Ionosphere Ray-Tracing of RF Signals and Solution Sensitivities to Model Parameters

摘要

Methods are developed to determine the refracted propagation paths of high-frequency RF signals in the ionosphere and to determine the sensitivities of these paths to changes of the input model parameters. These techniques are being developed to support the assimilation of data from mono-static and multi-static ionosondes with the goal of improving parameterized estimates of ionosphere electron density profiles. An additional application area is that of navigation using signals from a ground-based network of high-frequency beacons. A nonlinear two-point boundary value problem solver is developed using the shooting method with Newton updates. Robust convergence is achieved by seeding the algorithm with carefully designed first guesses of the wave vector's initial aiming angles and terminal group delay. Partial derivative sensitivities of the ray-path solution are calculated using the adjoint of the two-point boundary value problem. This approach speeds the calculations when the partial derivatives of many ionosphere model parameters need to be computed. The new algorithm has been applied successfully to determine the paths of O-mode and X-mode radio waves between known transmitter and receiver locations and to spitze reflection points. Spitze singularities pose no difficulties for the new algorithm because it uses a Hamiltonian ray-path formulation that remains non-singular at a spitze.