An efficient mathematical description of range models for high-order-motion targets in synthetic aperture radar

The paper proposes an efficient mathematical description for the range model of a moving target in synthetic aperture radar (SAR) geometry, without any limitations on the model order. The target may have high-order motions such as accelerations, jerks or micro-motions, and any-order one is decomposed in terms of azimuthal and radial directions. The relationship between target motion component, phase error order and SAR image characteristics are revealed with concise closed-form expressions, taking on an aesthetic sawtooth shape. Effects of accelerations, jerks and higher orders of target motion on SAR images are analyzed, and the effect negligibility condition is also given. The conclusion will serve as an important reference for motion parameter estimation as well as motion ambiguity resolution.