Estimation of Calibration Parameters 2 RADIOMETRIC AND PHASE CALIBRATION

The objectives of this memo are threefold. First, the antenna coordinate system used for antenna gain, steering computations and image time predictions is defined. Secondly, the look vector along the Doppler centroid (or locus of points of maximal gain at a specified range) is derived in terms of the yaw, pitch and roll of the platform, the antenna azimuth steering angle and the mounting angle of the antenna with respect to the platform. Finally, for calibration and other applications it is necessary to know when a given object is imaged along the flight trajectory. We derive the appropriate equation to determine the imaging position. Platform and Antenna Coordinates We begin by defining the antenna coordinate system, the azimuth and elevation angles, and look and steering vectors in these coordinates. In order to make precise the relationship between antenna and platform coordinate systems we begin by defining the aircraft body frame. The aircraft body frame, IJK is defined as the I axis directed along the fuselage oriented in the forward direction, the J axis is pointed perpendicular to the I axis in the direction of the left wing, and K is perpendicular to I and J pointing in the upward direction. Note, this differs from the traditional ijk aircraft body frame where i=I, j=-J and k=-K. Antenna face coordinates, erd, (elevation, radiation and deflection axes) are defined to be initially aligned with the IJK aircraft frame coordinates as shown in Figure 1 prior to rotation by the mounting angle, !. Figure 1. Aircraft frame, IJK, and antenna face, erd, coordinates are assumed to nominally aligned as above prior rotation by the antenna mounting angle. The antenna is mounted to the aircraft by rotation about the I axis of 45°. Thus the transformation from antenna face coordinates to aircraft body coordinates is given by I K