Refining ionospheric delay modeling for undifferenced and uncombined GNSS data processing

Abstract

To access the full capabilities of multi-frequency signals from the modernized GPS, GLONASS and newly deployed BDS, Galileo, the undifferenced and uncombined observable model in which the individual signal of each frequency is treated as independent observable has drawn increasing interest in GNSS community. The ionosphere delay is the major issue in the undifferenced and uncombined observable model. Though several ionosphere delay parameterization approaches have been promoted, we argue that the functional model with only deterministic characteristic may not follow the irregular spatial and temporal variations. On the contrary, when the ionosphere delay is estimated as random walk or even white noise with only stochastic characteristic, the ionosphere terms turn out to be non-estimable or not sensitive to their absolute value. In the authors’ previous study, we have developed the deterministic plus stochastic ionosphere model, denoted as DESIGN, in which the deterministic part expressed with second-order polynomial is estimated as piece-wise constant over 5 min and the stochastic part is estimated as random walk with constrains derived based on statistics of 4 weeks data in 2010. In this contribution, we further model the deterministic part with Fourier series and update the variogram of the stochastic part accordingly based on two-year data collected by about 150 stations. From the statistic studies, it is concluded that the main frequency components are identical for different coefficients, different stations, as well as different ionosphere activity status, but with varying amplitude. Thus, in the Fourier series expression of the deterministic part, we fix the frequency and estimate the amplitude as daily constant unknowns. Concerning the stochastic component, the variation of variogram is both, geomagnetic latitude and ionosphere activity status dependent. Thus, we use the Gaussian function and Epstein function to model the variation of geomagnetic latitude and ionosphere activity status, respectively. Based on the undifferenced and uncombined observable model with ionosphere constrained with DESIGN, both dual-frequency and single-frequency PPP are carried out to demonstrate its efficiency with three-month data collected in 2010, 2014, and 2017 with different ionosphere activity status. The experimental results suggest that compared with ionosphere-free model and our previous method, the averaged 3D improvement of our new method is 17.8 and 7.6% for dual-frequency PPP, respectively. While for single-frequency PPP, the averaged 3D improvement is 37.0 and 14%, respectively.