Autofocusing of SAR Images Using Quadratic MM-Method

Phase errors produced by trajectory instabilities of a radar carrier vehicle cause significant deterioration in the quality of images in synthetic aperture radar. Onboard navigation systems do not provide necessary accuracy of measuring trajectory instabilities to compensate the phase errors. Therefore, in modern synthetic aperture radars, autofocusing is an obligatory stage in the processing of received signals, which is performed by estimating and subsequent compensation of phase errors. Methods of searching for the optimum of some function of the quality of the radar image are often used to estimate phase errors. Despite the fact that the search methods are quite effective, this method of estimation is difficult to implement due to limited power of onboard computational tools. Therefore, the actual problem is the synthesis of direct algorithms for estimating phase errors. The article proposes an algorithm based on the optimization of surrogate quadratic quality functions. The essence of the proposed approach is to use at each step the estimating procedure a quadratic function, which is the majorant (minorant) for the quality function of radar images, which is selected for optimization. The proposed algorithm can be used with any quality function and allows to implement direct estimation of phase errors without organizing a search in the multidimensional space of the estimated parameters. Using the method of mathematical simulation, the article shows that this algorithm is highly efficient even with large phase errors and can be used for signal processing in synthesized aperture radars.