Effect of horizontal gradients on ionospherically reflected or transionospheric paths using a precise homing-in method

A homing-in method is presented for determining ionospheric reflected or tr ansionospheric paths between fixed transmitter and receiver locations in th e presence of ionospheric gradients or ripples. Both initial elevation and azimuth are automatically adjusted to find the path that arrives exactly at the receiver. The method can be used for any 3D ionospheric model to find precise ray paths and phase and group delays for both magneto-ionic modes. The method takes full account of path location, geomagnetic field orientati on and the bending of the ray path resulting from horizontal as well as ver tical gradients of electron density. It can also find multiple paths e.g. l ow and high angle, 1- and 2-hops for both ordinary and extraordinary modes. Examples of its use are given for both terrestrial HF links and Earth to S atellite paths. For paths reflected from the ionosphere, the effect of grad ients of both critical frequency and height of maximum electron density are determined and the comparative effect of gradients on high and low angle a nd 1- and 2-hops paths for both magneto-ionic modes investigated. Path vari ation with frequency for a fixed link is also studied and the bandwidth of the ionospheric background channel (dispersive bandwidth) and its reciproca l (the pulse rise time), important for wideband digital HF broadcasting or spread spectrum HF communications, is estimated for a range of frequencies, for high- and low-angle rays and 1- and 2-hop paths. For Earth-satellite p aths, the effect of the ionosphere and horizontal ionospheric gradients is determined for a range of frequencies and elevation angles. It is shown tha t the method can also enable the determination of second-order errors in sa tellite navigation methods, such as GPS, due to ionospheric gradients and t he effect of the geomagnetic field. (C) 2000 Elsevier Science Ltd. Ail righ ts reserved.