Numerical studies of conversion and transformation in a surveillance system employing a multitude of radars, part 1

Conversion error is considered in the application of stereographic projection to the planar representation of targets in multiple radar surveillance systems. The error is treated as the separation of images in a local radar plane of target positions (in terms of altitude, azimuth, and slant range) under ideal mapping formulas and system implementations. These images are viewed as elements of a complex plane in which the center of coordinates represents the radar site. Thus, conversion error can be expressed in terms of a range error equal to the difference in moduli of two complex numbers and an angle error equivalent to the difference between the arguments of the same numbers. As the image of target position under ideal conversion traverses a circle centered on the origin of coordinates, both the angle error and the range error oscillate about median values. The amplitude of each oscillation increases with the radius of the circle. In addition, the median range error is strongly dependent upon the radius of the circle. An error correction method and a commonly used minimax technique are considered as alternative means for controlling conversion error.