Exact Ray Calculations in a Quasi‐Parabolic Ionosphere With No Magnetic Field

Abstract

The equation of the parabolic ionosphere model is modified in a manner which introduces very slight changes in the electron-density distribution. Using this new "quasi-parabolic" (or QP) model, it is possible to derive exact expressions describing radio-ray trajectories without introducing the approximations which are needed when dealing with the parabolic ionosphere, although magnetoionic effects are not included. The consequent accuracy of computed rays is useful as an aid in evaluating the accuracy of more versatile ray-calculation methods. Also, the exact ray expressions can be of direct !lse in calculating slight differences between rays which are nearly identical, for in this process, small inaccuracies can become magnified.

Efficient time domain HF geolocation using multiple distributed receivers

“…Developed by Croft and Hoogasian [8], it is obtained by a slight modification of the parabolic model used to define the electron density profile of the ionosphere. The QP model provides analytic expressions describing ray path parameters of oblique propagation considering the ionospheric medium.…”

“…The QP model provides analytic expressions describing ray path parameters of oblique propagation considering the ionospheric medium. Using the QP model, the ground distance and group path distance can be evaluated between different Tx-Rx's pair for a specific elevation angle (β) from the Tx and operating frequency ( ) by the formulae provided in [8]. The group path is obtained by multiplying the signal transmission time with the speed of light.…”

“…where is the electron density having a maximum value at a maximum distance of , is the radial distance from the Earth's centre being equal to the sum of the Earth's radius and the height at which reflection occurs in the ionosphere, is the value of at the base of the layer and is the layer's semi-thickness [8]. The QP model of the ionosphere is a monolayer model providing ray path parameters considering reflection only from a specific layer in the ionosphere.…”

“…HF communication in the span of 2000 km is possible using a single hop mode. Further, to take into account the variable density of electrons in the ionosphere, a QP model of the ionosphere [8] is used. This model provides realistic group path lengths from which corresponding time delays are evaluated.…”

Analytic ray parameters for the quasi‐cubic segment model of the ionosphere

“…The ionosphere is considered to be isotropic and spherically stratified, and thus the ray path will be symmetric about its reflection point. Then the ground range R, group path P•, and phase path P can be written as [e.g., Croft and Hoogasian, 1968] …”