Abstract - This paper presents several correlation based methods for estimation of the Doppler parameters from SAR raw data in connection with the chirp ...
DOPPLER PARAMETERS ESTIMATION ALGORITHMS FOR SAR PROCESSING WITH THE CHIRP SCALING APPROACH Albert0 Moreira and Rolf Scheiber DLR, German Aerospace Research Establishment Institute for Radio Frequency Technology 82234 Oberpfaffenhofen, Germany
A b s t r a c t - This paper presents several correlation based methods for estimation of the Doppler parameters from SAR raw data in connection with the chirp scaling algorithm. For the estimation of the Doppler rate, a modified approach of the shift and correlate (SAC) algorithm is proposed. In this case, the auto-correlation function of each data set and the standard deviation of the velocity calculations are used in order to monitor the validity of the estimations. For resolving the P R F ambiguity, a new approach is proposed, which is based on the estimation of the range- frequency centroid as a function of the azimuth frequency. Several results of the Doppler parameters estimation are presented for airborne and spaceborne SAR data.
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I INTRODUCTION The determination of the Doppler parameters is essential for achieving high quality SAR image processing. The three main parameters to be determined are the Doppler rate, Doppler centroid (normally determined in base band) and the P R F ambiguity number. The most commonly used approaches for the Doppler rate estimation are the azimuth look correlation [l] and the shift and correlate SAC (21 algorithms, which basically work in the rangeDoppler domain after the range compression has been performed. The SAC algorithm is in this case preferable, since it has a lower computational requirement and achieves a similar accuracy as the look correlation approach. For the Doppler centroid estimation, the energy balancing approach [I] and the correlation Doppler estimator CDE are mostly used. The advantage of the CDE [3]lies on the fact that no F F T is used at all. The phase of the first coefficient of the auto-correlation function is used to estimate the Doppler centroid. As far as the P R F ambiguities are concerned, the multiple P R F technique [4], the look. range cross-correlation [5] and the wavelength diversity [6] algorithms can resolve the P R F ambiguities. The last two algorithms allow the determination of the absolute value of the Doppler centroid from the SAR data itself and avoid the additional P R F hopping before and/or after a data take. In comparison with the look range cross-correlation approach, the wavelength diversity algorithm requires much less computational effort and achieves a better performance for low contrast scenes. In this paper, we assume that the Doppler centroid is varying as a function of the range and azimuth distances. For accommodating this variation, a moving average operation is incorporated, which has an integration time smaller than the desired update rate of the Doppler centroid. Section I1 of this paper describes this approach in connection with the CDE algorithm. In section 111, a modified version of the SAC algorithm is analyzed, which uses the full azimuth bandwidth for the correlation and performs a small frequency shift as the original approach in order to achieve a high correlation degree for the estimations. Section IV presents a new algorithm for resolving the P R F ambiguity, which can be incorporated directly in the range-Doppler domain, without requiring any additional FFT’s. 0-7803-1497-2/94 $4.00 0 1994 IEEE
Section V discuss the necessary modifications for including the Doppler parameters estimation algorithms into the extended chirp scaling algorithm [SI. The extended chirp scaling approach is able to accommodate the variations of the Doppler centroid in range and azimuth and also to accommodate the motion compensation which is required for airborne SAR processing.
I1 - C O R R E L A T I O N D O P P L E R E S T I M A T O R The correlation Doppler estimator CDE algorithm uses the phase of the autocorrelation for a shift of one sample, in order to determine the frequency offset (Doppler centroid) contained in the data set. In order to accommodate the variations of the Doppler centroid in range and azimuth, the following procedure was adopted: - Use of the Sign-Doppler estimator SDE [3]instead of the CDE. In order to measure the Doppler variation as a function of range, the raw data must be first range compressed. This increases the dynamic range of the signal and also the standard deviation of the Doppler estimates. Since the SDE algorithm uses only the sign of each sample to evaluate the Doppler centroid, it equalizes the weighting for strong and weak targets. Thus, the SDE algorithm is more suitable for range compressed data with high contrast (see also fig.1). - Introduction of a moving average filter in azimuth into the SDE algorithm. The integration time in azimuth must be less than that necessary for update of the Doppler centroid. - Evaluation of the standard deviation of the Doppler centroid estimations. Before performing a regression in the range direction, the standard deviation of the centroid value from its local average is calculated and used to perform a weighted cubic regression in the range direction. This procedure gives more weight for the estimations of data sets with low contrast. Since the standard deviation of the Doppler centroid estimates is proportional to the scene contrast [6], the weighted regression will optimize the Doppler centroid estimation. Fig. 1 shows the results obtained for the Doppler estimation using range compressed raw data of the E-SAR system [9]. The standard deviation of the CDE estimations is higher than the estimations of the SDE for high contrast areas (see Fig. 1B for range = 4400 m). The weighted regression in fig. 1A gives a smaller weight for the estimations in this range.
111 - SHIFT A N D C O R R E L A T E A P P R O A C H The shift and correlate SAC approach [2] performs a cross correlation of distinct parts of the azimuth spectrum, one of these parts being conjugated and shifted by PRF/2 before the crosscorrelation. The result of the cross-correlation is a peak, which is time shifted proportionally to the actual velocity. In opposite to the CDE approach, the accuracy of the SAC approach improves for high contrast scenes and also for high correlated signals. In order to improve the correlation factor, we have decreased the frequency shift (PRF/2) applied in one azimuth spectrum by the SAC approach, so that the two parts of the azimuth spectrum are strongly correlated. This increases the
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