adaptive imaging for forward-looking ground penetrating radar

Adaptive Imaging forForward-Looking GroundPenetrating Radar

YANWEI WANG, Student, IEEE

XI LI, Member, IEEE

YIJUN SUN

JIAN LI, Fellow, IEEEUniversity of Florida

PETRE STOICA, Fellow, IEEEUppsala UniversitySweden

Most of the current forward-looking ground-penetrating radar

(FLGPR) systems use conventional delay-and-sum (DAS) based

methods to form radar images for detection of the target (such as

a landmine). However, DAS is a data-independent approach which

is known to suffer from low resolution and poor interference and

clutter rejection capability. We present a data-adaptive imaging

approach for FLGPR image formation based on APES (amplitude

and phase estimation) and rank-deficient RCB (robust Capon

beamforming). Due to the data-adaptive nature of both APES

and RCB, our approach has better resolution and much better

interference and clutter rejection capability than the standard

DAS-based imaging methods. The excellent performance of

the proposed method is demonstrated using experimental data

collected via two FLGPR systems recently developed by PSI

(Planning Systems, Inc.) and SRI (Stanford Research Institute).

Manuscript received February 3, 2004; revised August 5, 2004;released for publication April 1, 2005.

IEEE Log No. T-AES/41/3/856441.

Refereeing of this contribution was handled by E. S. Chornoboy.

This work was supported in part by the U.S. Army under ContractDAAB15-00-C-1024, the National Science Foundation GrantCCR-0104887, the Swedish Science Council (VR), and the SwedishFoundation for International Cooperation in Research and HigherEducation (STINT).

Authors’ addresses: Y. Wang, Y. Sun, and J. Li, Dept. of Electricaland Computer Engineering, University of Florida, Gainesville,FL 32611, E-mail: ([email protected]); X. Li, Beckman Coulter,Inc., Miami, FL; P. Stoica, Dept. of Information Technology, theDivision of Systems and Control, Uppsala University, PO Box 337,SE-75105 Uppsala, Sweden.

0018-9251/05/$17.00 c° 2005 IEEE

I. INTRODUCTION

The landmine crisis is a worldwide problem[1—3]. Over the last 10 to 15 years, the significantattention paid to the landmine problem has ledto a substantial increase in the efforts to developsafe and cost efficient techniques for detection andclearance of landmines [4]. However, due to variouslandmine types and complicated survey scenarios,efficient and accurate detection of landmines isstill an open problem. Some of the currently usedand ongoing research techniques include metaldetector, acoustic technology, electro-optical detection,FLIR (forward-looking infrared) sensor, chemicaldetection, quadrupole resonance detection, andground-penetrating radar (GPR) [4—6]. Among thesetechniques, GPR has many important advantages overthe others and is being considered as a very viablesurveillance tool for landmine detection [7].In GPR systems, an electromagnetic (EM) wave

is transmitted into the ground and the identificationof targets is obtained by examining the backscatteredfield. Since GPR is able to discern the discontinuitiesin the electric permittivity of the propagation medium,nonmetallic objects such as plastic-cased mines canalso be detected. Most GPRs are ultrawideband(UWB) systems with the working frequency rangefrom 0.5 to 3 GHz. Through the use of antenna array,the state-of-the-art GPRs can produce high resolutiontwo-dimensional (2-D) or three-dimensional (3-D)images of buried objects for landmine detection[8—12].Current landmine detection GPR systems can

be cast into two main categories as down-lookingGPR (DLGPR) and forward-looking GPR (FLGPR).DLGPR places its antennas very close to the groundsurface. Due to the short standoff distance andrelatively large landmine radar cross section (RCS),DLGPR has a good detection capability. However,DLGPR requires the removing of the strong specularreflection from the ground surface, which can alsocause the removal of mines, especially shallowlyburied mines. Additionally, it is time consuming touse DLGPR for a large area interrogation. Unlike itsdown-looking counterpart, FLGPR places its antennasin front of the vehicle and inspects the ground surfaceof interest with a long standoff distance. A diagramof such a system is shown in Fig. 1. The landmineRCS of FLGPR is smaller than that of DLGPR, whichmakes landmine detection by FLGPR a challengingproblem. However, there are many advantages ofFLGPR over DLGPR. FLGPR does not suffer fromthe problem of strong specular reflection from theground and is capable of collecting data for a muchlarger area in a much shorter time than DLGPR.Furthermore, FLGPR can usually provide multipleobservations on the same spot as the system movesforward, and can take advantage of multi-look

922 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 41, NO. 3 JULY 2005

Fig. 1. Diagram of FLGPR system used for landmine detection.

processing to improve its detection capability. Dueto these merits, FLGPR is considered an importanttechnology by the landmine detection community[10, 11].Since the FLGPR system detects buried targets

based on the reconstructed reflectivity image ofa scene, at least for prescreening, high qualityradar image formation is essential. However, highquality FLGPR imaging is a challenging task dueto the following reasons. EM waves scatter froma random rough ground surface in unpredictableways, contributing to clutter which distort andobscure the desired scattering field from a buriedtarget [13]. Problems such as refraction at theair/ground interface will also result in errors to simplepropagation models. Furthermore, array calibrationerrors and geo-registering errors will cause additionaluncertainties to our “steering vector.” (Usually, acalibration procedure is used to remove system offsetsand adjusts system gains [14]; a differential globalpositioning system is used to record the locations ofthe antennas [11].)The conventional imaging algorithm for FLGPR

is the delay-and-sum (DAS) method [15], whichis also known as the backprojection method [16].However, DAS is a data-independent approach, whichis known to suffer from low resolution and poorinterference rejection capability. In practical scenarioswhere strong clutter is present, the performanceof the DAS-based algorithms degrades severely,which can result in far too many false alarms forFLGPR systems. Many sophisticated radar imagingapproaches have been considered in the literature[17—26]. However, due to the near-field beamformingrequired by FLGPR, existing 2-D adaptive syntheticaperture radar (SAR) imaging algorithms are notdirectly applicable.We present a new adaptive imaging method

here, referred to as the APES-RCB approach, for

FLGPR image formation. The new method consistsof two major steps. First, the APES (amplitudeand phase estimation) algorithm is used to estimatethe reflection coefficients for the focal points ofinterest for each receiving channel. Since APES isa nonparametric data-adaptive matched-filterbank(MAFI) based algorithm, it preserves the robustnature of the nonparametric methods but at the sametime it improves the spectral estimates in the senseof narrower spectral peaks and lower sidelobesthan DAS, DFT (discrete Fourier transform), orFFT (fast Fourier transform) methods [26, 27].Second, a rank-deficient robust Capon beamformer(RCB) is used to estimate the reflection coefficientsfor the focal points of interest from the estimatesobtained via APES for all channels. By makingexplicit use of an uncertainty set for the array steeringvector, the adaptive RCB can tolerate both arraysteering vector errors and low snapshot numbers[28]. By allowing the involved “data” matrix tobe rank-deficient, our method can be applied topractical scenarios where the number of multi-looksis smaller than the number of sensors in the array.Furthermore, by using the rank deficient RCB, we canachieve much better interference and clutter rejectioncapability than most existing approaches, which isuseful in many applications such as target detectionand feature extraction. We apply the APES-RCBapproach to experimental data collected via tworecently developed FLGPR systems by PSI (PlanningSystems, Inc.) and SRI (Stanford Research Institute).Experimental results are used to demonstrate theexcellent performance of our new imaging approachas compared with the conventional DAS-basedmethods.The remainder of this paper is organized as

follows. In Section II, we present the data modeland formulate the problem of interest. In Section III,we give a brief review of the conventional DAS

WANG ET AL.: ADAPTIVE IMAGING FOR FORWARD-LOOKING GROUND PENETRATING RADAR 923

method. The APES-RCB imaging algorithm ispresented in Section IV. In Section V, we introducethe two experimental FLGPR systems and report thecorresponding experimental results. We conclude thepaper in Section VI.

II. DATA MODEL AND PROBLEM FORMULATION

As shown in Fig. 1, an FLGPR system is usedto detect the buried mines in front of the vehicle.Let x, y, and z denote the cross-range, down-range,and height (also depth) axes of a coordinate system.Let (xr,m,n,yr,m,n,zr,m,n) denote the location of the mthreceiver during the nth scan, and let (xt,d,n,yt,d,n,zt,d,n)denote the location of the dth transmitter, where m=0,1, : : : ,M ¡1, d = 0,1, : : : ,D¡ 1, and n= 0,1, : : : ,N ¡1 with M, D, and N denoting the total numbers ofreceiving antennas, transmitting antennas, and scans,respectively. The imaging region extends from xminto xmax in the cross-range dimension and from ymin toymax in the down-range dimension. Let p= fxF,yF,zFgrepresent the location of a focal point in the imagingregion, where zF = 0 denotes the ground surface andzF < 0 denotes the underground points. For simplicity,consider a focal point on the ground (zF = 0). At thenth scan, the time delay due to the system delay ¿sysand the EM wave propagation from the dth transmitterto the focal point p and then back to the mth receiveris

¿d,m,n(p) =1c[(xt,d,n¡ xF)2 + (yt,d,n¡ yF)2 + z2t,d,n]1=2

+1c[(xr,m,n¡ xF)2 + (yr,m,n¡ yF)2 + z2r,m,n]1=2 + ¿sys

(1)

where c is the velocity of the EM wave in the air. Thestepped frequencies of FLGPR have the form:

fk = f0 + k¢f, k = 0,1, : : : ,K ¡ 1 (2)

where f0 denotes the initial frequency, ¢f representsthe frequency step, and K is the total number ofstepped frequencies. Given a focal point p, themeasured kth stepped-frequency response yd,m,n(k)corresponding to the dth transmitter and the mthreceiver at the nth scan location has the form

yd,m,n(k) = ¯n(p)e¡j2¼fk¿d,m,n(p) + ed,m,n(k,p),

d = 0,1, : : : ,D¡ 1, m= 0,1, : : : ,M ¡ 1,n= 0,1, : : : ,N ¡ 1, k = 0,1, : : : ,K ¡1 (3)

where ¯n(p) denotes the “reflection coefficient” forthe focal point p at the nth scan, and ed,m,n(k,p)denotes the residual term at point p, which includesthe unmodeled noise and interference from scattererresponses other than p. In (3), we have assumed thatthe reflection coefficient may change from scan to

scan. This is based on the fact that, in practice, as theFLGPR system moves forward, the EM wave incidentangle relative to the fixed point p on the groundchanges. Consequently, the reflection coefficient forpoint p may differ from scan to scan as the radarmoves forward [29].The problem of interest herein is to estimate

f¯n(p)gN¡1n=0 , for each focal point of interest, from themeasured data set yd,m,n(k) with d = 0,1, : : : ,D¡ 1,m= 0,1, : : : ,M ¡ 1, n= 0,1, : : : ,N ¡ 1, and k =0,1, : : : ,K ¡ 1. These estimates can then be used toform FLGPR images.

III. DELAY-AND-SUM ALGORITHM

A brief overview of the conventional DAS methodfor FLGPR imaging is provided in this section.The discussion on the DAS method is helpful forpresenting our new approach later on.The idea of DAS is to sum all measured data

coherently at one focal point and repeat the processfor all points of interest. The DAS-based reflectioncoefficient estimates for the focal point p have theform

ˆn(p) =

1

D ¢PM¡1m=0 jwr(m)j2 ¢

PK¡1k=0 jwf(k)j2

£D¡1Xd=0

M¡1Xm=0

wr(m)K¡1Xk=0

wf(k)yd,m,n(k)ej2¼fk¿d,m,n(p),

n= 0,1, : : : ,N ¡ 1 (4)

where wf(¢) and wr(¢) denote the weights forthe frequency and receiver aperture dimensions,respectively. Based on the estimates f ˆn(p)gN¡1n=0 off¯n(p)gN¡1n=0 , we can obtain the radar image as

I1(p) =1N

N¡1Xn=0

ˆn(p): (5)

The above method is referred to as coherentmulti-look processing. In practice, the phases off¯n(p)gN¡1n=0 for buried mines may vary with the scanlocation. Consequently, the above coherent processingtends to fail when the phase variations along the scandimension become too large [29]. Hence, in thesecases, we can take the absolute values of individualimages before the multi-look image is formed. Thismethod is referred to as the noncoherent processingand can be expressed as

I2(p) =1N

N¡1Xn=0

j ˆn(p)j: (6)

For stepped-frequency FLGPR systems, the aboveDAS-based algorithms can be efficiently implementedas follows.


1) For each channel (transmitter/receiver pair),calculate the inner sum in (4) via the inverse FFT(IFFT) with zero padding.2) Calculate the two outer sums in (4) by

summing up the signals corresponding to the givenfocal point from all channels.3) Perform coherent or noncoherent multi-look

processing along the scan dimension.

Note that DAS is a data-independent approachwhich suffers from low resolution and poorinterference and clutter rejection capability. Wepresent next our data-adaptive imaging approach,referred to as APES-RCB, for FLGPR imageformation.

IV. APES-RCB ALGORITHM

The APES-RCB algorithm is an adaptive imagingapproach which consists of two major steps. First,instead of using the FFT-based method, APES isadopted to obtain more accurate reflection coefficientestimates for each receiving channel. This stepcorresponds to a bistatic down-range compression forthe various channels. Second, rank-deficient RCB isused to estimate the original reflection coefficientsbased on the estimates obtained via APES from allchannels. This step achieves cross-range compressionand multi-look fusion.

A. Step One: APES

Consider the data model in (3). Let

®d,m,n(p) = ¯n(p)e¡j!0¿d,m,n(p) = ¯n(p)e

¡j2¼f0¿d,m,n(p)

(7)and

!d,m,n(p) = 2¼¢f¿d,m,n(p): (8)

With these notations, (3) becomes

yd,m,n(k) = ®d,m,n(p)e¡jk!d,m,n(p) + ed,m,n(k,p),

d = 0,1, : : : ,D¡ 1, m= 0,1, : : : ,M ¡ 1,n= 0,1, : : : ,N ¡ 1, k = 0,1, : : : ,K ¡ 1: (9)

Let d, m, n, and p be fixed. Then (9) can be expressedas (whenever possible, we omit the dependence on d,m, n, and p to simplify the notation)

y(k) = ®(!)e¡jk! + e!(k), k = 0,1, : : : ,K ¡ 1:(10)

The problem of interest is to estimate ®(!) fromfy(k)gK¡1k=0 for any given !. This problem belongs tothe classical problem of complex spectral estimation.The conventional approaches to complex spectralestimation include DFT and its variants which aretypically based on smoothing the DFT spectralestimate or windowing the data [30]. These methods

do not make any a priori assumptions on the dataand consequently they are very robust. However,they suffer from low resolution and poor accuracyproblems.Nonparametric adaptive MAFI methods can

mitigate the low resolution and poor accuracyproblems of the DFT-based methods [26, 31]. Foreach frequency ! of interest, a MAFI method filtersthe data with a normalized finite-impulse response(FIR) filter h(!). The filter is chosen according to acriterion which is different for the various spectralanalysis methods, but with the common constraintthat a sinusoid with frequency ! should pass thefilter without any distortion. Following the filtering, asinusoid is fitted to the filtered data in a least-squares(LS) sense, and the amplitude of the so-obtainedsinusoid ®(!) is taken as the estimate of the amplitudespectrum at the frequency ! of interest. This class ofestimators includes the classical Capon algorithm andthe more recent APES approach. Note that it has beenshown that Capon is biased downward whereas APESis unbiased. In fact, both theoretical performanceanalysis and numerical examples have demonstratedthat APES can provide excellent accuracy for complexspectral estimation [27]. For FLGPR imaging, accuratereflection coefficient estimates for the focal points ofinterest for each receiving channel are essential. Aswe will show, APES works well for this practicalproblem. Additionally, APES is straightforward touse due to the fact that it requires no search over anyparameter space. To make this paper as self-containedas possible, we present a brief summary of APESestimator in the next paragraph.Assume the APES filter used here has P taps:

f(!) = [h1(!) h2(!) ¢ ¢ ¢hP(!)]T (11)

where (¢)T denotes the transpose. Lety(l) = [y(l) y(l+1) ¢ ¢ ¢y(l+P¡ 1)]T,

l = 0,1, : : : ,L¡1 (12)

be the forward overlapping vectors constructed fromthe data y(k), where L=K ¡P+1. Likewise, thebackward data vectors are constructed as

y(l) = [y¤(K ¡ l¡ 1) y¤(K ¡ l¡ 2) ¢ ¢ ¢y¤(K ¡ l¡P)]T,l = 0,1, : : : ,L¡1 (13)

where (¢)¤ denotes the complex conjugate. DefineaP(!) = [1 e

j! ¢ ¢ ¢ej(P¡1)!]T. Let g(!) and g(!) be thenormalized Fourier transforms of the forward andbackward vectors calculated as

g(!) =1L

L¡1Xl=0

y(l)e¡j!l (14)

and

g(!) =1L

L¡1Xl=0

y(l)e¡j!l: (15)


The (forward-backward) APES filter has the form (see[26]):

h(!) =Q¡1(!)aP(!)

aHP (!)Q¡1(!)aP(!)(16)

where Q(!) = RP ¡G(!)GH(!), G(!) =(1=p2)[g(!) g(!)], RP = (1=2)(

ˆRP + J

ˆRT

PJ), andˆRP = (1=L)

PL¡1l=0 y(l)y

H(l). The APES estimate of®(!) is given by

®(!) = hH(!)g(!) =aHP (!)Q

¡1(!)g(!)

aHP (!)Q¡1(!)aP(!): (17)

Note that a computationally efficient implementationof APES can be found in [31] where the inversion ofQ(!) for each ! can be avoid and various techniquescan be used to implement APES efficiently. Afterapplying the fast APES of [31], which requires auniform grid for !, the desired estimates at differentand possibly nonuniform values of ! (due to thenear-field beamforming required by FLGPR) can beobtained by using interpolation.From the APES estimate ®, we can readily obtain

intermediate reflection coefficient estimates based on(7):

ˆ¯d,m,n(p) = e

j!0¿d,m,n(p)®d,m,n(p),

d = 0,1, : : : ,D¡ 1, m= 0,1, : : : ,M ¡1,n= 0,1, : : : ,N ¡ 1: (18)

We remark that at this stage we have obtained a totalnumber of DMN reflection coefficient estimates foreach focal point since we have overparameterizedthe N unknowns f¯ngN¡1n=0 via DMN unknownsfff¯d,m,ngD¡1d=0 gM¡1m=0 gN¡1n=0 (see (7)) in order to useAPES in a direct manner. In the next step, we usethe rank-deficient RCB to estimate the original Nreflection coefficients for each focal point from theDMN estimates obtained via APES.

B. Step Two: Rank-Deficient RCB

For the focal point p, the reflection coefficientsestimated by APES satisfy

ˆ¯d,m,n(p) = ¯n(p)+¹d,m,n(p),

d = 0,1, : : : ,D¡ 1, m= 0,1, : : : ,M ¡1,n= 0,1, : : : ,N ¡ 1 (19)

where fff¹d,m,n(p)gD¡1d=0 gM¡1m=0 gN¡1n=0 denote the estimationerrors (such as caused by finite-sample effects andmismodeling) as well as any leftover interferences.(For each channel, the interferences from locations

other than p but having the same time delay (equal to¿d,m,n(p)) cannot be suppressed by APES.) Let

xn(p)=[ˆ¯0,0,n(p) ¢ ¢ ¢

ˆ¯0,M¡1,n(p) ¢ ¢ ¢

ˆ¯D¡1,0,n(p) ¢ ¢ ¢

ˆ¯D¡1,M¡1,n(p)]

T,

n= 0,1, : : : ,N ¡ 1 (20)and

¹n(p)=[¹0,0,n(p) ¢ ¢ ¢¹0,M¡1,n(p) ¢ ¢ ¢¹D¡1,0,n(p) ¢ ¢ ¢¹D¡1,M¡1,n(p)]T,n= 0,1, : : : ,N ¡ 1: (21)

Then (29) can be rewritten as

xn(p) = ¯n(p)a+¹n(p), n= 0,1, : : : ,N ¡ 1(22)

where a is theoretically equal to 1DM£1, with 1DM£1denoting a DM by 1 vector whose elements are allequal to one. Note that, in practice, the “steeringvector” a in (32) may be imprecise, in the sense thatthe elements in a may differ slightly from 1. This maybe due to many factors such as array calibration errorsand geo-registering errors for any given p. Our secondstep is to estimate ¯n(p).We choose rank-deficient RCB to perform the

cross-range compression and multi-look fusion dueto the following considerations. First, RCB caneffectively deal with the imprecise knowledge ofthe “steering vector” and small sample size andhence avoid the significant performance degradationsassociated with the standard Capon beamformer [28].Second, since the number of snapshots is usually sosmall that the sample covariance matrix is singular, itis natural to apply the rank-deficient RCB to estimatethe “waveform” ¯n(p) from the “snapshots” fxngN¡1n=0[32]. Third, compared with simple approaches suchas the LS, which is the same as DAS, and the totalLS, which usually performs similarly as LS [33], RCBhas much better interference and clutter suppressioncapability. To make this paper self-contained, weprovide a brief review of the rank-deficient RCB forestimating the “waveform” f¯n(p)gN¡1n=0 . We refer thereader to [32] for more detailed derivations of therank-deficient RCB.We make use of the following “sample covariance”

matrix

R(p) =1N

N¡1Xn=0

xn(p)xHn (p): (23)

Note that usually in applications we have N <DM.Hence R(p) is singular. Let N denote the rank of R(p)in (33). With probability one, N =N. Let

R(p) = [S U]·¤ 0

0 0

¸·SH

UH

¸(24)

where S is a DM £ N (DM > N) full column rankmatrix whose columns are the eigenvectors of R(p)corresponding to the non-zero eigenvalues of R(p), U


denotes the DM £ (DM ¡ N) orthogonal complementof S with the columns of U corresponding to thezero eigenvalues of R(p), and ¤ is an N £ N positivedefinite diagonal matrix whose diagonal elements arethe non-zero eigenvalues of R(p).Let a= 1DM£1 denote the nominal “steering

vector” as discussed above. (Note that 1DM£1 is theonly nominal “steering vector” needed here.) Owingto the small “snapshot” number and the impreciseknowledge of the true “steering vector” a, the “signalterm” in R(p) is not well described by j¯n(p)j2aaH ,but by j¯n(p)j2aaH with a being some vector in thevicinity of a and a 6= a. Consequently, if we designedthe weight vector w(p) by means of the standardCapon beamformer:

minw(p)

wH(p)R(p)w(p) subject to wH(p)a= 1

(25)

the Euclidean norm of w(p), denoted as kw(p)k,would be rather large since a is close to a and w(p)would pass the signal associated with a undistorted(see (25)) but attempt to suppress the signal associatedwith a. A large kw(p)k indicates a large noise gain,which may severely degrade the estimation accuracyof ¯n(p). It follows that we should design w(p) by

minw(p)

wH(p)Rw(p) subject to wH(p)a= 1

(26)

where we used a, instead of a, to avoid thesuppression of the signal term and a large noise gain.First, we assume that a is given (the determination

of a is discussed later on in this subsection), and solvethe above optimization problem in (26) by consideringthe following two cases.

Case 1 a belongs to the range space of R(p).Let a be written as a

¢= S° for some non-zero vector

°; we have ° = SH a. Then the weight vector has theform [32]

w(p) =S¤¡1°

°H¤¡1°=

R†(p)a

aHR†(p)a(27)

where R†(p) = S¤¡1SH is the Moore-Penrosepseudoinverse of R(p). Consequently, the finalestimates of the reflection coefficients can be obtainedas

ˆn(p) =w

H(p)xn(p) =°H¤¡1SHxn(p)

°H¤¡1°,

n= 0,1, : : : ,N ¡ 1: (28)

Case 2 a does not belong to the range space ofR(p). Let a be written as a= S°+ U ˆ for somenon-zero vectors ° and ˆ . In this case the final

estimate of ¯n(p) would be [32]

ˆn(p) = 0, n= 0,1, : : : ,N ¡ 1: (29)

Next, we determine a via a covariance fittingapproach. We assume that the only knowledge wehave about a is that it belongs to the followinguncertainty sphere:

ka¡ ak2 · ²: (30)

Furthermore, we want a to be such that j¯n(p)j2aaHis a good fit to R(p). This leads to the followingoptimization problem for a:

max¾2(p),a

¾2(p) subject to R(p)¡¾2(p)aaH ¸ 0

ka¡ ak2 · ² (31)

where ¾2(p) = j¯n(p)j2. The user parameter ² is usedto describe the uncertainty about a. Note that ² isdetermined by several factors such as N [34], thearray calibration errors, and the system geo-registeringerrors. Usually, ² is chosen experimentally fordifferent systems to make them robust against all thepossible errors mentioned above. Hence the smallerthe N or the larger the array steering vector andsystem errors, the larger should the ² be chosen.According to the previous discussion, a vector a

that is in the range space of S, i.e., a= S° for somenon-zero °, is what we are after since otherwise wewill get an estimate equal to zero. Observe that boththe signal power ¾2(p) and the “steering vector” a aretreated as unknowns in our covariance fitting approach(see (31)), hence there is a “scaling ambiguity”between these two unknowns [28]. To eliminate thisambiguity, we can impose the norm constraint thatkak2 = k°k2 =DM. To determine °, we first obtain ˆ°as follows:

max¾2(p),a

¾2(p) subject to R(p)¡¾2(p)aaH ¸ 0

a= S ˆ°, ka¡ ak2 · ²: (32)

(To exclude the trivial solution of ˆ° = 0, we requirethat ² < kak2 =DM.) Then ° is obtained as

° =

pDM ¢ ˆ°k ˆ°k

: (33)

Consider now the solution to (32). Let °¢= SH a and

²¢=²¡kUH ak2. We consider the following two cases.

Case 1 ² < 0, which occurs when a is “far” awayfrom the range space of S. Then the optimizationproblem in (32) is infeasible [32]. In such a case thereis no a of the form a= S ˆ° that satisfies the constraintin (32). Hence the vector a cannot belong to the range


space of S in this case and according to (29), we get

ˆn(p) = 0, n= 0,1, : : : ,N ¡ 1: (34)

Case 2 ²¸ 0, which occurs when a is “close” tothe range space of S and hence of R. In this case, an abelonging to the range space of R can be found withinthe uncertainty sphere in (32). By using the Lagrangemultiplier methodology to solve (32) in this case, weget [32]

ˆ° =

Ã¤¡1

¸+ I

!¡1° (35)

= °¡ (I+¸¤)¡1° (36)

where ¸¸ 0 is the Lagrange multiplier and the secondequality follows from the matrix inversion lemma;¸ can be obtained as the unique solution to theconstraint equation [32]:

g(¸)¢=k(I+¸¤)¡1°k2 = ² (37)

which can be solved efficiently via, for example, aNewton’s method. Once ¸ has been determined, weuse it in (35) to get ˆ°, which can be used in (33) tocompute °. Then we obtain the estimate of ¯n(p) byusing the ° in (28).

Combining the two cases discussed above, therank-deficient RCB estimate of ¯n(p) can be writtenas

ˆn(p) =

8><>:°H¤¡1SHxn(p)

°H¤¡1°²¸ 0

0 ² < 0

,

n= 0,1, : : : ,N ¡1: (38)

Note that the rank-deficient RCB requires O(N3)flops, which is mainly due to the eigen-decompositionof the rank-deficient (rank N) matrix R. (See [35] foran efficient eigen-decomposition of a rank-deficientmatrix.) Compared with the data-independent DASweight vector wDAS(p) = a(p)=ka(p)k2 = (1=DM) ¢1DM£1, our rank-deficient RCB w(p) can providebetter resolution and much better interference rejectioncapability.In conclusion, the APES-RCB algorithm can be

briefly summarized as follows.

Step 1 Use APES for each focal point p toestimate fff®d,m,n(p)gD¡1d=0 gM¡1m=0 gN¡1n=0 . Then, obtain

the intermediate estimates fff ˆ¯d,m,n(p)gD¡1d=0 gM¡1m=0 gN¡1n=0based on (28).Step 2 For each p, use the rank-deficient RCB to

obtain the final estimates f ˆn(p)gN¡1n=0 of f¯n(p)gN¡1n=0 .Step 3 The radar image is obtained by either

coherent or noncoherent multi-look processing basedon f ˆn(p)gN¡1n=0 .

Fig. 2. (a) Ground truth of landmines on test lane.(b) Photograph of metallic-cased mine.

V. EXPERIMENTAL RESULTS

PSI and SRI have developed FLGPR systemsunder contracts to the U.S. Army CECOM NightVision and Electronic Sensors Directorate [11]. Thesesystems are designed with the goal of assessingthe capability of FLGPR for detecting plasticand metallic-cased surface and buried mines onroadways. We concentrate here on the buried metalmine detection. Both of these systems are UWBstepped-frequency GPRs and can be used to form 2-D(or more precisely 3-D, but with poor resolution indepth) images of the ground. The performances of thesystems have been tested on the practice mine lanes.Results obtained from experimental data collectedby these systems are provided to demonstrate theperformance of our new adaptive imaging approach ascompared with the conventional DAS-based imagingmethods. Fig. 2(a) shows the data collection geometryfor the FLGPR systems and the ground truth for themine locations. In the concerned experiments, thereare 12 metallic-cased mines that are buried in groupsof 3 mines at depths of 0 (flush), 5, 10, and 15 cm,respectively. Fig. 2(b) shows the photograph of ametallic-cased mine.

A. PSI FLGPR Experimental Results

A photograph of the PSI FLGPR phase II systemis shown in Fig. 3. This system uses a vertical3-element transmitter array precombined as a singletransmitter and a receiver array consisting of twohorizontal 15-element subarrays. The height of thetransmitting antenna is about 2.5 m above the groundand the two receiving antenna subarrays are 1.9 m and2.05 m above the ground. Each transmitting/receivingelement uses a 14 cm Archimedean spiral antenna.The adjacent receiving antennas of each subarrayare 7.62 cm apart in the aperture dimension. Thestepped-frequency system operates with 201 discretefrequencies evenly spaced over a frequency rangefrom 0.766 to 2.166 GHz. This system works in thecircularly polarized mode. Data are recorded for eachstep of 0.1 m as the vehicle moves forward. At eachscan location, the image region is 5 m (cross-range)


Fig. 3. Photograph of PSI FLGPR phase II system.

by 3.5 m (down-range) with a 4.5 m standoff distanceahead of the vehicle. A pixel spacing of 4 cm ischosen in both the down-range and cross-rangedimensions for radar imaging.Fig. 4 shows the single-look imaging results (the

modulus is shown). In this example, 12 evenly spacedscans (each scan covering 2 m in down-range) areused to form the entire image covering 24 m in thedown-range. The images formed by different scansare nonoverlapping. In this figure, three differentimaging methods are compared. Fig. 4(a) shows theconventional DAS imaging result where the IFFTwithout windowing is used. It can be observed thatthe imaging result is poor due to the high sidelobesand strong clutter. Fig. 4(b) shows the DAS imagingresult where the windowed IFFT is used. (We use

Fig. 4. PSI single-look imaging results. (a) DAS imaging result. (b) WDAS imaging result. (c) APES-RCB imaging result with ²= 23.

the Kaiser window with parameter 4.) This methodis referred to as the “WDAS.” (No weighting is usedin the aperture dimension for the DAS and WDASimages.) From this figure, it is clear that the sidelobesin the down-range dimension are reduced. However,the image resolution in down-range is decreased aswell. Note also that due to the poor performance ofthe DAS beamformer, deeply buried mines can hardlybe identified from Figs. 4(a) and (b). Fig. 4(c) showsthe APES-RCB imaging result. We use ²= 23 anda= 1DM£1 with M = 30 and D = 1 for the PSI system.From this figure, we can see that the sidelobes andclutter are effectively mitigated. Note that all 12 minescan be identified.The multi-look imaging results based on

noncoherent processing are shown in Fig. 5. Theoutput for each focal point in the image is obtainedusing 10 consecutive scans with the standoff distancefrom 4.5 to 5.4 m. Figs. 5(a) and (b) are the DASand the WDAS images, respectively. It is clearthat, compared with their single-look counterparts,the multi-look images are better. However, thestrong clutter and sidelobes can still be observed inFigs. 5(a) and (b). Fig. 5(c) shows the noncoherentAPES-RCB image, where ²= 14 is used in therank-deficient RCB. Again, the adaptive imagingapproach appears to be the best. Note also that themulti-look APES-RCB image is less sensitive tothe choice of ² as compared with its single-lookcounterpart.Fig. 6 shows the ROC (receiver operating

characteristic) curves for the PSI system based onfour imaging methods, i.e., “single-look WDAS,”“multi-look WDAS,” “single-look APES-RCB,”


Fig. 5. PSI noncoherent multi-look processing results. (a) DAS imaging result. (b) WDAS imaging result. (c) APES-RCB imagingresult with ²= 14.

Fig. 6. Comparison of ROC curves for PSI FLGPR system viafour different imaging methods.

and “multi-look APES-RCB.” To obtain each ROCcurve, each image is first segmented into connectedregions by using a reasonably low threshold. For eachregion, the peak value and its location are retained andthe rest of the pixels are set to zero. Then a simplethreshold detector is used to perform the detection.The threshold increases in small steps. For each valueof the threshold, we obtain a list of alarms, which isused to evaluate the probability of detection and thefalse alarm number. Based on the ground truth, foreach mine, we define a detection circle. The centerof the circle indicates the true location of the mineand the area of the circle is 1 m2. The alarms fallingwithin the circle are considered successful: the minewas detected. Otherwise, they are counted as falsealarms.

It is clear from Fig. 6 that, as compared with theconventional DAS-based methods, our APES-RCBimaging approach improves the landmine detectioncapability for both single-look and multi-look cases.For example, to detect all mines, the noncoherentmulti-look APES-RCB approach reduces the numberof false alarms from 17 to 1 as compared with itsnoncoherent multi-look WDAS counterpart. Notealso that the detection results based on multi-lookprocessing are better than those based on single-lookprocessing.

B. SRI FLGPR Experimental Results

A photograph of the SRI FLGPR systemis shown in Fig. 7. This system consists of 2transmitters and 18 receivers using quad-ridgedhorn antennas. The height of the transmitters (twolarge horns) is about 3.3 m above the groundand their phase centers are 3.03 m apart. The18 receiving antennas are horizontally equallyspaced with 17 cm center-to-center spacing and theheight for the bottom row is about 2 m above theground. The stepped-frequency system operates at893 discrete frequencies evenly spaced over thefrequency range from 0.5 to 2.9084 GHz. The twotransmitters work sequentially and all the receiverswork simultaneously. Hence there is a total numberof DM = 36 channels of received signals that can beobtained for each scan. This system can work in bothVV (vertically-polarized transmitter and receiver) andHH (horizontally-polarized transmitter and receiver)modes. Data are recorded while the vehicle is moving


Fig. 7. Photograph of SRI FLGPR system.

and the distance between two adjacent scans is about0.5 m. The GPS (Global Positioning System) isused to measure the location of the system for eachscan. At each scan location, the image region is 5 m(cross-range) by 8 m (down-range) with an 8 mstandoff distance ahead of the vehicle. Again, a pixelspacing of 4 cm is chosen in both the down-rangeand cross-range dimensions for the radar imaging.During the data collection for the SRI system, somemetal cans were placed on the sides of the mine lane.To clearly illustrate the landmine imaging results, wehave masked out the metal can returns in the imagesshown below.Fig. 8 shows the single-look imaging results.

(Only the VV data are used here. Similar results can

Fig. 8. SRI single-look imaging results. (a) DAS imaging result. (b) WDAS imaging result. (c) APES-RCB imaging result with ²= 28.

be obtained from the HH data.) In this example, 9evenly sampled scans (each scan covering 2.7 min down-range) are used to form the entire imagecovering 24 m in the down-range. The images formedusing different scans are nonoverlapping. Figs. 8(a)and (b) show the DAS and WDAS imaging results,respectively. Note that the mines buried at the depthsof 10 and 15 cm can hardly be seen in these figuresdue to the high sidelobes and strong clutter. Fig. 8(c)shows the APES-RCB imaging result, where wehave used ²= 28 and a= 1DM£1 with M = 18 andD = 2 for the SRI system. It can be noticed fromthis figure that the sidelobes and clutter have beeneffectively removed due to the excellent performanceof APES-RCB, and that all 12 mines can be identified.Note also that the SRI radar images have higherresolution in the down-range dimension than the PSIradar images due to the larger system bandwidth ofthe SRI FLGPR system.The multi-look imaging results based on

noncoherent processing are shown in Fig. 9. Theoutput for each focal point in the image is obtainedusing 9 consecutive scans with the standoff distancefrom 9 to 14 m. Figs. 9(a) and (b) show the DAS andWDAS imaging results, respectively. Fig. 9(c) showsthe noncoherent APES-RCB image with ²= 14. It canbe noticed that by using APES-RCB in the multi-lookprocessing mode, high quality imaging results can beobtained.Fig. 10 shows the ROC curves for the SRI system

based on four different methods. The same detectionmethod as used for the PSI system is applied here.We can see from this figure that, as compared withthe conventional DAS-based methods, the APES-RCB


Fig. 9. SRI noncoherent multi-look processing results. (a) DAS imaging result. (b) WDAS imaging result. (c) APES-RCB imagingresult with ²= 14.

Fig. 10. Comparison of ROC curves for SRI FLGPR system viafour different imaging methods.

imaging approach improves the landmine detectioncapability for both single-look and multi-look cases.In particular, to detect all mines, the noncoherentmulti-look APES-RCB approach reduces the numberof false alarms from 5 to 1 as compared with thenoncoherent multi-look WDAS.Finally, we remark that different ²s are used in

the examples above for the two different FLGPRsystems due to their different array calibration errorsand system geo-registering errors. We also note that,in general, multi-look APES-RCB images vary lesswith ² than their single-look counterparts.

VI. CONCLUSIONS

In this paper, we have presented a new algorithm,referred to as APES-RCB, for adaptive FLGPR

imaging. The new method consists of two majorsteps. First, APES is used to obtain accurate reflectioncoefficient estimates for each receiving channel.Second, the rank-deficient RCB is employed toestimate the original reflection coefficients based onthe estimates obtained via APES. Using experimentalFLGPR data, we have shown that the images obtainedvia APES-RCB have significantly reduced clutteras compared with those obtained via the standardDAS-based methods. We have also shown that thelandmine detection performance of the FLGPRsystem is also significantly improved by using theAPES-RCB imaging approach.

REFERENCES

[1] International campaign to ban landmines, Sept. 2003.http://www.icbl.org.

[2] The global mine problem, Sept. 2003http://www.landmine.org.

[3] Hidden killers, the global landmine crisis.Report of the United States Department of State, Bureauof Political-Military Affairs, 1998.

[4] Bruschini, C., and Gros, B.A survey of current technology research for the detectionof landmines.The Journal of Humanitarian Demining (Feb. 1998),http://maic.jmu.edu/journal/2.1/bruschini.htm.

[5] Siegel, R.Land mine detection.IEEE Instrumentation and Measurement Magazine, 5 (Dec.2002), 22—28.

[6] Broach, J. T., Harmon, R. S., and Dobeck, G. J. (Eds.)Detection and remediation technologies for mines andminelike targets VII.Proceedings of SPIE, 4742 (2002).


[7] Witten, T. R.Present state-of-the-art in ground penetrating radars formine detection.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetIII, vol. 3392, 1998, 576—585.

[8] Bradley, M., Witten, T., McCummins, R., and Duncan, M.Mine detection with ground penetration synthetic apertureradar.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVII, vol. 4742, 2002, 248—258.

[9] Gu, K., Wu, R., Li, J., Bradley, M., Habersat, J., andMaksymonko, G.SAR processing for GPSAR systems.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVII, vol. 4742, 2002, 1050—1060.

[10] Kapoor, R., Ressler, M., and Smith, G.Forward-looking mine detection using an ultra-widebandradar.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetV, vol. 4038, 2000, 1067—1076.

[11] Kositsky, J., Cosgrove, R., Amazeen, C., and Milanfar, P.Results from a forward-looking GPR mine dectectionsystem.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVII, vol. 4742, 2002, 206—217.

[12] Sun, Y., and Li, J.Time-frequency analysis for plastic landmine detectionvia forward-looking ground penetrating radar.IEE Proceedings–Radar, Sonar and Navigation, 150, 4(Aug. 2003), 253—261.

[13] Linnehan, R., and Rappaport, C.Mitigating ground clutter effects for mine detection withlightweight artificial dielectrics.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVII, vol. 4742, 2002, 259—268.

[14] Duston, B., and Lang, D.Statistical processing of ground penetrating radar signalsfor mine detection.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVI, vol. 4394, 2001, 494—502.

[15] Van Trees, H. L.Optimum Array Processing, Part IV of Detection,Estimation, and Modulation Theory.New York: Wiley, 2002.

[16] Lertniphonphun, W., and McClellan, J. H.Migration of underground targets in UWB-SAR systems.In Proceedings of the International Conference on ImageProcessing, vol. 1, 2000, 713—716.

[17] DeGraaf, S. R.SAR imaging via modern 2-D spectral estimationmethods.IEEE Transactions on Imaging Processing, 7, 5 (May1998), 729—761.

[18] Benitz, G. R.High-definition vector imaging.Lincoln Laboratory Journal, 10, 2 (1997), 147—170.

[19] Pastina, D., Farina, A., Gunning, J., and Lombardo, P.Two-dimensional super-resolution spectral analysisapplied to SAR images.IEE Proceedings–Radar, Sonar and Navigation, 144, 5(Oct. 1998), 281—290.

[20] Nuthalapati, R.High resolution reconstruction of ISAR images.IEEE Transactions on Aerospace and Electronic Systems,28, 2 (Apr. 1992), 462—472.

[21] Fornaro, G., Serafino, F., and Soldovieri, F.Three-dimensional focusing with multipass SAR data.IEEE Transactions on Geoscience and Remote Sensing, 41,3 (Mar. 2003), 507—517.

[22] Lombardini, F., and Reigber, A.Adaptive spectral estimation for multibaseline SARtomography with airborne L-band data.In Proceedings of IGARSS 2003, vol. 3, July 2003,2014—2016.

[23] Gini, F., and Lombardini, F.Multilook APES for multibaseline SAR interferometry.IEEE Transactions on Signal Processing, 50, 7 (July2002), 1800—1803.

[24] Gini, F., Lombardini, F., and Montanari, M.Layover solution in multibaseline SAR interferometry.IEEE Transactions on Aerospace and Electronic Systems,38, 4 (Oct. 2002), 1344—1356.

[25] Lombardini, F., Montanari, M., and Gini, F.Reflectivity estimation for multibaseline interferometricradar imaging of layover extended sources.IEEE Transactions Signal Processing, 51, 6 (June 2003),1508—1519.

[26] Li, J., and Stoica, P.An adaptive filtering approach to spectral estimation andSAR imaging.IEEE Transactions on Signal Processing, 44, 6 (June1996), 1469—1484.

[27] Li, H., Li, J., and Stoica, P.Performance analysis of forward-backwardmatched-filterbank spectral estimators.IEEE Transactions on Signal Processing, 46, 7 (July1998), 1954—1966.

[28] Li, J., Stoica, P., and Wang, Z.On robust Capon beamforming and diagonal loading.IEEE Transactions on Signal Processing, 51, 7 (July2003), 1702—1715.

[29] Liu, G., Wang, Y., Li, J., and Bradley, M.SAR imaging for a forward-looking GPR system.In Proceedings of SPIE Conference on Detection andRemediation Technologies for Mines and Minelike TargetVIII, vol. 5089, 2003.

[30] Stoica, P., and Moses, R. L.Introduction to Spectral Analysis.Upper Saddle River, NJ: Prentice-Hall, 1997.

[31] Larsson, E. G., Li, J., and Stoica, P.High-resolution nonparametric spectral analysis: theoryand applications.In Y. Hua, A. B. Gershman, and Q. Cheng, (Eds.),High-Resolution and Robust Signal Processing, New York:Marcel-Dekker, 2004.

[32] Wang, Y., Li, J., and Stoica, P.Rank-deficient robust Capon filter-bank approach tocomplex spectral estimation.Submitted to IEEE Transactions on SignalProcessing, 2003. (Available on the website:http://www.sal.ufl.edu/RankDeficientRCB.pdf).

[33] Rao, B. D., and Hari, K. V. S.Performance analysis of ESPRIT and TAM indetermining the direction of arrival of plane waves innoise.IEEE Transactions on Acoustics, Speech, and SignalProcessing, 37, 12 (Dec. 1989), 1990—1995.


[34] Feldman, D. D., and Griffiths, L. J.A projection approach for robust adaptive beamforming.IEEE Transactions on Signal Processing, 42, 4 (Apr.1994), 867—876.

Yanwei Wang (S’04) received the B.Sc. degree from Beijing University ofTechnology, China, in 1997 and the M.Sc. degree from University of Florida,Gainesville, in 2001, both in electrical engineering. He received the Ph.D. degreein 2004, also from the University of Florida.Since January 2000, he has been a research assistant with the Department of

Electrical and Computer Engineering, University of Florida. His current researchinterests include spectral estimation, tomographic imaging, and radar/array signalprocessing.

Xi Li (S’01–M’04) received B.Sc. and Ph.D. degrees in electronic engineeringfrom Nanjing University of Science and Technology (NUST), Nanjing, China, in1995 and 1999, respectively. He received his second Ph.D. from the University ofFlorida, Gainsville, in 2003, in electrical engineering.From May 2000 to May 2003, he was a research assistant with the

Department of Electrical and Computer Engineering (ECE), University of Florida(UF), Gainesville. From June 2003 to January 2004, he was a postdoctoralassociate with the ECE Department at the University of Florida. Since February2004, he has been with the Clinical Diagnostics Division, Beckman Coulter,Inc, Miami, FL. His research interests include spectral estimation and signalprocessing for acoustic, radar, and medical applications.

Yijun Sun received the B.S. degrees in both electrical and mechanicalengineering from Shanghai Jiao Tong University, Shanghai, China, in 1995,and the M.S. and Ph.D. degrees in electrical engineering from the University ofFlorida, Gainesville, in 2003 and 2004, respectively.From 1995 to 2000, he was an electrical engineer with Siemens, Shanghai,

China. Since 2000, he has been a research assistant in the Department ofElectrical and Computer Engineering at the University of Florida. His currentresearch interests include pattern recognition, machine learning, time-frequencyand wavelet analysis, as well as their applications to handwritten digitrecognition, SAR automatic target recognition, and landmine detection usingground penetrating radar.

[35] Wang, Y., Li, J., Liu, G., and Stoica, P.Polarimetric SAR target feature extraction and imageformation via semi-parametric methods.Digital Signal Processing–A Review Journal, 14, 3 (May2004), 268—293.


Jian Li (S’87–M’91–SM’97–F’05) received the M.Sc. and Ph.D. degrees inelectrical engineering from The Ohio State University, Columbus, in 1987 and1991, respectively.From April 1991 to June 1991, she was an adjunct assistant professor with the

Department of Electrical Engineering, The Ohio State University. From July 1991to June 1993, she was an assistant professor with the Department of ElectricalEngineering, University of Kentucky, Lexington. Since August 1993, she hasbeen with the Department of Electrical and Computer Engineering, Universityof Florida, Gainesville, where she is currently a professor. Her current researchinterests include spectral estimation, statistical and array signal processing, sensornetworks, machine learning, and their applications.Dr. Li is a fellow of IEEE and a Fellow of IEE. She is a member of Sigma Xi

and Phi Kappa Phi. She received the 1994 National Science Foundation YoungInvestigator Award and the 1996 Office of Naval Research Young InvestigatorAward. She was an executive committee member of the 2002 InternationalConference on Acoustics, Speech, and Signal Processing, Orlando, FL, inMay 2002. She was an associate editor of the IEEE Transactions on SignalProcessing from 1999 to 2005. She has been an associate editor of the IEEESignal Processing Magazine since 2003. She is presently a member of two ofthe IEEE Signal Processing Society technical committees: the Signal ProcessingTheory and Methods (SPTM) Technical Committee and the Sensor Array andMultichannel (SAM) Technical Committee.


Petre Stoica (F’94) received the D.Sc. degree in automatic control from thePolytechnic Institute of Bucharest (BPI), Bucharest, Romania, in 1979 and anhonorary doctorate degree in science from Uppsala University (UU), Uppsala,Sweden, in 1993.He is a professor of systems modeling with the Division of Systems and

Control, the Department of Information Technology at UU. Previously, wasa professor of system identification and signal processing with the Faculty ofAutomatic Control and Computers at BPI. He held longer visiting positions withEindhoven University of Technology, Eindhoven, The Netherlands; ChalmersUniversity of Technology, Gothenburg, Sweden (where he held a JubileeVisiting Professorship); UU; The University of Florida, Gainesville, FL; andStanford University, Stanford, CA. His main scientific interests are in the areasof system identification, time series analysis and prediction, statistical signal andarray processing, spectral analysis, wireless communications, and radar signalprocessing.Dr. Stoica has published nine books, ten book chapters, and some 500 papers

in archival journals and conference records. The most recent book he coauthored,with R. Moses, is Spectral Analysis of Signals (Prentice-Hall, 2005). He is on theeditorial boards of six journals: Journal of Forecasting, Signal Processing, Circuits,Signals, and Signal Processing, Digital Signal Processing–A Review Journal,Signal Processing Magazine, and Multidimensional Systems and Signal Processing.He was a co-guest editor for several special issues on system identification, signalprocessing, spectral analysis, and radar for some of the aforementioned journals,as well as for IEE Proceedings. He was corecipient of the IEEE ASSP SeniorAward for a paper on statistical aspects of array signal processing. He was alsorecipient of the Technical Achievement Award of the IEEE Signal ProcessingSociety. In 1998, he was the recipient of a Senior Individual Grant Award ofthe Swedish Foundation for Strategic Research. He was also co-recipient ofthe 1998 EURASIP Best Paper Award for Signal Processing for a work onparameter estimation of exponential signals with time-varying amplitude, a 1999IEEE Signal Processing Society Best Paper Award for a paper on parameterand rank estimation of reduced-rank regression, a 2000 IEEE Third MillenniumMedal, and the 2000 W. R. G. Baker Prize Paper Award for a paper on maximumlikelihood methods for radar. He was a member of the international programcommittees of many topical conferences. From 1981 to 1986, he was a Directorof the International Time-Series Analysis and Forecasting Society, and he wasalso a member of the IFAC Technical Committee on Modeling, Identification,and Signal Processing. He is also a member of the Royal Swedish Academy ofEngineering Sciences, an honorary member of the Romanian Academy, and afellow of the Royal Statistical Society.


adaptive imaging for forward-looking ground penetrating radar

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