Comparison of Doppler Centroid Estimation Methods in SAR

This paper compares five Doppler centroid estimation methods which are :energy balancing, matched-correlation , maximum likelihood, correlation Doppler estimator(CDE) and sign Doppler estimator (SDE). Their estimation performances in raw data domain and image domain are studied. The computer simulation results are presented. ERS-1 raw data are also used to test the performances of every method. Introduction Synthetic aperture radar (SAR) is a class of high resolution radar which obtains fine azimuth resolution by coherent processing of backscattered Doppler histories. An important parameter in relation to the azimuth processing is the Doppler centroid, which is used to generate the azimuth matched-filters, together with the Doppler frequency rate. In principle, it is possible to calculate Doppler centroid from orbit and attitude data. However, measurement uncertainties will limit the accuracy. This error leads to the degradation in signal-to-noise ratio and signal-toazimuth ambiguity ratio. This paper studies the Doppler centroid estimation methods from the received echo data, which is also referred to as “clutterlock”. So far, there are about five methods proposed by people. They are: ( 1)Energy balancing[’], (2)Matched-correlation estimation[’], (3) Maximum-likelihood estimationP1, (4) Correlation Doppler estimator (CDE)[41, (5)Sign Doppler estimator (SDE)[41. The first three methods are implemented with azimuth power spectrum. The last two ones directly use the complex raw data. The every method mentioned above can also be carried out in complex image domain15], so the bias arised from the strong scatterers passing part of the synthetic aperture will be avoided. However, estimation in image domain is always an iterating procedure. R. Bamler[*] has pointed out that all the methods are equivalent to the correlation of the signal power spectra with a particular weighting function and finding the minimum value of the correlation results. The different weighting function achieves different estimation variance. Special case of a correlation1015 based estimator is the maximum-likelihood estimator that can achieve the Cramer-Rao bound. He has compared the first four methods and derived their variances in theory. This paper reviews all these methods and compares their performance when they are implemented in image domain. The iterating coefficients used for estimation in image domain are derived. The computer simulation results are presented. All the methods also have been tested by the data from ERS1. 11. Estimating Doppler centroid in data domain The principal of the estimation use the fact that the high azimuth bandwidth time product of a SAR locks Doppler frequency to the position along tracks. Thus, the components at any particular Doppler frequency originate from the targets in a specific part of the radar beam. As a consequence, the azimuth power spectrum S(f) should follow the shape of the two-way azimuth power pattern G2(f) of the antenna. If this pattern is symmetry, the center frequency can be found by finding the energy centroid of the azimuth power spectrum, as shown by the following equation where Bd is Doppler band and fdc is the Doppler centroid. This idea is often implemented by correlating the azimuth power spectrum with some odd reference function R(f) and finding the zero position of the correlation result D(f) as (2) D ( f > = j S ( P ) . W P f)dP D < L 1 = 0 ( 3 ) . According to the reference function chosen, three methods can be constructed. They are energy balancing (EB) with CH360 15-97/0000-1015 $1 .OOO 1997 IEEE matched-correlation (MC) with where W(f) is the nominal antenna two-way power pattern as and maximum-likelihood (ML) with R ( f ) = W” ( 5 ) W f ) = G ’ ( f > (6)