V.I. Proskurin

The engineering design procedure of continuously changing phase trajectories at multipath radio-waves propagation in spherically layered medium is offered to interests of a location and communication with the mobile objects. With reference to spherically layered medium with a constant refractive index of each stratum on the basis of a Fermat's principle reflexion and refractive requirements are formulated. For a two-beam trajectory with unitary reflexion on sphere the algebraic equation of 4-th degree for a sine of a geocentric corner of a point of reflexion is gained. For any kusochno-linear phase trajectories iterative procedure of consecutive improvement of co-ordinates of points of reflexion and a refractive is offered. Co-ordinates of special points in initial approach are spotted from system of the linear equations with 3-diagonal matrix of system. The descent direction to the optimum standing of points corresponding to the shortest trajectory (Fermat's principle), is spotted on expressions for requirements of reflexion and a refractive in each point. Formulas for evaluation derivative of the full length of a phase trajectory on co-ordinates of the initial or terminating points, are gained. They are necessary at evaluations of the Doppler bias of frequency of a signal and fading at multipath propagation.