Perissin, C. Prati, M. E. Engdahl, and Y. L. Desnos, “Validating the
SAR wavenumber shift principle with the ERS–Envisat PS coherent com-
bination,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 9, pp. 2343–
2351, Sep. 2006.
 A. Ferretti, G. Savio, R. Barzaghi, A. Borghi, S. Musazzi, F. Novali,
C. Prati, and F. Rocca, “Submillimeter accuracy of InSAR time series:
Experimental validation,” IEEE Trans. Geosci. Remote Sens., vol. 45,
no. 5, pp. 1142–1153, May 2007.
 F. Chaabane, A. Avallone, F. Tupin, P. Briole, and H. Maître, “A multitem-
poral method for correction of tropospheric effects in differential SAR
interferometry: Application to the Gulf of Corinth earthquake,” IEEE
Trans. Geosci. Remote Sens., vol. 45, no. 6, pp. 1605–1615, Jun. 2007.
 A. K. Gabriel, R. M. Goldstein, and H. A. Zebker, “Mapping small
elevation changes over large areas: Differential radar interferometry,” J.
Geophys. Res., vol. 94, no. B7, pp. 9183–9191, 1989.
 D. Massonnet, M. Rossi, C. Carmona, F. Adragna, G. Peltzer, K. Fiegl,
and T. Rabaute, “The displacement field of the Landers earthquake
mapped by radar interferometry,” Nature, vol. 364, no. 6433, pp. 138–
142, Jul. 1993.
 R. Horn, “The DLR airborne SAR project E-SAR,” in Proc. IGARSS,
Lincoln, NE, May 27–31, 1996, vol. 3, pp. 1624–1628.
 Y. Kim, Y. Lou, J. van Zyl, L. Maldonado, T. Miller, T. Sato, and
W. Skotnicki, “NASA/JPL airborne three-frequency polarimetric/
interferometric SAR system,” in Proc. IGARSS, Lincoln, NE, May 27–31,
1996, vol. 3, pp. 1612–1614.
 S. Uratsuka, M. Satake, T. Kobayashi, T. Umehara, A. Nadai,
H. Maeno, H. Masuko, and M. Shimada, “High-resolution dual-bands
interferometric and polarimetric airborne SAR (π-SAR) and its applica-
tions,” in Proc. IGARSS, Toronto, ON, Canada, Jun. 24–28, 2002, vol. 3,
 E. Christensen, N. Skou, J. Dall, K. W. Woelders, J. Jorgensen,
J. Granholm, and S. Madsen, “EMISAR: An absolutely calibrated polari-
metric L- and C-band SAR,” IEEE Trans. Geosci. Remote Sens., vol. 36,
no. 6, pp. 1852–1865, Nov. 1998.
 P. Prats, A. Reigber, and J. J. Mallorqui, “Topography-dependent mo-
tion compensation for repeat-pass interferometric SAR systems,” IEEE
Geosci. Remote Sens. Lett., vol. 2, no. 2, pp. 206–210, Apr. 2005.
 K. A. C. de Macedo and R. Scheiber, “Precise topography- and aperture-
dependent motion compensation for airborne SAR,” IEEE Geosci. Re-
mote Sens. Lett., vol. 2, no. 2, pp. 172–176, Apr. 2005.
PRATS et al.: ESTIMATION OF THE TEMPORAL EVOLUTION OF THE DEFORMATION USING AIRBORNE DINSAR1077
 X. Zheng, W. Yu, and Z. Li, “A novel algorithm for wide beam SAR
motion compensation based on frequency division,” in Proc. IGARSS,
Denver, CO, Jul. 31–Aug. 4, 2006, pp. 3160–3163.
 R. J.Bullock, R.Voles,A.
P. V. Brennan, “Estimation and correction of roll errors in dual
antenna interferometric SAR,” in Proc. IEE Radar, Edinburgh, U.K.,
Oct. 14–16, 1997, pp. 253–257.
 A. Reigber, “Correction of residual motion errors in airborne SAR inter-
ferometry,” Electron. Lett., vol. 37, no. 17, pp. 1083–1084, Aug. 2001.
 P. Prats and J. J. Mallorqui, “Estimation of azimuth phase undulations
with multisquint processing in airborne interferometric SAR images,”
IEEE Trans. Geosci. Remote Sens., vol. 41, no. 6, pp. 1530–1533,
 A. Reigber, P. Prats, and J. J. Mallorqui, “Refined estimation of time-
varying baseline errors in airborne SAR interferometry,” IEEE Geosci.
Remote Sens. Lett., vol. 3, no. 1, pp. 145–149, Jan. 2006.
Inst. Electr. Eng.—Radar Sonar Navig., vol. 153, no. 2, pp. 163–176,
for residual motion errors with application to airborne repeat-pass SAR
interferometry,” in Proc. IGARSS, Barcelona, Spain, Jul. 23–27, 2007,
 A. L. Gray and P. J. Farris-Manning, “Repeat-pass interferometry with
airborne synthetic aperture radar,” IEEE Trans. Geosci. Remote Sens.,
vol. 31, no. 1, pp. 180–191, Jan. 1993.
 A. Reigber and R. Scheiber, “Airborne differential SAR interferometry:
First results at L-band,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 6,
pp. 1516–1520, Jun. 2003.
 H. Zebker, P. A. Rosen, R. M. Goldstein, A. Gabriel, and C. Werner,
“On the derivation of coseismic displacement fields using differential
radar interferometry: The Landers earthquake,” J. Geophys. Res., vol. 99,
no. B10, pp. 19617–19634, 1994.
 K. A. C. de Macedo and R. Scheiber, “Controlled experiment for analy-
sis of airborne D-InSAR feasibility,” in Proc. EUSAR. Ulm, Germany,
May 25–29, 2004, pp. 761–764.
 J. Groot, “River dike deformation measurement with airborne SAR,”
IEEE Geosci. Remote Sens. Lett., vol. 1, no. 2, pp. 94–97, Apr. 2004.
 G. Fornaro, R. Lanari, E. Sansosti, G. Francheschetti, S. Perna, A. Gois,
and J. Moreira, “Airborne differential interferometry: X-band experi-
ments,” in Proc. IGARSS, Anchorage, AK, Sep. 20–24, 2004, vol. 5,
 K. A. C. de Macedo, C. Andres, and R. Scheiber, “On the requirements
of SAR processing for airborne differential interferometry,” in Proc.
IGARSS, Seoul, Korea, Jul. 25–29, 2005, pp. 2693–2696.
 S. Perna, C. Wimmer, J. Moreira, and G. Fornaro, “X-band airborne
differential interferometry: Results of the OrbiSAR campaign over the
Perugia area,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 2, pp. 489–
503, Feb. 2008.
 A. Moreira, J. Mittermayer, and R. Scheiber, “Extended chirp scaling
algorithm for air- and spaceborne SAR data processing in stripmap and
ScanSAR imaging modes,” IEEE Trans. Geosci. Remote Sens., vol. 34,
no. 5, pp. 1123–1136, Sep. 1996.
 R. Scheiber and A. Moreira, “Coregistration of interferometric SAR im-
ages using spectral diversity,” IEEE Trans. Geosci. Remote Sens., vol. 38,
no. 5, pp. 2179–2191, Jul. 2000.
and Signal Processing. New York: Wiley, 1991.
 G. Franceschetti and R. Lanari, Synthetic Aperture Radar Processing.
Boca Raton, FL: CRC, 1999.
 I. G. Cumming and F. H. Wong, Digital Processing of Synthetic Aper-
ture Radar Data. Algorithms and Implementation. Boston, MA: Artech
 M. Y. Jin and C. Wu, “A SAR correlation algorithm which accommodates
large-range migration,” IEEE Trans. Geosci. Remote Sens., vol. 22, no. 6,
pp. 592–597, Nov. 1984.
 C. Cafforio, C. Prati, and F. Rocca, “SAR data focusing using seismic
migration techniques,” IEEE Trans. Aerosp. Electron. Syst., vol. 27, no. 2,
pp. 194–207, Mar. 1991.
 R. K. Raney, H. Runge, R. Bamler, I. Cumming, and F. H. Wong, “Pre-
cision SAR processing using chirp scaling,” IEEE Trans. Geosci. Remote
Sens., vol. 32, no. 4, pp. 786–799, Jul. 1994.
 D. Blacknell, A. Freeman, S. Quegan, I. A. Ward, I. P. Finley, C. J. Oliver,
R. G. White, and J. W. Wood, “Geometric accuracy in airborne SAR
images,” IEEE Trans. Aerosp. Electron. Syst., vol. 25, no. 2, pp. 241–258,
Currie, H. D. Griffiths,and
 S. Buckreuss, “Motion errors in an airborne synthetic aperture radar sys-
tem,” Eur. Trans. Telecommun. Relat. Technol., vol. 2, no. 6, pp. 55–64,
 G. Fornaro, “Trajectory deviations in airborne SAR: Analysis and com-
pensation,” IEEE Trans. Aerosp. Electron. Syst., vol. 35, no. 3, pp. 997–
1009, Jul. 1999.
 H. Qi and J. B. Moore, “Direct Kalman filtering approach for GPS/INS
integration,” IEEE Trans. Aerosp. Electron. Syst., vol. 38, no. 2, pp. 687–
693, Apr. 2002.
 P. Prats, K. A. C. de Macedo, A. Reigber, R. Scheiber, and J. J. Mallorqui,
“Comparison of topography- and aperture-dependent motion compensa-
tion algorithms for airborne SAR,” IEEE Geosci. Remote Sens. Lett.,
vol. 4, no. 3, pp. 349–353, Jul. 2007.
 D. R. Stevens, I. G. Cumming, and A. L. Gray, “Options for airborne
interferometric SAR motion compensation,” IEEE Trans. Geosci. Remote
Sens., vol. 33, no. 2, pp. 409–420, Mar. 1995.
 P. Prats, A. Reigber, J. J. Mallorqui, P. Blanco, and A. Moreira, “Es-
timation of the deformation temporal evolution using airborne differ-
ential SAR interferometry,” in Proc. IGARSS, Denver, CO, Jul. 31–
Aug. 4, 2006, pp. 1894–1897.
 R. Bamler and M. Eineder, “Accuracy of differential shift estimation by
correlation and split-bandwidth interferometry for wideband and Delta-k
SAR systems,” IEEE Geosci. Remote Sens. Lett., vol. 2, no. 2, pp. 151–
155, Apr. 2005.
 A. Reigber, “Airborne polarimetric SAR tomography,” Ph.D. dissertation,
Inst. Navigation der Univ. Stuttgart, Stuttgart, Germany, Oct. 2001.
 A. Reigber, “Range dependent spectral filtering to minimize the base-
line decorrelation in airborne SAR interferometry,” in Proc. IGARSS,
Hamburg, Germany, Jun. 28–Jul. 2, 1999, vol. 3, pp. 1721–1723.
 M. Costantini and P. A. Rosen, “A generalized phase unwrapping
approach for sparse data,” in Proc. IGARSS, Hamburg, Germany,
Jun. 28–Jul. 2, 1999, vol. 4, pp. 267–269.
 A. Reigber and J. Moreira, “Phase unwrapping by fusion of local and
global methods,” in Proc. IGARSS, Singapore, Aug. 3–8, 1997, vol. 2,
 A. Reigber and A. Moreira, “First demonstration of airborne SAR to-
mography using multibaseline L-band data,” IEEE Trans. Geosci. Remote
Sens., vol. 38, no. 5, pp. 2142–2152, Sep. 2000.
 M. Nolan and D. R. Fatland, “Penetration depth as a DInSAR observable
and proxy for soil moisture,” IEEE Trans. Geosci. Remote Sens., vol. 41,
no. 3, pp. 532–537, Mar. 2003.
Pau Prats (S’03–M’06) was born in Madrid, Spain,
in 1977. He received the Ingeniero degree in
telecommunication engineering and the Ph.D. degree
Barcelona, Spain, in 2001 and 2006, respectively.
In 2001, he was with the Institute of Geomatics,
Barcelona, Spain, as a Research Assistant, designing
a subaperture SAR processor. In 2002, he joined the
Department of Signal Theory and Communications,
pass interferometry and airborne differential SAR
interferometry. From December 2002 to August 2006, he was an Assistant
Professor in the Department of Telecommunications and Systems Engineering,
Universitat Autónoma de Barcelona (UAB), Barcelona. Since August 2006, he
has been with the SAR Processing Group, Microwave and Radar Institute,
German Aerospace Center (DLR), Oberpfaffenhofen, as a Research Scientist,
working in the field of SAR processing and interferometry. His research
pass interferometry, and differential interferometry with airborne systems.
Dr. Prats received the First Prize at the Student Paper Competition, Interna-
tional Geoscience and Remote Sensing Symposium 2005, Seoul, Korea.
1078 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 46, NO. 4, APRIL 2008
Andreas Reigber (M’02) was born in Munich,
Germany, in 1970. He received the Diploma de-
gree in physics from the University of Constance,
Constance, Germany, in 1997 and the Ph.D. degree
from the University of Stuttgart, Stuttgart, Germany,
From 1996 to 2000, he was with the Microwave
and Radar Institute, German Aerospace Center
(DLR), Oberpfaffenhofen, where he worked in the
field of polarimetric SAR tomography. In 2001, he
was with the Antenna, Radar, and Telecom Labo-
ratories, University of Rennes 1, Rennes, France, for a postdoctoral position
on radar polarimetry and polarimetric interferometry. Since 2002, he has
been a Research Associate with the Computer Vision and Remote Sensing
Laboratories, Berlin University of Technology, Berlin, Germany. His current
main research interests include the various aspects of multimodal SAR, like
SAR interferometry, SAR polarimetry, SAR tomography, and time–frequency
analyses but also hyperspectral remote sensing and the application of computer
vision and machine learning approaches in remote sensing.
Dr. Reigber was the recipient of the European SAR Conferences 2000
Student Prize Paper Award for an article on SAR remote sensing of forests, the
IEEE GRSS Transactions Prize Paper Award in 2001 for a work on polarimetric
SAR tomography, as well as the IEEE GRSS Letters Prize Paper Award in
2006 for a work on multipass SAR processing. He also coauthored three papers
which have been successful at the student paper competitions of IGARSS’05
(first prize), EUSAR’06 (third prize), and IGARSS’07 (second prize).
Jordi J. Mallorquí (S’93–M’96) was born in
Tarragona, Spain, in 1966. He received the Ingeniero
degree in telecommunications engineering and the
Ph.D. degree in telecommunications engineering for
his research on microwave tomography for biomed-
ical applications from the Universitat Politècnica de
Catalunya (UPC), Barcelona, Spain, in 1990 and
In 1993, he was an Assistant Professor and, since
1997, he has been an Associate Professor with the
Department of Signal Theory and Communications,
UPC. His teaching activity involves microwaves, radio-navigation systems, and
remote sensing. In 1999, he spent a sabbatical year with the Jet Propulsion
Laboratory, Pasadena, CA, where he worked on interferometric airborne SAR
calibration algorithms. He is currently working on the application of SAR
interferometry to terrain deformation monitoring with orbital, airborne, and
ground data, vessel detection and classification from SAR images, and 3-D
electromagnetic simulation of SAR systems. He is also collaborating in the
design and construction of a ground-based SAR interferometer for landslide
control. Finally, he is currently developing the hardware and software of a bista-
TerraSAR-X as sensors of opportunity. He has published more than 80 papers
on microwave tomography, electromagnetic numerical simulation, and SAR
processing, interferometry, and differential interferometry in referred journals
and international symposia.
Rolf Scheiber received the Diploma degree in elec-
trical engineering from the Technical University of
Munich, Munich, Germany, in 1994 and the Ph.D.
degree in electrical engineering from the University
of Karlsruhe, Karlsruhe, Germany, in 2003, with a
thesis on airborne SAR interferometry.
Since 1994, he has been with the Microwaves and
Radar Institute, German Aerospace Center (DLR),
Oberpfaffenhofen, where he developed the opera-
tional high-precision interferometric SAR processor
for its Experimental SAR (E-SAR) airborne sensor.
Since 2001, he has been heading the SAR Signal Processing Group, SAR
Technology Department, where he is presently responsible for the E-SAR cam-
paign data processing, as well as the development of the processing software
for the new airborne sensor F-SAR. His current research interests include
algorithm development for high-resolution air- and spaceborne SAR focusing,
SAR interferometry, differential SAR interferometry, SAR tomography, as well
as radio-sounding algorithms and applications.
Dr. Scheiber received the IEEE TRANSACTIONS ON GEOSCIENCE AND
REMOTE SENSING Transactions Prize Paper Award in 1997 as a coauthor of
the contribution, “Extended Chirp Scaling Algorithm for Air- and Spaceborne
SAR Data Processing in Stripmap and ScanSAR Imaging Modes.”
Alberto Moreira (M’92–SM’96–F’04) was born in
São José dos Campos, Brazil, in 1962. He received
the B.S. and M.S. degrees in electrical engineering
from the Aeronautical Technological Institute, São
José dos Campos, in 1984 and 1986, respectively,
and the Dr.Eng. degree (with honors) from the Tech-
nical University of Munich, Munich, Germany, in
From 1996 to 2001, he was a Chief Scientist
and Engineer with the SAR Technology Department,
Microwaves and Radar Institute, German Aerospace
Center (DLR), Oberpfaffenhofen, where since 2001, he has been the Director
with the Microwaves and Radar Institute. The institute contributes to several
scientific programs and space projects for actual and future air- and spaceborne
SAR missions. Recently, the mission proposal TanDEM-X led by his institute
has been approved for the realization phase. He is the Initiator and Principal
Investigator for this mission. In 2003, he was a Full Professor in the field
of microwave remote sensing with the University of Karlsruhe, Karlsruhe,
Germany. He pioneered research on high-resolution radar signal processing
and innovative SAR system concepts and associated techniques like radar
tomography, digital beamforming, and advanced imaging modes. His profes-
sional interests and research areas encompass radar end-to-end system design
and analysis, innovative microwave techniques and system concepts, signal
processing and remote sensing applications.
Prof. Moreira is currently serving as a member of the IEEE GRSS Adminis-
trative Committee (1999–2001, 2004–2009), has been the Chair of the German
Chapter, GRSS, since 2003, and is currently actively serving as an Associate
Editor for the IEEE GEOSCIENCE AND REMOTE SENSING LETTERS. Since
2003, he has also been serving as a member of the Board of Directors of the
Information Technology Society of VDE (German Association for Electrical,
Electronic, and Information Technologies). In 1995, he was the recipient of the
DLR Science Award. He and his colleagues were the recipients of the GRSS
Transactions Prize Paper Awards in 1997 and 2001. He was also the recipient
of the IEEE Nathanson Award in 1999 and the IEEE Kiyo Tomiyasu Award in
2007. He has been contributing to the successful series of the European SAR
conferences since 1996 as a member of the Technical Program Committee, as
Technical Chairman in 2000, as an Awards Chairman from 2002 to 2004, and
as a General Chairman in 2006.