Refraction compensation in a spherically stratified ionosphere

For satellite orbit determinations, it is necessary to know the range to the satellite with great accuracy. The presence of the ionosphere with a frequency-dependent index of refraction produces errors in range measurements made by either CW (Doppler) or pulse radio techniques. A measurement scheme is proposed that gives the instantaneously-corrected range for a spherically stratified ionosphere without recourse to any further assumptions about the electron density profile. The corrected range is given by the average of the CW and pulse range measurements and is free of the first-order error contributed by the inverse frequency-squared term in the refractive index. This scheme is shown to be slightly more effective than a scheme combining the results of two CW range measurements. Expressions are also derived for the higher-order residual errors which remain after the proposed compensation, and the expressions for the variation in arrival angle with frequency are given. These expressions depend upon the integrated effect of the free electrons; consequently, a calculation with a simple profile should yield typical results. The compensated range error and the residual errors are given for a satellite at a height of 640 km, arrival angles in the first quadrant, and at a frequency of 100 Mc. This compensation scheme cancels all but a few per cent of the original range error.