Problem of determination of coordinates, orientation, and speed of an autonomous vehicle by a geophysical field

A new mathematical model is given for navigation of an autonomously controlled vehicle, i.e., determination on the basis of a geophysical field (as a whole and by fragment of it), not only coordinates and orientation, but also the vehicle speed at each instant. The notion of a field fragment is refined in the model. In connection with the problem of economical storage of the onboard information about the geophysical field as a whole, the necessary conditions are given for a stored function that belongs to a given class, approximates the field, and minimizes navigation error.