SIMPLE ANALYTICAL FUNCTIONS WHICH PROVIDE MAGNITUDES OF RANGE AND ANGLE ERRORS FOR PROPAGATION IN AN EXPONENTIAL ATMOSPHERE

Abstract

Abstract : The calculation of range and angle errors has been attempted by integrating the ray equations along the slant path and assuming an exponentially decreasing index of refraction with height. These equations are represented by error functions which are not simple analytical solutions. There is a further difficulty in relating the true elevation angle to the apparent elevation angle. The following paper shows how these equations may be modified to provide simple analytical functions. In the process the functions permit a range and apparent elevation angle term to be included which not only correct for the approximate solution at small angles but also generate functions which remain continuous through zero elevation angle. A comparison with ray-tracing calculations demonstrates that these functions can be used to compute meaningful magnitudes of range, elevation angle and doppler velocity errors.