The Radar Problem

The controlling system for a multiradar display, in an air traffic long-distance control center, receives different information from different kinds of radars on the globe. The information coming from each radar contains among others the coordinates x, y and z (with respect to the Cartesian coordinate system of the given radar) of an airplane which is “seen” by the radar. The two-dimensional situation in the case of two radars R 1, R 2 is shown on Figure 10.1. We can see that the airplane is described by the coordinates $$[x_{R_{1}}, y_{R_{1}}]$$ of the radar R 1 and by the coordinates $$[x_{R_{2}}, y_{R_{2}}]$$ of the radar R 2. For the controlling system of the multiradar display it is necessary to work with the “absolute” coordinate system (with the origin R). The data from all the radars concerning the position of the airplane A are transformed into this system. That means that in this coordinate system the airplane A is described by several points which can be processed using appropriate criteria. (For example, the airplane will be represented by the point which corresponds to its most probable position). In the coordinate system with the origin R, the long-distance control is able to follow the relative position of airplanes from the visual information on the display. The controlling program for a multiradar display is then able to watch the whole region of operation of the airplane using chosen windows. For simplicity let the absolute coordinate system with the origin R be identical to the coordinate system of the radar R 2 .