Ground-to-Air Tropospheric Mapping Function for Very Low Elevation Angles

Abstract

This paper proposes a real-time capable tropospheric delay model for terrestrial radio navigation systems used for aviation. Its functional scope ranges from elevation angles below the local horizon to zenith. Flight experiments were carried out to quantify the improvement in service coverage achieved for measurements close to and below the local horizon, with aircraft distances in the order of 250 km. Mismodeling tropospheric delays at these elevation angles and aircraft distances can result in slant-range error several order of magnitude greater than the accuracy of terrestrial nav-aids, and adequately accounting them translates into improved accuracy and tighter integrity bounds. The proposed method uses a polynomial representation of the atmospheric refractivity instead of the traditional exponential distribution used in GNSS. The resulting method provides tropospheric corrections accurate to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.5 cm for elevation angles above 5 degrees, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 15 cm at an elevation of 0.2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> . In addition, the proposed model offers a reduction in the horizontal position error in terms of an order of magnitude from 14 meters (for uncompensated tropospheric delay) to below 1.6 cm for all flight segments, that will enable terrestrial systems to support increasingly demanding performance based navigation systems.