Tropospheric refractive angle and range error corrections utilizing exoatmospheric sources

Abstract

Tropospheric refractive range and angle errors limit the performance of radar and navigation systems that operate at low elevation angles. For some locations and for many applications, antenna pointing corrections based on surface refractivity alone or, if necessary, a vertical refractivity profile are adequate. However, new systems that operate at very low elevation angles require improved accuracies. More accurate angle error corrections can be obtained by utilizing calibration sources (often referred to as ‘targets of opportunity’), such as the limb of the sun, radio sources, or satellites, the angular positions of which are precisely known. Since the angle error is dependent on the target distance, an expression for angle error as a function of target height is derived. Unfortunately, radio sources cannot be used for range calibration, and since the ranges of most satellites are not known to a sufficient accuracy, the range error correction is still a problem. It is shown in this paper that it is possible to develop a method for obtaining an improved range error correction by utilizing measured angle error data for the same ray path. An expression for the refractive angle error correction for a target based on the measured angle error of the calibration source is first derived; also the angular refraction is expressed as a function of the angle error. It is then shown that the range error correction for a target can be expressed as a function of the angular refraction and can thus be calculated from a set of angle error measurements, thereby providing an improved correction. In the formulation of this problem a time independent spherically stratified nonionized atmosphere with a monotonically decreasing index of refraction with altitude is adopted, so the solution is only valid at frequencies above which ionospheric effects are negligible and for atmospheres which do not have inversion layers in refractivity. Also, it is assumed that both the calibration source and target are above the troposphere.