Accurate determination of ionospheric effects on satellite‐based positioning systems in terms of residual range error

Abstract

Positioning systems using artificial satellites like Navsat or Navstar systems offer facilities for accurate three‐dimensional position fixes for both navigational and geodetic purposes. The signals from these satellites, when propagated through the ionosphere, are subjected to phase delay, refraction, and dispersion. The ionospheric effects consequently lead to some degree of uncertainty in the position determination. Various approximations have been made to the complex refractive index of the ionosphere in order to evaluate these uncertainties. The dual‐frequency compensation eliminates the first‐order ionospheric effects. The higher‐order terms in the refractive index and the bending of the optical path give rise to a residual range error (RRE). The complete Appleton‐Hartree formula for the refractive index without any approximation has been utilized in the investigation. Consequently, a three‐dimensional ray‐tracing program, modified to give ‘homing’ facilities, has been used to study the variation of the RRE with the angle of elevation. The computed RRE values for the Navsat system, operating on 150 MHz and 400 MHz, are compared with the results of earlier approximate methods. The effect of the magnetic field on the RRE has been evaluated for both the Navsat and the Navstar (GPS) systems. The magnetic field can be completely neglected in the Navstar system operating on 1200 MHz and 1600 MHz. The RRE has also been computed for various electron density profiles for a constant total electron content (TEC). The RRE can be obtained for all practical profiles by using a simple Chapman profile with the same TEC and almost the same slab thickness as the experimental profile. The accuracy in RRE obtained by using the simple Chapman profile is high enough for geodetic applications.