Doppler frequency estimation and the Cramer-Rao bound

This paper addresses the problem of Doppler frequency estimation in the presence of speckle and receiver noise. An ultimate accuracy bound for Doppler frequency estimation is derived from the Cramer-Rao inequality. It is shown that estimates based on the correlation of the signal power spectra with an arbitrary weighting function are approximately Gaussian distributed. Their variance is derived in terms of the weighting function. It is shown that a special case of a correlation-based estimator is a maximum-likelihood estimator that reaches the Cramer-Rao bound. These general results are applied to the problem of Doppler centroid estimation from SAR data. Different estimators known from the literature are investigated with respect to their accuracy. Numerical examples are presented and compared with experimental results. Keywords-Doppler frequency estimation, Cramer-Rao bound, Synthetic Aperture Radar, Doppler centroid estimation.