Positioning with two satellites and known receiver clock, barometric pressure and radar elevation

Abstract

We investigate the feasibility of completing an aircraft precision approach using two global navigation satellite systems (GNSS) satellites from different constellations in combination with a stable frequency reference (SFR), barometric height and a radar altimeter. Before the start of two-satellite positioning, a full GNSS solution is used to calibrate the SFR and the vertical solution relative to the aircraft touchdown point. The theoretical clock and position error covariance is derived as a function of measurement error, satellite geometry, SFR stability, barometric height and radar altimeter performance. Detailed error models for each of the navigation sensors are developed for the covariance analysis. This is followed by both simulations and evaluations using flight test data to verify the positioning accuracy and the feasibility of completing an aircraft precision approach with only two satellites from different constellations. With respect to category I precision approach requirements of 16 m (95 %) horizontal and 4 m (95 %) vertical, the horizontal 95 % positioning performance is approximately 6 m, while the vertical 95 % positioning performance is approximately 4 m.