Sar Imaging Algorithm Based On Legendre Expanded

As is known, the Taylor polynomials have been basically used in current Synthetic Aperture Radar (SAR) algorithms. And the two-Dimension (2-D) echo signal is expanded in the Taylor series to the third term with ignoring the higher order terms. And the phase expansion error rises. To obtain the high resolution SAR image the echo phase has to be accurately expanded.Taking the missile-borne SAR as research background, the characteristics of the side-looking and the squint mode have been analyzed. And a new expansion method-the Legendre expansion has been proposed to the Range Doppler Algorithm (RDA) and Chirp Scaling Algorithm (CSA). The algorithms are logically demonstrated and the phase compensation functions, which have close relationship with Legendre polynomials, have been calculated. The main content of the dissertation are organized as followed:1.To the side-looking and the squint working mode, the space geometries have been given. And the range formulas and the length varieties of the synthetic aperture are mathematically calculated. Based on the above analysis, the different 2-D phases of the returned echo pulse have been derived.2.To the side-looking and the squint working mode, the Legendre-based RDA has been studied and the phase compensation functions are obtained. Through the point target simulations, the comparisons have been made between the Legendre-based RDA and the Taylor-based RDA. And it can be concluded that Legendre polynomials can be reasonably applied to the RDA. Meanwhile, the rightness of the application has been proved via the analysis of the phase error.3.To the side-looking and the squint working mode, a novel CSA based on Legendre expansion is proposed, and the three important phase correction functions have been derived through the Legendre polynomials coefficients. The simulations of point targets are implemented to demonstrate the validity and the feasibility of the Legendre–based CSA..