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

In city canyons or natural valleys, diffraction effect occurs when Global Navigation Satellite System (GNSS) signal approaches to the edge of buildings, trees and slopes etc., resulting in a large diffraction error, which is the dominant error source for the low ambiguity fixing rate (AFR), the reduction of positioning accuracy and the frequent gross error in real-time kinematic positioning and high precise static positioning. However, the theoretical formula derivation and the numerical modeling of the diffraction error has been rarely studied, and the diffraction error mostly processed with the multipath processing methods in present. Therefore, in this study, we derived the theoretical formula of the diffraction error based on ray-tracing, i.e., using satellite-reflector-antenna geometries to model the diffraction errors according to the theory of diffraction effect. After that, we estimated and extracted the realistic diffraction error from the GNSS data collected in high occlusion environments to study the time-varying characteristics of diffraction errors and the effectiveness of the diffraction numerical modeling formulas. The results show that the time-varying characteristics of diffraction error can be precisely simulated with the vertical and horizontal diffraction formulas proposed, and the diffraction error estimated with double-differencing (DD) model generally has a linear character of positive increasing or negative decreasing monotonously, and according to the sign of the error, we can identify which station the diffraction effect occurs at. The amplitude of the diffraction error could be larger than 50mm to 200mm, and even larger, which is extremely larger than the multipath effect. Large diffraction error usually corresponds to a low SNR, with less than 40 dB/Hz, and the differenced SNR of the reference station and the monitoring station is generally greater than 5 dB/Hz. Based on this, we proposed the diffraction error removal strategies with SNR mask and SNR differencing threshold between stations. The results of GNSS data processing in two groups of high-occlusion complex environments show that the SNR mask and SNR differencing strategies can effectively eliminate the influence of large diffraction errors. The single epoch AFR can achieve to more than 90%, and millimeter-level positioning accuracy can be realized in the real-time kinematic positioning mode. The SNR differencing strategy is more effective in practical monitoring applications. The numerical modeling formulas and conclusions in this study will have important practical applications in high-precision positioning area, such as IGS data processing, deformation monitoring and vehicle navigation, etc.