Line-of-sight tropospheric calibration from measurements in arbitrary directions

Tropospheric inhomogeneities limit the accuracy with which a path delay in an arbitrary direction can be estimated from calibration measurements in different directions. This article demonstrates a mathematical procedure that has the potential for minimizing errors in the estimated geometrical and tropospheric path delays. The error is minimized by applying least-squares estimation to a combined set of observables in the calibration directions and the direction to be calibrated. A simulated test of this procedure was conducted using a model set of error-free calibration measurements. In the absence of geometrical delay mismodeling, the simulation yielded delay errors which vary from about 1 mm at zenith to about 1 cm at 10 degrees. The main principles of how this procedure could be applied to improve accuracy of deep space tracking using global positioning system (GPS) data are also discussed.