ON THE DIMENSION AND NON-LINEAR DYNAMICS THEORY APPLICATION IN A NEW FORM AND METHOD OF RADIO LOCATION

Abstract

Intensive evolution of the modern radar equipment and technologies put new requirements for the radio location theory as well. The work objective is not only to state our viewpoint, to define and discover a new type and a new method of radio location on the basis of fractal-and-scaling or scale-invariant principles but also, just as important, to call attention to conventional questions of the general statistical theory from the point of view of the fractal analysis, fractional calculation and the global fractal-and-scaling approach which was designed and being developed by the author during last 40 years in IREE AS of USSR (IREE RAS). The author was the first who proposed and substantiated the new type and the new method of the modern radio location namely fractal-scaling or scale-invariant radio location (Potapov, 2017, 2018). Efficiency of functionals which are determined by topology, fractional dimension, and texture of a sensed multidimensional signal was proved for synthesis of the new non-energy detectors of low-contrast objects in presence of noise. Fractal radio location is based on three postulates: - intellectual signal/image processing which is based on the fractional measure and scaling effects theory for calculating the field of fractal dimensions; - sampling of a received noisy signal relates to a class of stable non-Gaussian distributions of probabilities of fractal dimension D; - the topology maximum at the energy minimum of a received random signal. Sensitivity of a radio system has been confirmed (what is equal to an increase of the range) while using fractal and textural signature in topological detectors. It results in drastic changes in the mathematical apparatus of the theoretical radio location. The research was supported by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».