Quantum Nature of Distortion and Delay of Satellite Signals II

Abstract

A detailed analysis of the influence of Rydberg states to the behavior of GPS satellite signals in the D and E atmospheric layers has been carried out. It is demonstrated that these states are the main reason for the GPS signal distortion. It is shown that the behavior of satellite signals is associated with the spectral characteristics of the UHF radiation of the Rydberg states depending on the geomagnetic conditions of ionosphere. The foundations of the quantum theory of distortion and delay of GPS satellite signal propagation through D and E atmospheric layers are analyzed and expounded. The problem reduces to the resonant scattering of photons, moving in the electromagnetic field of the signal, to the Rydberg complexes populated in a two-temperature non-equilibrium plasma. The processes of creation of additional photons because of stimulated emission and resonance scattering of photons are considered. In the present work, the quantum theory of the propagation of a satellite signal in the Earth's upper atmosphere, firstly earlier proposed by the same authors, is described in detail. The general problems of the theory and possible theoretical and applied consequences are discussed. It is explained that two main processes occurring here, are directly related to the resonant quantum properties of the propagation medium. The first process leads to a direct increase in the power of the received signal, and second-to a shift in the signal carrier frequency ν ∆ and the time delay τ ∆ of its propagation. The main reasons of the processes are scattering of the Rydberg electron by the ion core and presence of the neutral medium molecule in the intermediate autoionization states of the composite system populated by the strong non-adiabatic coupling of electron and nuclear motions. The main purposes of our investigation are the physical justification of the formation of parameters ν ∆ and τ ∆ using the quantum dynamics of the electron behavior in the intermediate state of the Rydberg complex A**M and the esti-

Single point positioning with vertical total electron content estimation based on single-epoch data

“…The geodetic coordinates of the GPS antenna, GPS observing time (in seconds) as well as azimuth and elevation of observed satellites as viewed from the receiver are needed to be known. The formula to calculate the vertical ionospheric delay based on the Klobuchar algorithm is as follows (Hofmann-Wellenhof et al, 2008):…”

“…Thus, the concept of the ionospheric point has to be expanded as a piercing point of the GPS wave path and the ionospheric single layer on the specified altitude. Thus, the satellite zenith angle at the piercing point z should first be indicated (Hofmann-Wellenhof et al, 2008):…”

“…Therefore, the mapping function can be used as an inverse of the cosine function (Hofmann-Wellenhof et al, 2008):…”

“…Additionally, an ionosphere-free linear combination as an independent positioning approach can also be well adapted to minimize the ionosphere negative impact on GPS positioning (Teunissen and Kleusberg, 1998). However, Hofmann-Wellenhof et al (2008) stated that "ionosphere free" is not an entirely correct name, caused by the approximation existing in the process of making the refractive index. Those authors studied an ionosphere-free approach in the SPP and achieved a beneficial magnitude of error reduction (50 %-60 %) in relation to the reference SPP model without ionospheric corrections.…”