Numerical modeling and analysis of GNSS carrier-phase diffraction error in occlusion environments

In urban canyons or natural valleys, diffraction effect occurs when the signal of Global Navigation Satellite Systems (GNSS) transmits to the edge of obstructions, such as buildings, trees, and slopes, resulting in large diffraction error, which is one of the important error sources in carrier-phase-based precise positioning. However, the theoretical formula derivation and numerical modeling of the diffraction error have been rarely studied. In this study, we derived the theoretical formula of the diffraction error based on the geometrical structure of the signal propagation path in satellite-obstruction-antenna geometry. Then, the diffraction error extraction and modeling method were proposed to study the time-varying characteristics of diffraction error and verify the validity of the theoretical formula of the diffraction error. Based on the GNSS data collected in occlusion environment, a designed experiment was carried out. The results show that the diffraction error generally increases or decreases monotonically, and mostly the amplitude of it could be larger than 50 mm and even reach 200 mm. The time-varying characteristics of diffraction error can be precisely simulated with the vertical and horizontal diffraction formulas developed, and the diffraction error model established could be applied in sidereal filtering method to correct the diffraction error. From the experiment, the fixed rate of ambiguity resolution can be improved from 76.8 to 98.87%, and the positioning reliability is improved from 80 to over 98% with the diffraction correction. The results of this paper provided theoretical basis and experience for the processing of GNSS diffraction error and show the significance in applications of high-precision positioning.