Determination of the coordinates and orientation of an unmanned airborne vehicle from a geophysical field

The navigation of an unmanned airborne vehicle (UAV) over a geophysical field is considered. The components of the field are the elevation and brightness of the ground surface over a specified region. The navigation problem consists of the determination of the UAV's center-of-mass coordinates and orientation, i.e., a rotation transformation of the original frame of reference in space to a local frame rigidly tied to the UAV. The navigation is performed using the entire geophysical field stored aboard the UAV and its fragment measured by the vehicle in flight. The entire field can be represented by an approximating function of simple structure. A new concept of a field fragment is introduced as a function defined on the cone of scanning beams. The informativeness of the field is examined in the case of such a fragment. Necessary conditions on a function of the given class that approximates the field and ensures the smallest navigation error are given. Necessary conditions are indicated on a smooth trajectory between two points on which the geophysical field is most informative.