Analytic Yaw–Pitch Steering for Side-Looking SAR With Numerical Roll Algorithm for Incidence Angle

In side-looking synthetic aperture radars (SARs), the rotation of the Earth introduces a corrupting residual Doppler shift. Recently, methods using both yaw and pitch maneuvers have been introduced to cancel residual Doppler. In this paper, the condition for zero residual Doppler independent of a coordinate system is used as a starting point to derive formulas for yaw-then-pitch steering angles that achieve zero residual Doppler for strip-mode SAR. The advantage is that the resulting formulas are analytic in the position and velocity of the radar vehicle. In addition, the magnitude of residual Doppler due to both the offset of the radar phase center from the vehicle center of mass and an ellipsoidal Earth is bounded. To take advantage of the final degree of freedom in roll, a bisection-based roll algorithm is presented that achieves a desired radar incidence angle. The algorithm assumes an ellipsoidal Earth but can incorporate digital elevation and geoid models. Finally, numerical examples illustrate yaw-then-pitch steering, the sensitivity of these angles to the specific orbit, and calculation of the roll angle.