Ray-tracing options to mitigate the neutral atmosphere delay in GPS
Abstract
As the radio signals emanating from GPS satellites propagate through the Earth’s electrically neutral (i.e., un-ionized) atmosphere, they suffer refraction. The effect of refraction on GPS timing measurements is a delay compared to what would be measured had the signal propagated in a vacuum. Equivalently, assuming vacuum speed of propagation, refraction makes the apparent distance measured with GPS larger than the geometric distance between receiver and satellite. If not adequately mitigated, that delay corrupts estimates, such as receiver position, obtained from GPS observations. One way of quantifying the neutral atmosphere radio propagation delay is supposing the signal to be a ray, and tracing that ray along its path, from satellite to receiver, through a model for the atmosphere; we call such a procedure ray-tracing, and it constitutes our main interest in this work. Raytracing has connections to many different subject areas. Among those, we see the present work falling under the umbrella of geodesy. More specifically, we see it situated along the thread of developments of the so-called mapping functions for radio space geodetic applications.
The main research contribution from this work is the identification, classification, and comparison of alternative models for the ray-path and the atmospheric structure employed in ray-tracing. It is a three-part contribution, parts that we now discuss. First we distinguished among the ray-tracing options known as atmospheric source, atmospheric structure, and ray-path model. Such distinction classifies the myriad of options available in ray-tracing in separate groups, disentangling aspects that are typically (sometimes arguably conveniently) lumped together. For example, a sentence such as “this ray-tracer assumes spherical symmetry” actually makes separate statements about the assumed raypath and the atmospheric structure models. Secondly, we identified model alternatives within each of the three options above, namely, spherical concentric, spherical osculating, ellipsoidal, gradient, and 3d atmospheric structures; and zenith, straight-line, bent-2d, and bent-3d ray-path models. Thirdly, we compare experimentally different models. More specifically, we quantified the discrepancy in delay between different models and we also assessed their impact in GPS positioning. In addition to the three-part main contribution above, a secondary contribution is a classification of the delay mitigation techniques available in GPS, developed to support the design of the GPS experiments.
The findings of this work are as follows. (i) Regarding the ray-path, the bent-2d model, albeit not strictly valid in a 3d atmosphere, introduces only negligible errors, compared to the more rigorous bent-3d model (in a 15km horizontal resolution atmospheric model). Regarding atmospheric structures, we found that (ii) the oblateness of the Earth cannot be neglected when it comes to predicting the neutral atmosphere delay, as demonstrated by the poor results of a spherical concentric atmosphere; (iii) the spherical osculating model is the only one exhibiting azimuthal symmetry; (iv) the oblateness of the Earth is adequately accounted for by a spherical osculating model, as demonstrated by the small discrepancy between a spherical osculating and a more rigorous ellipsoidal model; (v) a gradient atmosphere helps in accounting for the main trend in azimuthal asymmetry exhibited by a 3d atmosphere, but there remains secondary directions of azimuthal asymmetry that only a full 3d atmosphere is able to capture. Furthermore, (vi) we found experimental evidence confirming the theoretical expectation that gradient and especially 3d atmospheric structures offer promising benefits for GPS positioning. Finally, beyond the comparison of atmospheric
structures above, an interesting side conclusion regarding atmospheric sources was that (vii) atmospheric models of higher resolution might offer significant improvements in mapping functions.