Ionosphere effects on navigational and positioning signals full-wave solutions

Full-wave, numerical, and analytical solutions are obtained for navigational signals reflected or transmitted through an inhomogeneous anisotropic layer such as the ionosphere. The transfer functions used in these solutions are obtained by using a nonsingular transformation matrix to convert Maxwell's equations (for the transverse electromagnetic field components) into a set of loosely coupled first-order differential equations for the forward and backward traveling ordinary and extraordinary wave amplitudes. These transformation matrices which are also suitable for critical coupling regions (characterized by strong reflections or coupling between the ordinary and extraordinary waves) are constructed through the use of generalized characteristic vectors. Analytical and numerical techniques are used to obtain the signal distortions and instantaneous phase anomalies due to the medium. These are used to determine the time of the third zero crossing, which is generally regarded as the effective arrival time of the signal.