Robust Doppler Centroid Estimate for ERS andENVISAT

M. De Stefano, A. Monti Guarnieri.Dipartimento di Elettronica - Politecnico di MilanoPiazza Leonardo da Vinci 32 - 20133 Milano Italy

FAX +39 02 23993413 - TEL +39 02 2399 3645, +39 02 2399 3446E-mail:destefan@elet.polimi.it

Abstract—The algorithm presented is capable of retrievingthe correct DC ambiguity and to fit a fine polynomial estimateboth on uniform and contrasted scenes. The core of the algo-rithm exploits a block wise processing: in each block a coarseunambiguous estimate is provided by exploiting both a secondorder statistic estimator (WDAR) and a higher order technique(MLBF). The final, fine estimate of the unambiguous Doppler isachieved by jointly exploiting the coarse unambiguous estimatewith a fine, ambiguous one. The proposed algorithm accountscarefully for large variation of DC with range, like for recentEmergency Backup Mode of ERS and RADARSAT.The final estimate and its confidence is provided by a weightedaverage of the block measures. Tuning of the weights andadditional check ensure robustness. The estimate of the offsetfrequency constant is then approached and a solution for cali-brating its value is provided.

I. INTRODUCTION

We address the problem of estimating the Doppler Centroid(DC) starting from a range-compressed dataset acquired byconventional single-PRF SAR spaceborne sensor, like ERS,or ENVISAT-ASAR and RADARSAT. The constraint of ope-rating on range-compressed data is required for efficiency.Doppler centroid (DC) frequency can be divided in two

portions: the ambiguous DC (that is the central frequencybetween −PRF/2 and PRF/2) and the ambiguity:

fDC = (Dc + p) · PRF (1)

where fDC is the absolute DC frequency, Dc is the normalizedDC ambiguous frequency and p is the ambiguity (an integernumber).

Because of the absence of accurate information on attitude,we implement a blind estimator.

II. CONSTANT DOPPLER CENTROID ESTIMATE

Several techniques have been proposed in the past forambiguous and unambiguous DC estimate. These techniqueswork quite well when DC is practically constant.

The ambiguous estimate techniques are based on powerspectrum estimation. The simplest one, that we choose, is theautocorrelation one (see [8])

Dc =�raz (1)

2π(2)

Fig. 1. Block diagram of the algorithm.

where Dc is the estimate for DC and �raz (1) is the estimatedphase of the first sample of the azimuth autocorrelation.

For the unambiguous estimate we choose two techniques:one of them is a second order statistic and it is useful inpresence of homogeneous targets (speckle). Both WavelengthDiversity Ambiguity Resolving algorithm (WDAR) or MultiLook Cross Correlation (MLCC) (see [1], [4]) will work. Theirestimate has always to be corrected with an offset frequency(see [2]), a feature of the sensor. It is possible to show thatWDAR is less sensitive to the offset frequency than MLBF.

The second technique is based on higher order statistics: itworks better in presence of contrasts and it is not affected bythe offset frequency. We choose Multi Look Beat Frequency(MLBF) among those present in literature (see [4], [5], [7])because this is the only one suited for range-compressed data.

III. RANGE AND AZIMUTH VARIANT DOPPLER ESTIMATE

When DC varies with range and azimuth (as always is) itis necessary a block wise processing. A block diagram of theglobal algorithm is shown in Fig. 1: it is a combination ofthe ambiguous estimation and WDAR and MLBF techniques.First, data is block-divided. For each block, the ambiguousestimate is done. Then, on the estimated data, a polynomialinversion is applied. The model is

Dc (nrg, naz) = an2rg + bnrg + cnaz + h (3)

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Fig. 2. Ambiguous Doppler centroid regression.

where nrg and naz are range and azimuth indexes of thesample at the center of each block and a, b, c and h arethe polynomial coefficients to be estimated. Because of thepossible folding of the ambiguous estimate between −PRF/2and PRF/2, the inversion has to be done in two steps: firstwe regress a wrapped plane

ej2πDcp(nrg,naz) = ej2π(bpnrg+cpnaz+hp) (4)

This step is performed by zero-padded bidimensional FFTof exp(j2πDc). Then we invert the model on the residualsDcres (nrg, naz) = Dc (nrg, naz) − Dcp (nrg, naz), whichare supposed not to be wrapped (this avoids the use phaseunwrapping techniques). This is done as follows:

m =(GT C−1

D G)−1

GT C−1D d (5)

where

G =

n 2rg (1) nrg (1) naz (1) 1

n 2rg (2) nrg (2) naz (2) 1

......

......

n 2rg (N) nrg (N) naz (N) 1

m =[

ares bres cres hres

]T

d =[

Dcres (1) Dcres (2) · · · Dcres (N)]T

N is the number of processed blocks, m are the coefficientsof the model in (3), computed for the residuals1, and CD isthe data covariance matrix, which has this expression:

CD = diag{σ2

1 , σ22 , . . . , σ2

N

}Coefficients a, b, c and h can now be computed:

a = ares b = bp + bres c = cp + cres h = hp + hres

The bidimensional ambiguous DC estimate is shown in Fig. 2.

1Coefficients bres, cres and hres should be very small because the lineartrend of the model has already been estimated with bp, cp and hp.

1.5 2 2.5 3 3.5 4 4.5 5−20

−15

−10

−5

0

5

10

contrast

WDA

R am

biguit

y

Fig. 3. WDAR ambiguity estimate versus contrast. The true ambiguity was−6. The threshold was 2.15 (Paris 30/06/02, ERS data).

For each block, we then estimate the unambiguous DC,using either WDAR or MLBF. The selection between thefirst or the second technique is mainly done by means ofa threshold on the contrast parameter (see also [1]) Kc =E

[I2

]/E2 [I] where I is the pixel intensity. It could be shown

that the theoretical value of contrast, in presence of speckle, isKc,th = 2. If strong targets are present, contrast value is muchmore high than two. Although contrast should be defined onthe focused image, we have found that its estimate on range-compressed data is sufficient to provide good results.So unambiguous DC is estimated with WDAR in low contrastblocks and with MLBF in the others. These estimates aredetrended by subtracting the polynomial model in (3). Aweighted average of these measures gives the final ambiguityestimate. The weights are tuned accordingly with the signal tonoise ratio and the contrast (see [1]). The ambiguity estimateis rejected if saturation is present in the processed block (sa-turation is detected thresholding the ratio raz (0) / |raz (1)|).With the value of the ambiguity (p) and the polynomialparameters (a, b, c, h), the unambiguous DC polynomial hasthis expression:

Dcu (nrg, naz) = an2rg + bnrg + cnaz + hu (6)

where a, b, c are the same of (3), while hu = h + p.

IV. MLBF THRESHOLDING

A new threshold was introduced to select the measures touse in the MLBF algorithm (see [4]). The spectrum of thebeat signal presents a big peak in correspondence of the beatfrequency and several other secondary peaks due to noise. TheMLBF estimate is as much precise as the ratio primary-peak-amplitude to secondary-peak-amplitude (PP ratio) is greater.

As an example, Fig. 4 shows the MLBF ambiguity estimatesas function of PP ratio. As expected, the variance of theestimate decreases with the inverse of PP ratio. This thresholdrevealed itself very robust also in presence of null lines in theblocks.

V. OFFSET FREQUENCY ESTIMATE

The offset frequency is necessary for WDAR and its esti-mate is quite simple. After ambiguity computation by means

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0 1 2 3 4 5 6 7 8 9−15

−10

−5

0

5

peak to peak ratio [dB]

MLB

F ab

iguity

Fig. 4. MLBF ambiguity estimate versus Peak to peak ratio. The trueambiguity was −6. The threshold was 2.5 dB (Paris 30/06/02, ERS data).

TABLE I

OFFSET FREQUENCY ESTIMATES ON ENVISAT DATA (σres ARE THE

STANDARD DEVIATIONS OF THE RESIDUALS OF THE POLYNOMIAL

REGRESSION).

orbit date swath offset [Hz] σres [Hz]1536 16/06/2002 IS2 −1912.5 32.02209 02/08/2002 IS2 4812.5 66.12161 30/07/2002 IS3 7468.6 3.90892 02/05/2002 IS4 9029.7 80.3

2875 10/07/2002 IS5 8956.8 3.102445 18/08/2002 IS5 5954.3 69.71987 17/07/2002 IS6 4494.3 84.21758 01/07/2002 IS7 6561.7 66.2

whether of WDAR or of MLBF, we assume that the ambiguityestimate based on the MLBF technique only is correct (thatis true if contrasts are present). Then, the offset frequency isestimated with a subtraction of the MLBF estimate from theWDAR one.

VI. EXPERIMENTAL RESULTS

TABLE II

AMBIGUITY ESTIMATES ON ERS/ENVISAT DATA (FULL FRAME).

area/ date blocks WDAR mna MLBF mnaorbit blocks blocks

Ancona 24/03/99 455 329 29% 108 95%Paris 21/04/01 455 259 30% 186 83%Paris 30/06/01 455 198 29% 256 70%Etna 28/01/01 455 261 26% 100 87%1875 10/07/02 741 741 18% 0 −2161 30/07/02 780 779 26% 0 −

The proposed algorithm was tested on ERS images (about1800 frames also in Emergency Backup Mode) and on thefirst few ENVISAT image mode data. The correct ambiguitywas always found and ambiguous estimate was always correctwithin a standard deviation of 6 − 7% of PRF . In Tab. IIwe show some results of ambiguity estimates. The first fourare obtained from ERS data, while the others, from ENVISATdata. For each frame are shown the total number of processedblocks, the number of blocks for which WDAR or MLBF

was used and, for each technique, the percentage of measureswhose distance from the true ambiguity is less than PRF(mna stands for measures near ambiguity). We stress thatin the last two frames, contrasts were not present and, forthis reason, MLBF did not work. Some tests have been madealso on RADARSAT images (twelve images in standard beamand 22 images in fine beam) and the ambiguity estimate wasalways correct although, in some cases, few MLBF goodmeasures were used.

VII. CONCLUSIONS

The proposed Doppler centroid estimation algorithm hasbeen proved faultless on the tested datasets. This robustnessis mainly due to contrast weighting (WDAR) and MLBFthreshold (PP ratio). The algorithm is also useful to providetracking of offset frequency with time in systems with activeantenna array (see Tab. I, in which estimates made on the sameswaths are highlighted).

REFERENCES

[1] R.Bamler, H.RungePRF-Ambiguity Resolving by Wavelength DiversityIEEE Trans. on Geoscience and Remote Sensing, Vol. 29, N.6, November1991.

[2] R.BamlerWavelength diversity PRF-ambiguity resolver: calibration and test forERS-1 SAR Bamler, R.; Geoscience and Remote Sensing Symposium,1993. IGARSS ’93. ’Better Understanding of Earth Environment’., Inter-national , 18-21 Aug 1993

[3] R.BamlerDoppler Frequency Estimation and the Cramer-Rao BoundIEEE Trans. on Geoscience and Remote Sensing, Vol. 29, N.3, May 1991.

[4] F.Wong, I.G.CummingA Combined SAR Doppler Centroid Estimation Scheme Based uponSignal PhaseIEEE Trans. on Geoscience and Remote Sensing, Vol. 34, N.3, May 1996.

[5] I.G.Cumming, P.F.Kavanagh, M.R.ItoResolving the Doppler Ambiguity for spaceborne Synthetic ApertureRadarProc. IGARSS ’86 Symp., Zurich, Ref. ESA SP-254, 1986.

[6] S.N.MadsenEstimating The Doppler Centroid of SAR DataIEEE Trans. on Aerospace and Electronic Systems, Vol. AES-25, N.2,March 1989.

[7] Prati, C.; Rocca, F.; Kost, Y.; Damonti, E.;Blind deconvolution for Doppler centroid estimation in high frequencySAR IEEE Transactions on Geoscience and Remote Sensing, Vol. 29,Issue: 6 , Nov 1991.

[8] Pickard, T.; The effect of noise upon a method of frequency measurementIEEE Transactions on Information Theory, Vol.: 4 Issue: 2 , Jun 1958

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