The Cramér-Rao bound and the optimal parameter estimation method of internal waves in SAR images

Parameters estimation of internal waves is one of the most important applications of oceanic synthetic aperture radar (SAR) images. Several methods are widely applied to estimate internal waves parameters such as wavelet analysis method, curve fitting method and empirical mode decomposition (EMD) method. Most of these methods suppose the signals processed are affected by the additive random noise. However, the multiplicative noise model of SAR images is not applied to these methods. The result is that these methods could not reach the Cramér-Rao bound (CRB). This paper assumes that SAR images are affected by speckle noise, and take the speckle signal described by a gamma distribution as an example. In this model, this paper derives the CRB for internal waves parameters estimation. Based on the multiplicative noise model and the CRB, this paper proposes an optimal parameters estimation method of internal waves, and the results could reach the CRB. The real image experiments can prove that the proposed method is more accurate and effective than other methods.