Combined Effects of Geometric Rotation and Antenna Calibration Patterns on GNSS Phase Windup

This article examines global navigation satellite system (GNSS) phase windup, which we define to be the combined effects of 3-D rotation and antenna phase patterns on carrier-phase measurements. Specifically, phase windup equations are presented for antennae with spatially varying phase patterns, for instance, phase patterns defined as a function of the satellite line-of-sight direction, as might be characterized by azimuth and zenith angles. We observe that a description both of the geometric rotation and, also, of the antenna phase pattern are needed to accurately evaluate phase windup for a general antenna. Furthermore, we show that there is not a unique approach for computing phase windup; in fact, correctly computing phase windup requires adjusting the model to match the calibration method used to obtain the antenna phase pattern.