Phase Offset Calculation for Airborne InSAR DEM Generation Without Corner Reflectors

Phase Offset Calculation for Airborne InSAR DEM Generation Without Corner Re?ectors

Stefano Perna,Member,IEEE,Carmen Esposito,Paolo Berardino,Antonio Pauciullo,

Christian Wimmer,and Riccardo Lanari,Fellow,IEEE

Abstract—Digital elevation model(DEM)generation through interferometric processing of synthetic aperture radar(SAR)data requires the calculation of a constant phase offset present in the unwrapped interferograms.This operation is usually carried out by exploiting the external information provided by GPS mea-surements in correspondence of corner re?ectors(CRs)properly deployed over the illuminated area.This is,however,expensive in terms of cost and time.Moreover,deployment of CRs along with the corresponding in situ GPS measurements can be dif?cult(if not impossible)in unfriendly areas or in natural disaster scenarios. To circumvent these limitations,we address in this work the esti-mation of the required phase offset by exploiting a low-accuracy external DEM,without using CRs.More speci?cally,a two-step approach is proposed.The?rst step exploits the synthetic phase computed by means of the external DEM and represents a straightforward extension of the procedure that is usually applied in the presence of CRs.Subsequently,in order to re?ne the achieved solution,a second step is introduced.It is based on a least squares approach that properly exploits the difference between the available low-accuracy DEM and the interferometric DEM generated by means of the phase offset value roughly estimated through the?rst step.The presented approach is very easy to implement and allows us to achieve an accurate and fast estimate of the needed phase offset,even in the presence of an external DEM affected by a vertical bias and/or a planar shift.The algorithm per-formances improve in the presence of a large variation of the look angle,as it generally happens in airborne systems.On the other side,the effectiveness of the algorithm may be impaired by the pos-sible presence of artifacts in the unwrapped interferograms,such as those due to the residual motion errors typical of repeat-pass airborne SAR scenarios.Accordingly,the proposed solution is par-ticularly suitable for single-pass interferometric airborne SAR sys-tems,as demonstrated through the presented experimental results achieved on real data.

Index Terms—Synthethic aperture radar(SAR),SAR interfer-ometry(InSAR),airborne SAR,digital elevation model(DEM). Manuscript received March28,2014;revised July9,2014and September12,2014;accepted October13,2014.

S.Perna is with the Dipartimento di Ingegneria,Universitàdegli Studi di Napoli“Parthenope,”80143Napoli,Italy,and also with the IREA-CNR,80124 Napoli,Italy(e-mail:perna@uniparthenope.it).

C.Esposito is with the Dipartimento di Ingegneria,Universitàdegli Studi del Sannio,82100Benevento,Italy,and with the IREA-CNR,80124Napoli,Italy (e-mail:esposito.c@https://www.360docs.net/doc/2f8884621.html,r.it).

P.Berardino, A.Pauciullo,and https://www.360docs.net/doc/2f8884621.html,nari are with the IREA-CNR, 80124Napoli,Italy(e-mail:berardino.p@https://www.360docs.net/doc/2f8884621.html,r.it;pauciullo.a@https://www.360docs.net/doc/2f8884621.html,r.it; lanari.r@https://www.360docs.net/doc/2f8884621.html,r.it).

C.Wimmer is with the Bradar,12244-000S?o Josédos Campos,SP,Brazil (e-mail:of?ce@wimmer-christian.de).

Color versions of one or more of the?gures in this paper are available online at https://www.360docs.net/doc/2f8884621.html,.

Digital Object Identi?er10.1109/TGRS.2014.2363937

I.I NTRODUCTION

S YNTHETIC aperture radar(SAR)interferometry(InSAR) allows the generation of the digital elevation model(DEM) of an area by exploiting the phase difference(interferogram) between SAR data pairs relevant to the same observed scene and received from slightly different view angles.Following the interferogram generation operation,the InSAR processing chain[1]–[3]requires the application of a phase unwrapping (PhU)procedure to retrieve the absolute phase signals from their(measured)modulo-2πrestricted components.The PhU procedure,however,provides the unwrapped interferogram up to a constant offset,which must be estimated.

Such an estimation procedure is commonly addressed by making use of a number of corner re?ectors(CRs)prop-erly deployed over the observed area,provided that accurate knowledge of their positions has been achieved[4].To this aim,once the CR positions are known,the corresponding topographic phases(which,in SAR jargon,are referred to as synthetic phases)are calculated.Evaluation of the required phase offset can be then carried out by solving an optimization problem whose objective function is the properly de?ned dis-tance between the CR synthetic phases and the corresponding unwrapped phases.A very ef?cient implementation of such an optimization is provided by the least squares(LS)solution, which leads to an estimate that,in the following,is referred to as phase-based estimate(PBE).

It is worth stressing that the use of CRs for the calculation of the needed phase offset requires,apart from the deployment of the CRs themselves over the illuminated scene,in situ dif-ferential GPS(brie?y DGPS)measurements of their positions. This may be expensive in terms of both cost and time.More-over,deployment of CRs,along with the corresponding in situ DGPS measurements,may be dif?cult(if not impossible)in unfriendly areas or in natural disaster scenarios.Accordingly, in several cases of practical interest,the CR-based algorithms for the evaluation of the required InSAR phase offset,although guaranteeing high performances[4],cannot be applied.

To circumvent these limitations,some alternative methods have been addressed in the literature[5]–[9].In particular,in [5],the redundancy offered by two different subbands of the entire range bandwidth of the InSAR data pair is exploited.The methods in[6]–[8]are instead based on the redundancy offered by different interferometric data pairs relevant to the same area. In particular,in[6],two interferometric acquisitions carried out on parallel tracks by opposite directions are exploited,whereas in[7]and[8],a proper combination of several multibaseline

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interferograms is performed.A different strategy is adopted in [9],where the geometric information provided by an accurate coregistration step based on cross-correlation maximization is exploited.As a matter of fact,all these methods do not take(or take just marginally,see[9])bene?t from possible information coming from available external DEMs.

We present in this work a solution that allows us to estimate the interferogram offset by effectively exploiting external low-accuracy DEMs characterized by signi?cant height errors and vertical biases.

To this regard,it is noted that an attractive application scenario of the proposed approach is represented by airborne interferometric systems,where we use a low-accuracy external DEM,such as an ASTER[10]or an SRTM[11]–[15]one, to correctly apply motion compensation procedures during the focusing step[16]–[19].

The presented approach consists of two processing steps. The?rst step extends the procedure usually exploited in the presence of CRs:it is based on the PBE algorithm,and it is applied to the synthetic phase computed by means of the ex-ternal DEM.

Subsequently,a second step is introduced in order to re?ne the achieved solution.This processing operation is based on a LS approach that properly exploits the difference between the external low-accuracy DEM and the InSAR DEM generated by means of the phase offset value roughly estimated through the ?rst step.

To this regard,in order to fully clarify the context of the proposed procedure,we perform a preliminary analysis that shows why the estimate provided by the?rst step needs to be re?ned through the second step.

The effectiveness of the proposed algorithm enhances in the presence of a large variation of the look angle,as it generally happens in airborne systems.On the other side,the perfor-mances of the algorithm may worsen when the unwrapped interferograms are affected by artifacts,such as those due to the so-called residual motion errors typical of repeat-pass airborne SAR data pairs.Accordingly,the proposed approach is par-ticularly suitable for single-pass well-calibrated interferometric airborne SAR systems.

The overall procedure is computationally ef?cient and very easy to implement.

It has been applied on real airborne single-pass InSAR data acquired on a test area where,for comparison purposes,a num-ber of CRs have been deployed,and the corresponding in situ DGPS measurements have been carried https://www.360docs.net/doc/2f8884621.html,parisons with these DGPS measurements demonstrate the effectiveness of the presented approach.

This paper is organized as follows.In Section II,we clarify the procedure context by brie?y recalling the PBE algorithm and discussing its performances.The proposed two-step approach is described in Section III.Section IV shows the experimental results.Section V is dedicated to some concluding remarks.

II.P HASE-B ASED E STIMATE(PBE)A LGORITHM

Let us consider a2-D unwrapped interferogram, e.g.,?uw(x,r),where x and r are the azimuth and range coordi-nates,respectively.As recalled above,the interferogram

?uw(x,r)is given but for a constant offset,e.g.,φo?.Accord-ingly,our problem consists in?nding the constant quantityφo?. Hereafter,any object providing external information on the topography(that is,either a CR of known position or a point of an available external DEM)will be referred to as ground control point(GCP).

Let us assume that K is the number of available GCPs,rang-ing from some units to tens in case we exploit CRs or millions in case we exploit an external DEM.The position of each GCP is assumed to be known,in a generic reference system, with a given degree of uncertainty.Also,the interferometric acquisition geometry is assumed to be known.Accordingly,the application of the backward geocoding procedure extensively discussed in[1],[2],and[20]allows calculating the SAR coordinates,e.g.,x GCP

k

(azimuth)and r GCP

k

(range),and the

so-called synthetic phase?GCP

k

of the generic k th GCP,k∈{1,...,K}.Accordingly,?GCP and?uw represent the vectors

collecting,respectively,the synthetic phases?GCP

k

and the

phases?uw

k

picked up from the unwrapped interferogram in correspondence of the available GCPs.

In principle,our problem consists in?nding the constant valueφo?such that

?uw?1φo?=?GCP(1) where1=[1,...,1]T.However,the presence of noise,which may affect both the vectors?uw and?GCP,renders(for values of K>1)unsolvable the overdetermined problem in (1).Accordingly,in the cases of practical interest,the following optimization problem is addressed:

?φ

o?

=arg min

ξ∈R

dist(?uw?1ξ,?GCP)(2)

where dist(·)represents the properly de?ned distance between vectors?uw?1ξand?GCP,whereas the symbol∧stands for estimator.By considering the Euclidean distance,the optimiza-tion problem in(2)can be addressed via the LS approach[21], which leads to

?φ

o?PBE

=(1T1)?11T(?uw??GCP)=

1

K

K

k=1

?uw k??GCP

k

.

(3) It is noted that the subscript PBE in(3)stands for phase-based estimate to emphasize that the objective function of the corresponding optimization is a phase.

It is worth stressing that the PBE in(3)represents the mean of the vector?uw??GCP.Obviously,its computation is very easy and fast even for values of K on the order of millions,as it happens when we want to exploit an external DEM and we deal with a large SAR data set.

In order to assess the performances of the PBE in(3),we have evaluated the estimation error

ε=?φo?

PBE

?φo?(4) as a function of K.To this aim,we have simulated a typical airborne SAR acquisition geometry(main parameters are col-lected in Table I)with a height of ambiguity[2]equal to159m

PERNA et al.:PHASE OFFSET CALCULATION FOR AIRBORNE INSAR DEM GENERATION WITHOUT CRs 2715

TABLE I

S IMULATED SAR S

YSTEM

at midrange.Within the simulated illuminated area,we have considered a variable number of GCPs,that is,we have set different values for K in (3).The positions of the GCPs have been randomly set.Moreover,for the sake of simplicity,in the

expression (3)we have supposed only the terms ?GCP k

to be affected by noise,thus considering ?uw

not noisy.Obviously,the unavoidable presence of noise in the unwrapped interfer-ograms (due to possible atmospheric artifacts,PhU errors [1],[2],and,in the case of airborne systems,the so-called residual motion errors [22])generally impairs the performances of the PBE.Accordingly,the following analysis provides,in practical cases,upper bounds for the accuracy of the PBE.

In order to render ?GCP noisy,we have added to the actual topographic height of the GCPs a uniformly

distributed random variable on the interval [μ?√3σ,μ+√3σ].In particular,the stat-istical expectation μaccounts for the possible presence of a ver-tical bias of the topographic information provided by the GCPs.Moreover,the vertical inaccuracy around such a (possibly)biased height is accounted for by the standard deviation σ.We have then set different values for the parameters μand σ,simulating two different scenarios:we have ?rst considered σon the order of some centimeters,as it happens when using accurate DGPS measurements on CRs;subsequently,we have set σon the order of some meters,as it may happen when using an external DEM with a relatively poor accuracy.

As a ?rst example,we have set μ=0m and considered two values for σ:σ=1cm and σ=5cm.In Fig.1(a),the standard deviation (evaluated over 1000trials)of εis plotted versus the number of exploited GCPs.As expected,the higher the accuracy of the topographic information provided by the GCPs,the less the number of GCPs necessary to achieve a desired estimation accuracy.In particular,it can be seen that,for the considered geometry,even for σ=5cm,a number of GCPs greater than 7allows calculating the desired phase offset with an uncertainty less than 0.05?.To this regard,we recall that the error εin (4)induces the following topographic error in the ?nal InSAR DEM [1]:

z (x,r,?φo?PBE

)?z (x,r,φo?)≈β(x,r )ε(5)

where,as said,x and r are the azimuth and range SAR

coordinates,respectively.Moreover,z (x,r,?φo?PBE

)is the

to-Fig.1.Relevant to the PBE.(a)Standard deviation (evaluated over 1000

trials)of the estimation error εin (4)versus the number of exploited GCPs.(b)Height error variation from near to far range induced by the estimation error εin Fig.1(a).The external topographic information provided by the GCPs is characterized by a bias μ=0m and standard deviation σ∈{1,5}cm.Simulated SAR system parameters are collected in Table I.

pographic height,in SAR grid,of the InSAR DEM obtained starting from ?uw (x,r )and using,within the InSAR process-ing chain [1],[2],the phase offset factor ?φo?PBE

.Instead,z (x,r,φo?)is the topographic height of the InSAR DEM that we would obtain by using the correct phase offset φo?.Finally,the coef?cient β(·)in (5)can be obtained by consid-ering the ?rst-order Taylor expansion of z (x,r,·)around φo?[1],[2],i.e.,

β(x,r )=?

λr sin ?(x,r )2aπb ⊥(x,r )

(6)

being ?(·)the look angle and b ⊥(·)the so-called orthogonal

baseline [1](which depends,in turn,on ?);moreover,the coef-?cient a depends on the considered interferometric con?gura-tion (a =1for bistatic systems,whereas a =2for monostatic ones).It is worth noting that the error in (5)varies from near to far range (particularly in airborne con?gurations where the variability of both ?(·)and b ⊥(·)within the range swath is signi?cant).For the InSAR DEM relevant to the simulated system of Table I we have thus evaluated,by means of (5),the height error variation from near to far range induced by the estimation error εreported in Fig.1(a).Results are plotted in Fig.1(b)and show that,as expected,the PBE in (3)guarantees good performances for values of K on the order of a few units,

2716IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.53,NO.5,MAY

2015

Fig.2.As in Fig.1,but for σ∈{1,5,10,15}

m.

Fig.3.As in Fig.2,but for μ=7m.

provided that the accuracy of the topographic information given by the GCPs is on the order of some centimeters,as it happens when we exploit CRs whose position is measured with DGPS in situ campaigns.Similar results,not reported here for brevity,have been achieved also with SAR systems and con?gurations other than those considered in Table I.

Turning to the case of our interest,which consists in the exploitation of a low-accuracy external DEM,we have impaired the so-called relative vertical accuracy [11]of the GCPs by increasing the standard deviation of the added noise term.More speci?cally,we have set four values of σranging from 1to 15m;the expectation μhas been instead retained equal to 0m (as in Fig.1).Corresponding results are collected in Fig.2.As expected,a number of GCPs signi?cantly larger than that observed in Fig.1are now needed to achieve acceptable esti-mation accuracy.Notwithstanding,even for σ=15m,which overestimates the typical relative vertical accuracy of the easily available worldwide ASTER [10]or SRTM [11]DEMs,a number of GCPs on the order of 10000(well below the number of pixels of typical airborne SAR data)are suf?cient to estimate the desired phase offset with an uncertainty less than 0.5?.This leads,in the simulated interferometric system,to a ?nal InSAR DEM with a height error variation from near to far range less than 35cm.

Unfortunately,the accuracy of the PBE signi?cantly worsens when the topographic information provided by the GCPs is affected by a vertical bias.This is clearly shown in the plots of Fig.3,which have been obtained by setting μ=7m and retaining the same values of σconsidered in Fig.2.From the curves in Fig.3it turns out that the solution of the PBE asymptotically converges to a completely wrong estimate of the needed phase offset.In particular,the error εis always larger than 18?:this leads to a ?nal InSAR DEM with 11m of height error variation from near to far range.Accordingly,we can draw the conclusion that the evaluation of the PBE using an external DEM is not appropriate when the latter is affected by a vertical bias of some meters.

To this regard,it is worth stressing that the presence of vertical biases is quite common in easily accessible DEMs.For instance,the absolute and relative vertical accuracy require-ments of SRTM are 16m (90%)and 6m (90%),respectively [11].This means that,within a 225×225Km 2area [11],the SRTM height errors may have a variation of ±6m (90%)super-imposed to a bias whose absolute value,in principle,may reach up to 10m.Note that the presence of vertical biases affecting the SRTM DEM has been con?rmed by validation campaigns [11]–[15].For instance,in a study focused on Costa Rica [14],it is shown that the vertical bias of the SRTM C-band DEM is on the order of 4.5m in “bare Earth”regions and increases in vegetated areas.Moreover,in [11]it is shown that,in the scale of 225km,the height error of the SRTM X-band DEM relevant to the South of Australia ocean may reach a vertical bias on the

PERNA et al.:PHASE OFFSET CALCULATION FOR AIRBORNE INSAR DEM GENERATION WITHOUT CRs2717 order of10m.Accordingly,the valueμ=7m considered in

the examples of Fig.3represents a realistic one.

III.S LOPE-T OPOGRAPHY-B ASED

E STIMATE(ST OP BE)A LGORITHM

In order to circumvent the problems related to the presence

of a vertical bias affecting the available external DEM,a proper

procedure consisting of two main steps is now proposed.

The?rst step straightforwardly carries out the PBE by ex-

ploiting a low-accuracy external DEM.

The second step is aimed at estimating and correcting the

PBE error,i.e.,εin(4),resulting from the?rst step.To this

aim,we will exploit the available DEM.However,differently

from the?rst step,we perform an optimization operation whose

objective function is a topographic height;moreover,a mathe-

matical model capable of accounting for the presence of both

the residual errorεin(4)and the relative bias between the

external DEM and the one that we are going to generate is

adopted.More details are now in order.

Let z GCP(x,r)be the topographic height provided by the

available low-accuracy https://www.360docs.net/doc/2f8884621.html,e of(5)allows expressing

the difference between the InSAR DEM obtained by using the

roughly estimated phase offset?φo?

PBE and the external DEM

as follows:

z(x,r,?φo?

PBE

)?z GCP(x,r)=β(x,r)ε+Θ(x,r)(7) whereβ(x,r)is de?ned in(6),whereas

Θ(x,r)≈z(x,r,φo?)?z GCP(x,r).(8)

The difference in(7)is given by two contributions.The?rst term is proportional to the PBE error,through the coef?cient β(x,r)in(6),which varies over the illuminated scene and depends on the acquisition geometry.The second term,see(8), accounts for the different vertical accuracy of the external DEM and the InSAR DEM that we would generate by using the correct phase offsetφo?.

In order to estimate the residual errorεin(7),it is convenient to rewrite(7)in a more manageable form.To this aim,let us collect all the K terms of the left-hand side of(7)within the vectorΔ,which can be thus expressed as

Δ=βε+Θ(9)

beingΘandβthe vectors collecting all the valuesβ(x,r) andΘ(x,r)in(7).The estimate of the residual errorεcan be obtained from the vectorΔby means of a LS approach.To this regard,it is worth noting that,according to(8),the noise term Θin(9)is a nonzero-mean vector,which can be conveniently rewritten as follows:

Θ=1ν+Θ0(10)

whereνis the mean ofΘ,andΘ0is a zero-mean vector.It is noted thatνrepresents the relative bias between the DEM

that Fig.4.Pictorial view of the vectorΔin(9)along with the?tting line(white line)estimated through the STopBE.

we are going to generate and the external DEM.1Use of(10)in (9)leads to

Δ=βε+1ν+Θ0.(11)

From(11),it turns out that the residual errorεand the relative biasνcan be jointly estimated by solving the following opti-mization problem:

(?ε,?ν)=arg min dist(βξ1+1ξ2,Δ)

(ξ1,ξ2)∈R2.(12)

By considering the Euclidean distance,the optimization prob-lem in(12)can be addressed(as in Section II)via the LS approach[21],which now leads to

?εSTopBE

?ν

=(H T H)?1H TΔ(13) where the K×2matrix H is given by

H=[β1].(14)

It is noted that the subscript STopBE in(13)stands for slope-topography-based estimate to emphasize that the estimate in (13)provides the line?tting of the vectorΔ[which contains the topographic difference in(7)]and that the needed parameter ?εSTopBE represents the angular coef?cient(i.e.,the slope)of such a?tting line,depicted in the pictorial plot in Fig.4. Hereafter in this paper,for the sake of simplicity,the whole joint estimate in(13)is referred to as STopBE.

Some further considerations are now in order.

First,it is noted that the?tting line in Fig.4very marginally depends on possible“ramp”errors of the external DEM corre-lated to topographic slopes present in the observed area.Indeed, adjacent samples of the experimental data depicted in Fig.4are adjacent samples of the vectorΔsorted according to increasing values of the coef?cientβ(·)in(6).Accordingly,they are typ-ically not adjacent pixels of the original SAR image,and thus, they are not expected to show,at least in general,high topo-graphic correlation.In other words,the“ramp”errors of the ex-ternal DEM are typicallyβindependent,particularly when the generation processes of our InSAR DEM and the external DEM are independent of each other,as it happens in the airborne case when the external DEM is the worldwide ASTER[10]or SRTM[11]one.Of course,this does not hold when the external

1When only the external DEM is affected by a vertical biasμ(as assumed in Section II),we haveν=?μ.

2718IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,VOL.53,NO.5,MAY 2015

ill-calibrated DEM has been generated with the same acquisi-tion geometry of our InSAR DEM,because in this particular case,the “ramp”errors of the external DEM are likely to become βdependent.This means that in the airborne case,if we ?y by carrying out adjacent and overlapping acquisitions (as it commonly happens to cover areas wider than the range swath),we cannot think to generate an arbitrarily ill-calibrated DEM (by using an arbitrary phase offset)for the ?rst strip and then successfully apply the STopBE in (13)for the adjacent and overlapping strips by exploiting the ?rst ill-calibrated DEM.Second,it is worth noting that the higher the variance of the vector β,the more accurate the STopBE in (13).To show this,we observe that the estimation error involved in (13)is given by the projection of the noise Θ0in (11)onto the sub-space spanned by the columns of the system matrix H in (14)see [21].It can be easily shown [21]that such a projection is inversely proportional to the determinant of the matrix H T H ,which,in our case,is given by

det(H T H )=K 2??1K K k =1

β2k ? 1K

K

k =1

βk 2??

(15)and it is thus proportional to the variance of the vector β,being

K 2the corresponding proportionality constant.This implies ?rst of all that (not surprisingly)the higher the number K of available GCPs,the less the estimation error involved in (13).More important,the higher the variance of β(·)in (6),the less the estimation error involved in (13).For the latter reason,the STopBE in (13)turns out to be particularly suitable for airborne (rather than satellite)acquisitions,which are characterized by higher variations of the look angle ?and,thus,of the parameter β(·)in (6).

Regarding the use of airborne SAR systems,it must be re-called on the other hand that the presence of the so-called resid-ual motion errors [22],which typically affect the interferograms obtained with repeat-pass acquisitions or with ill-calibrated single-pass systems [4],may impair the performances of the STopBE in (13).Indeed,such residual phase errors,when converted to height,introduce azimuth-dependent [22]vertical errors possibly superimposed to a vertical bias [4].The latter effect renders the parameter ?νestimated in (13)dependent not only on the vertical bias affecting the external DEM but also on the vertical bias of the DEM that we are going to generate.More important,the former effect increases the variance of the noise term Θin (10)[i.e.,the variance of Θ0in (10)and (11)],thus involving a lower matching between the linear model adopted in (12)and the experimental data Δ,with a corresponding impair-ment of the overall estimate carried out by the STopBE in (13).According to the above considerations,the proposed STopBE turns out to be particularly suitable for single-pass airborne data pairs acquired by well-calibrated systems.

Turning to the calculation of the parameter β(x,r ),which depends on the topography of the observed scene (through ?and b ⊥),we stress that it can be accurately carried out by exploiting the available external DEM,even when this has a low accuracy.Indeed,starting from (6),it can be easily shown that topographic errors are reduced approximately by a factor λ/(2aπb ⊥)when they are “transferred”to β

.

Fig.5.Flow diagram of the processing chain of the proposed two-step algorithm.

It is remarked that the STopBE in (13)can be easily rear-ranged in order to account also for the application of proper weights depending,for instance,on the interferometric coher-ence of the available data.In this case,(13)is replaced by the weighted LS (WLS)solution,i.e.,

?εSTopBE

?ν = H T WH

?1H T WΔ(16)where the K ×K matrix W is given by

W =M T M

(17)

and

M =diag (m 1,...,m k ,...,m K )

(18)being m k the aforementioned weights.As a matter of fact,the

expression in (17)simpli?es as W =M when m k ∈{0,1},that is,when the performed weighting carries out just a masking operation.

The processing chain of the presented two-step approach is shown in the ?ow diagram in Fig.5,and it is summarized in the following.

The ?rst step requires:

?calculation of the synthetic phase relevant to the external

DEM,i.e.,calculation of the terms ?GCP k

in (3);?calculation of the PBE ?φo?PBE

in (3);whereas the second step requires:

?calculation of the term z (x,r,?φo?PBE

)in (7)via a phase-to-height conversion step [1]that uses the phase offset ?φo?PBE

estimated through the ?rst step;

PERNA et al.:PHASE OFFSET CALCULATION FOR AIRBORNE INSAR DEM GENERATION WITHOUT CRs2719?calculation of the vectorΔin(13)collecting the differ-

ence between z(x,r,?φo?

PBE )and the external DEM;

?calculation of the parameterβ(·)in(6)and,in turn,of the matrix H in(14);

?application of the STopBE in(13)and(14)(or(16)–(18) in the weighted case)in order to?nd?εSTopBE;?calculation of the re?ned InSAR DEM by exploiting both the estimates carried out at the?rst and second steps,i.e., calculation of z(x,r,?φo?

PBE

??εSTopBE).

Note that the proposed two-step approach is very simple to implement.Indeed,in the airborne case,the synthetic phase ?GCP as well as the parameterβ(·)can be straightforwardly obtained by terms that are usually needed to implement motion compensation procedures[16]–[19].Accordingly,in addition to the processing procedures usually needed by the standard processing chain leading from the acquired SAR data to the generation of the?nal DEM,the?rst step of the overall algo-rithm just involves the computation of the arithmetical mean in(3),whereas the second step just requires?nding the LS estimate in(13)and(14)(or(16)–(18)in the weighted case). Some?nal considerations are now in order.

At?rst sight,one could argue that the?rst step of the pro-cedure is unnecessary since the second step can be applied,in principle,by exploiting an InSAR DEM obtained with a generic

phase offset,e.g.,φstart,other than?φo?

PBE .However,it must be

noted that it is preferable to deal with a value ofφstart as close as possible toφo?.Indeed,the smaller the quantity|φstart?φo?|,the more accurate the approximation involved in(5) and thus in(8).This involves higher matching between the linear model adopted in(12)and the experimental dataΔ, thus rendering more accurate the estimate carried out by(13) and(14)(or(16)–(18)in the weighted case).Accordingly,the PBE at the?rst step plays an important role,since it repre-sents a starting value forφstart not signi?cantly far from the neededφo?.

Moreover,in order to further improve the performances of the STopBE in(13)and(14),we can iteratively apply the second step of our procedure,thus taking advantage from the in-creased matching,obtained at each iteration,between the linear model adopted in(11)and the updated experimental data. Iterative application of the second step can be easily imple-mented following the?ow diagram reported in Fig.6,where the threshold T must be properly set according to the desired DEM accuracy,the subscript i indicates the iteration number,

and the initialization value for?φo?

i is?φo?

1

=?φo?

PBE

.With

reference to the symbols used in the diagram in Fig.5,it is noted

that in Fig.6,?εSTopBE

1=?εSTopBE,andΔ1=Δ.Clearly,

if the iterative procedure in Fig.6stops at the?rst iteration, the solution coincides with the PBE,whereas if it stops at the second iteration,the solution coincides with the cascade of the PBE and STopBE shown in Fig.5.

IV.R ESULTS

The presented algorithm has been tested on real data ac-quired by the airborne OrbiSAR system[23],which operates at X-band and P-band.In particular,the results reported in this section are relevant to a single-pass interferometric data pair acquired at X-band over the city of S?o Josédos Campos,

SP,Fig.6.Flow diagram of the iterative application of the second step of the proposed algorithm sketched in Fig.5.

TABLE II

O RBI SAR X-B AND S YSTEM AND M ISSION P

ARAMETERS Brazil.The main parameters of the used X-band iterferometric system are listed in Table II along with the mission parameters. It is remarked that exploitation of a single-pass system has limited the impact of the residual motion errors[22].To this regard,it is stressed that the OrbiSAR system exploits a modern embedded GPS/Inertial Navigation System(INS)equipment [23].In addition,an accurate system calibration consisting in the precise measurement of the antennas’phase centers and the corresponding lever arms(i.e.,the distances between the antennas’phase centers and the measurement center of the INS) has been carried out(along the lines shown in[4]).This allowed very precise measurement of the?ight parameters for accurate application of the motion compensation procedure[16],[17], thus further reducing the residual motion errors affecting the obtained single-pass interferograms.

The external DEM exploited in the following examples is the C-band SRTM,whose absolute and relative vertical accuracy requirements are16m(90%)and6m(90%),respectively [11].Moreover,as shown in[11]–[15]and already observed in Section II,the aforementioned accuracy requirements for the SRTM DEM are compatible with the presence of vertical biases on the order of some meters.

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Fig.7.Amplitude multilook image of the observed scene.White squares have been superimposed in correspondence of the CRs deployed over the area.Moreover,a range cut of the SRTM DEM height in correspondence of the white line is shown at the bottom of the

?gure.

Fig.8.Left column shows (a)Mask 1,(c)Mask 2,and (e)Mask 3applied in the experiments of Section IV.Right column shows (b)Mask 1,(d)Mask 2,and (f)Mask 3superimposed to the original multilook amplitude SAR image shown at the top of Fig.7.

The SRTM DEM has been used also during the focusing step to perform accurate motion compensation [16]–[18].

Eight CRs have been deployed over the range direction within the illuminated area,and DGPS measurements of their positions have been carried out.It is stressed that such CRs and DGPS measurements have been used just for comparison purposes,since they are not exploited by our method.In par-ticular,they have been used ?rst of all to obtain,by means of the PBE,a benchmark solution for the required phase offset and for the corresponding InSAR DEM.Moreover,CRs and DGPS measurements have been used also to directly evaluate the accuracy of the obtained InSAR DEMs.

Fig.7shows the multilook amplitude image of the illumi-nated area:the eight CRs are highlighted with white squares.The observed scene is quite heterogeneous since it includes a mountainous area,a ?at rural region,and an urban zone.Therefore,the observed topographic pro?le is quite variable,as it can be seen in the plot shown at bottom of the ?gure,which presents a cut of the SRTM DEM topography in correspondence of the white line highlighted in the SAR image.

The presented algorithm has been applied to multilook in-terferograms of 512range ×1981azimuth pixels,obtained following a 16range ×64azimuth pixel averaging window.Interpolation and subsequent regridding of the SRTM DEM height into the SAR grid has thus led to about 1million of GCPs.As detailed in the following,some areas of the illuminated scene have been however masked,thus leading to a reduction of the used GCPs.

PERNA et al.:PHASE OFFSET CALCULATION FOR AIRBORNE INSAR DEM GENERATION WITHOUT CRs 2721

TABLE III

E XPERIMENTAL R

ESULTS

In the following examples,the second step of the algorithm has been iteratively applied along the scheme of Fig.6,setting the threshold T equal to 0.03?.

As a ?rst example,we show the results obtained by masking the pixels of the unwrapped interferograms with a coherence value less than 0.4.The achieved mask,referred to as Mask 1,is shown in Fig.8.In this case,the whole procedure stopped just at the second iteration,and the estimated phase offset (given in this case by ?φo?2=?φo?PBE

??εSTopBE 1,see Fig.6)turned out to be equal to ?45.09?,which differs by 2.56?from the benchmark solution obtained by using the CRs (see Table III,which summarizes the overall experimental results).Fig.9(a)shows the vector Δobtained just after the ?rst step,along with the ?tting line (white line)estimated via the STopBE at the ?rst iteration.Fig.10(a)shows (stars)the difference between the ?nal InSAR DEM (obtained along the scheme of

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Fig.9.Top plots are relevant to the use of the original SRTM DEM:(a)the vectorΔ,(b)the vectorΔ2,along with the corresponding?tting lines(white lines) estimated via the STopBE at the corresponding iterations of the procedure in Fig.6.Bottom plots are relevant to the use of the SRTM DEM modi?ed with an additional vertical bias of15m:(c)the vectorΔ,(d)the vectorΔ3,along with the corresponding?tting lines(white lines)estimated via the STopBE at the corresponding iterations of the procedure in Fig.6.

Fig.6),sampled in correspondence of the eight CRs,and the

DGPS measurements.The standard deviation of this difference

(reported in Table III)is equal to25cm.To better appreciate

the effectiveness of the proposed algorithm,in Fig.10(a)the

difference between the benchmark InSAR DEM(obtained by

exploiting the CRs)and the DGPS measurements is also plotted

(crosses):its standard deviation is equal to18cm(see again

Table III)and thus just slightly better than that achieved by

estimating the phase offset with our approach.In any case,as

expected,Fig.10(a)shows that due to the residual difference

(2.56?)between the phase offset estimated with our algorithm

and the benchmark phase offset,the difference between the two

corresponding InSAR DEMs increases over range,see(5)and

(6)(it is recalled that the eight CRs are deployed over the range

direction).In particular,the measured height difference ranges

from30cm(in correspondence of the CR at near range,for

whichβ=6.23m/rad)to80cm(in correspondence of the CR

at far range,for whichβ=17.75m/rad).

Turning to the estimate?νin(16),as expected,it remains

practically constant at both iterations.In particular,it is equal

to?5.8m;this means that a relative bias exists between the

?nal InSAR DEM that we have generated and the external

DEM.The presence of this relative vertical bias can be seen

in Fig.9(b),which shows the vectorΔ2along with the?tting

line estimated through the STopBE at the second iteration.

It is worth stressing that in agreement with the analysis in

Section II,this relative bias has rendered inaccurate the PBE

at the?rst step,as con?rmed by the fact that in this case

?εSTopBE

1=34.49?,that is,the STopBE has signi?cantly mod-

i?ed the estimate?φo?

PBE obtained through the?rst step.On

the other side,it is worth remarking that the application of the PBE at the?rst step was not unnecessary.Indeed,due to the exploitation of the(even rough)estimate provided by the PBE,the whole procedure stopped just at the second iteration.

Differently,by initializing the iterative procedure in Fig.6

with a starting phase offset?φo?

1

=φstart different from?φo?

PBE and signi?cantly far from the neededφo?,additional iterations

would have been needed to reach the?nal estimate,with an

overall increase of the corresponding computational effort.To

better clarify this point,we have evaluated the performances

of the STopBE and,more generally,of the overall iterative

procedure in Fig.6for starting values?φo?

1

=φstart other than ?φ

o?PBE

.More speci?cally,Fig.11(a)shows(continuous line)

the estimation error|?φo?

2

?φo?|as a function ofφstart?φo?,where?φo?

2

=φstart??εSTopBE1is the estimate obtained by applying once the STopBE,whereasφo?is the bench-mark solution obtained by using the CRs.As expected(see Section III),the higher the value|φstart?φo?|,the worse the estimate carried out by applying once the STopBE.Fig.11(a) shows also(dotted line)the estimation error(still as a function ofφstart?φo?)of the estimate?φo?obtained by applying the iterative(and automatic)algorithm in Fig.6,where,as observed above,we have set the threshold T equal to0.03?.Finally, Fig.11(b)shows the number of iterations needed to achieve the estimate?φo?plotted in Fig.11(a).The plots in Fig.11show that the?nal estimate?φo?achieved with the iterative scheme in Fig.6is not in?uenced by the initial value of the phase offset?φo?

1

=φstart;however,this initial value has an impact

on the number of iterations needed by the algorithm to achieve

such a?nal estimate.To this regard,as observed in Section III,

the PBE at the?rst step generally provides a starting value for

φstart not dramatically far from the neededφo?(in the plots of

Fig.11,the value?φo?

PBE

?φo?is highlighted with black points on the x-axes),and thus allows reducing the computational effort of the whole algorithm(one iteration of the PBE comes practically at zero cost,differently from an additional

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2723

Fig.10.Differences (stars)between the InSAR DEMs obtained with the proposed algorithm and the DGPS measurements.First line (a),(b),and (c):the used external DEM is SRTM.Second line (d),(e),and (f):the used DEM is SRTM with an additional vertical bias of 15m.Third line (g),(h),and (i):the used DEM is SRTM with an additional range shift of about 180m.First column (a),(d),and (g):it has been used Mask 1.Second column (b),(e),and (h):it has been used Mask 2.Third column (c),(f),and (i):it has been used Mask 3.In all the cases,the difference (crosses)between the benchmark InSAR DEM,obtained evaluating the PBE with the DGPS measurements on CRs,and the DGPS measurements themselves is overplotted.Standard deviations of the plotted differences are reported in Table III.

iteration of the STopBE,as better clari?ed in the following),without in?uencing,however,the accuracy of the ?nal result.To further investigate the in?uence of the vertical bias of the external DEM on the performances of the proposed algorithm,as a second example we have removed from the SRTM DEM the vertical bias estimated above.Then,we have used this

modi?ed SRTM DEM to evaluate the PBE,obtaining ?φo?PBE

=?43.15?,which differs only by 0.62?

from the benchmark solution.Therefore,as expected,in the absence of a relative vertical bias between the external DEM and the ?nal one,the sole PBE represents a satisfactory estimate of the required phase offset.This is better quanti?ed in Table III,which reports the standard deviation of the difference between the DGPS measurements on the CRs and the InSAR DEM generated

by using the so-estimated ?φo?PBE

:in this case,the sole PBE allows achieving practically the same result (actually,slightly better)as that obtained in the ?rst experiment (that is,without removing from the external DEM the 5.8m bias)with the whole two-step procedure.This con?rms the validity of the numerical analysis performed in Section II,which demonstrates that the second step of the overall algorithm is mandatory only in the presence of a relative vertical bias between the InSAR DEM that we are going to generate and the available external DEM.To this regard,in order to further test the robustness of the overall procedure with respect to vertical biases of the external DEM,as a third example we have further increased by an amount of ?15m the above estimated relative vertical bias between our InSAR DEM and the SRTM DEM.Then,we have applied the proposed algorithm by using the so-modi?ed SRTM DEM.The corresponding vector Δ,along with the correspond-ing estimated ?tting line (white line),is shown in Fig.9(c).The span of this ?tting line is now about 40m [against the about 10m in Fig.9(a)],thus con?rming that increasing the relative vertical bias between the external DEM and our InSAR DEM impairs the PBE.In this case,three iterations of the second step were necessary,and the estimated phase offset (given in

this case by ?φo?3=?φo?PBE

??εSTopBE 1??εSTopBE 2)turned out to be equal to ?45.03?,which differs from the benchmark solution by 2.5?.In Fig.9(d)the vector Δ3along with the corresponding ?tting line (white line)estimated through the STopBE at the last iteration is plotted.The difference between the InSAR DEM generated in this case and the DGPS measure-ments on CRs is reported in Fig.10(d):the standard deviation of this difference (reported,as usual,in Table III)is 25cm.Accordingly,even further increasing the relative bias between the external DEM and our InSAR DEM,the performances achieved with the presented algorithm remain practically the same.

One additional consideration particularly relevant is now addressed.

The resolution of the exploited external DEM (90m)is almost two orders of magnitude worse than that of the ?nal

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Fig.11.Relevant to the iterative procedure in Fig.6.(a)The estimation error

|?φo?

2?φo?|(continuous line)and the estimation error|?φo??φo?|(dotted

line)as functions ofφstart?φo?,whereφstart is the initializing value of the

algorithm(denoted as?φo?

1

in Fig.6),φo?is the benchmark solution obtained by using the CRs,?φo?is the estimate obtained by iteratively and automatically

applying the algorithm,?φo?

2=φstart??εSTopBE

1

is the estimate obtained

by stopping the procedure at the second iteration.(b)Number of iterations needed to achieve the estimate?φo?plotted in Fig.11(a).The plots are relevant to the experiment carried out by exploiting the original SRTM DEM,Mask1, and a threshold T=0.03?.The black points on the x-axes indicate the value ?φ

o?PBE?φo?and show that,in this case,the PBE at the?rst step allowed the iterative procedure to stop just at the second iteration.

InSAR DEM that we have generated.Accordingly,a signi?-cant planar misalignment between the topographic information provided by these two DEMs may occur.This,in general,may increase the effect of the additive noise termΘ0in(11),thus rendering worse the matching between the linear model adopted in(12)and the experimental dataΔand,in turn,less accurate the STopBE in(13)and(14)(or(16)–(18)in the weighted case). As a matter of fact,this effect is more critical in those areas where the topography is steeper;accordingly,masking these areas could allow improving the performances of the second step,also because these areas are more likely to be affected by unwrapping errors.To investigate this point,we have set two different thresholds for the SRTM slopes,thus generating two different masks(shown in Fig.8),hereafter named Mask2and Mask3,both including the Mask1de?ned before.The?rst and third experiments described above have been then repeated by exploiting these two masks(instead of Mask1):the difference between the obtained InSAR DEMs and the DGPS measure-ments on the CRs is plotted in Figs.10(b)and(c),(e)and(f), whereas the corresponding standard deviations are reported in Table III along with the corresponding estimated values of the needed phase offset.As expected,masking the areas where the topography is steeper allows improving the performances of the algorithm:in particular,in the two considered cases,we have achieved practically the same accuracy as that obtained with the PBE carried out on the CRs.

To better show the advantages related to the use of such a topography-based masking,we have further investigated the robustness of the STopBE with respect to planar misalignments between the external DEM and our InSAR DEM.To this aim,we have applied to the original SRTM DEM a shift of 6arcsec in the north direction,which corresponds to about two pixels(180m)of the original SRTM grid.This represents a signi?cant misalignment between our?nal InSAR DEM and the external SRTM DEM.Then,we have applied our algorithm by exploiting this modi?ed SRTM DEM and all the three masks de?ned above:the differences between the obtained InSAR DEMs and the DGPS measurements on the CRs are plotted in Fig.10(g)–(i),whereas the corresponding standard deviations are reported in Table III(as usual,along with the corresponding estimated values of the needed phase offset). Also in this case the results obtained with Mask2and Mask3 are better than those achieved with Mask1.More important, also in the presence of a severe planar misalignment between the external SRTM DEM and our InSAR DEM,the accuracy of the estimate carried out by our algorithm is practically the same as the benchmark phase offset obtained by using the DGPS measurements on CRs.

Few information on the computational performances of the proposed algorithm are?nally provided.

Since the PBE just involves the computation of the mean in(3),we focused on the second step of the presented pro-cedure only.For all the experiments discussed in this sec-tion,computation of the STopBE in(16)–(18)took at worst a few milliseconds by using a3.4-GHz Intel i5CPU with 16-GB RAM.Accordingly,the computational effort of the overall procedure is mainly due to the iterative implementation of the phase-to-height conversion step in Fig.6.However,such a phase-to-height conversion step must be carried out at worst two or three times because,as shown above,two or three iterations of the second step are enough to reach a satisfactory accuracy in the computation of the needed phase offset.

V.C ONCLUSION

A new solution to estimate the phase offset present in the unwrapped SAR interferograms has been addressed in this work.Our approach exploits a low-accuracy external DEM and allows us to avoid the use of CRs along with the corresponding in situ DGPS measurements of their positions.

To fully clarify the context of the proposed approach,a preliminary analysis has been performed on simulated data.In particular,we have shown that the straightforward implemen-tation to an external DEM of the same solution exploited for CRs,referred to as the PBE approach,may lead to dramatically inaccurate results.More speci?cally,it has been shown that the PBE is not appropriate when the external DEM is affected by a nonnegligible vertical bias,as it may happen with commonly available DEMs.

Based on this analysis,a two-step procedure has been de-veloped.The?rst step carries out the PBE by exploiting the aforementioned external DEM,thus providing a rough estimate of the needed phase offset.The second step compensates for the residual error occurred at the?rst step and is based on a LS approach.In particular,it carries out an estimate,named STopBE,which is able to account for the presence of a relative bias between the external and the computed InSAR DEM. Iterative application of this second step can be applied to improve the accuracy of the obtained estimate.

PERNA et al.:PHASE OFFSET CALCULATION FOR AIRBORNE INSAR DEM GENERATION WITHOUT CRs2725

The effectiveness of the presented algorithm enhances in the presence of a large variation of the look angle;on the other side,it may worsen when the unwrapped interferograms are corrupted by artifacts.Accordingly,the presented approach is particularly appropriate for single-pass well-calibrated airborne systems,which guarantee a large variation of the look angle by allowing,at the same time,the generation of interfero-grams only marginally affected by the so-called residual motion errors,which may be instead critical in repeat-pass airborne InSAR scenarios.

Accordingly,the proposed procedure has been applied to a single-pass InSAR data set acquired by the OrbiSAR X-band airborne system.Moreover,we have exploited a SRTM DEM whose vertical accuracy and resolution are about one and two orders of magnitude worse than those achieved through the OrbiSAR system.

The presented results demonstrate the effectiveness of the algorithm.

In particular,it has been shown that the overall procedure is robust with respect to both severe vertical biases(on the order of20m)and signi?cant horizontal shifts(on the order of 180m)that may affect the external https://www.360docs.net/doc/2f8884621.html,parisons with DGPS measurements carried out on CRs,properly deployed on the illuminated scene,have been included to get an estimate of the method accuracy.These results have also been used to show that the proposed method guarantees almost the same accuracy achievable by exploiting accurate DGPS measurements on CRs. Our algorithm is very easy to implement;moreover,it is computationally ef?cient,because it just involves two or three iterations in order to compute the InSAR DEM.

It is?nally worth remarking that the presented procedure can be pro?tably used for the generation of airborne InSAR DEMs of wide and even unfriendly areas,by drastically reducing cost,time,and logistic limitations imposed by the use of CRs. Accordingly,our procedure represents a useful and appealing tool that can be exploited in different scenarios,not necessarily limited to the scienti?c context,such as the massive generation of DEMs of wide regions or the fast generation of DEMs in case of emergency scenarios.

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2008.

Stefano Perna(S’03–M’07)received the Laurea

degree(summa cum laude)in telecommunication

engineering and the Ph.D.degree in electronic and

telecommunication engineering from the Università

degli Studi di Napoli Federico II,Naples,Italy,in

2001and2006,respectively.

From2001to2002,he was with Wise S.p.A.,

Naples.In2003,2005,and2006,he received grants

from the Italian National Research Council(CNR)

to be spent at the Istituto per il Rilevamento Elet-

tromagnetico dell’Ambiente(IREA),Naples,for re-search in the?eld of remote sensing.Since2003,he has been collaborating with Orbisat Remote Sensing,Brazil,for interferometric processing of air-borne synthetic aperture radar(SAR)data.Since2006,he has been with the Dipartimento per le Tecnologie,Universitàdegli Studi di Napoli“Parthenope,”Naples,where he is currently a Researcher in electromagnetics.He is also an Adjunct Researcher with the IREA-CNR.His main research interests are in the ?elds of microwave remote sensing and electromagnetics,speci?cally airborne SAR data modeling and processing,airborne differential SAR interferometry, modeling of electromagnetic scattering from natural surfaces,and synthesis of antenna arrays.

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Carmen Esposito received the Master’s degree (summa cum laude)in telecommunication engi-neering from the Universitàdegli Studi di Napoli “Parthenope”,Naples,Italy,in2012.She is currently working toward the Ph.D.degree at the Universitàdegli Studi del Sannio,Benevento,Italy.

Since2011,she has been with the Istituto per il Ril-evamento Elettromagnetico dell’Ambiente(IREA), an Institute of the Italian National Research Council (CNR),Naples,where she is currently a scholarship holder.Her main research interests include airborne

synthetic aperture radar(SAR)data processing and

interferometry.

Paolo Berardino was born in Avellino,Italy,in

1971.He received the Laurea degree in nautical

sciences from the Naval Institute University,Naples,

Italy,in1998.

In1999,he joined the Istituto per il Rilevamento

Elettromagnetico dell’Ambiente(IREA),an Institute

of the Italian National Research Council(CNR),

Naples,where he is a Researcher.He is interested in

the development of algorithm geocoding of synthetic

aperture radar(SAR)images and studies of surface

deformation by using differential SAR interferome-try.He has collaborated in the development of a new approach for the analysis of the temporal evolution of the deformation of the Earth’s surface based on the combination of differential interferograms(SBAS technique).Over the years,he has actively participated in the upgrading of technical SBAS(high resolution,geometric registration,data integration ERS/Envisat,GIS integra-tion).He has participated in several studies on volcanic areas,seismogenic, landslide areas,and urban areas using the technique SBAS and collaborating with different national and international scienti?c institutions.He is working on the acquisition and processing of SAR data plane with particular attention to aspects of motion compensation errors and realization of interferometric

products(Digital Surface

Map).

Antonio Pauciullo was born in Cercola,Italy,on October10,1969.He received the Dr.Eng.degree (with honors)and the Ph.D.degree in informa-tion engineering from the Universitàdegli Studi di Napoli Federico II,Naples,Italy,in1998and2003, respectively.

Since2001,he has been with the Istituto per il Ril-evamento Elettromagnetico dell’Ambiente(IREA) of the Italian National Research Council(CNR), Naples,where he is a Researcher.Since2004,he has been an Adjunct Professor of digital signal process-

ing with the University of Cassino,Cassino,Italy.His current research interests include statistical signal processing with emphasis on synthetic aperture radar

processing.

Christian Wimmer was born in Ergoldsbach,

Germany,on September21,1966.He received the

Ph.D.degree(magna cum laude)in semiconduc-

tor physics from the University of Regensburg,

Regensburg,Germany,in1997.

From1997to2001,he was with the SAR Pro-

cessing Group,Aero-Sensing Radarsysteme GmbH,

Oberpfaffenhofen,Germany.Since2001,he has

been collaborating with Bradar(former Orbisat),

Brazil.Since2006,he has been collaborating with

the remote sensing group of the Istituto per il Rile-vamento Elettromagnetico dell’Ambiente(IREA),Naples,Italy,in the?eld of airborne differential synthetic aperture radar(SAR)interferometry.His main research interests include airborne SAR data modeling and processing with preference for P-band repeat-pass interferometry and X-band high-accuracy digital elevation model

generation.

Riccardo Lanari(M’91–SM’01–F’13)received the

Laurea degree(summa cum laude)in electronic en-

gineering from the Universitàdegli Studi di Napoli

Federico II,Naples,Italy,in1989.

In the same year,he joined IRECE and after IREA,

both Research Institutes of the Italian Council of

Research(CNR).He was a Visiting Scientist with

different foreign research institutes,including the

Institute of Space and Astronautical Science,Japan

(1993);the German Aerospace Research Establish-

ment(DLR),Germany(1991and1994);and the Jet Propulsion Laboratory,California(1997,2004,and2008).He was an Adjunct Professor of electrical communication with the University of Sannio, Benevento,Italy,from2000to2003and a main lecturer with the Institute of Geomatics,Barcelona,Spain,from2000to2008.Moreover,he has recently achieved the National Scienti?c Habilitation as a Full Professor of telecom-munications(December2013)and of geophysics(February2014).He has lectured in several national and foreign universities and research centers.Since November2011,he has been the Director of the IREA-CNR.On his topics of interest,he is the holder of two patents and has authored or coauthored the book Synthetic Aperture Radar Processing(1999,CRC Press)and more than 80international journal papers,which currently have more than5000citations (source:Google Scholar).His main research activities are in the microwave remote sensing?eld,particularly for what attains the development of synthetic aperture radar(SAR)and SAR interferometry(InSAR)digital data processing methods.

https://www.360docs.net/doc/2f8884621.html,nari received from the National Aeronautics and Space Administration a recognition(1999)and a group award(2001)for his activities related to the Shuttle Radar Topography Mission project based on the InSAR experiments carried out in2000,within a mission of the Space Shuttle Endeavour.He served as a Chairman and/or a Scienti?c Program Committee Member for many international conferences.He is also a Distinguished Speaker of the IEEE Geoscience and Remote Sensing Society.