On Modelling of Second-Order Ionospheric Delay for GPS Precise Point Positioning

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such technique is commonly known as Precise Point Positioning (PPP). A significant challenge of PPP, however, is that about 30 minutes or more is required to achieve centimetre to decimetre-level accuracy. This relatively long convergence time is a result of the un-modelled GPS residual errors. A major residual error component, which affects the convergence of PPP solution, is higher-order Ionospheric Delay (IONO). In this paper, we rigorously model the second-order IONO, which represents the bulk of higher-order IONO, for PPP applications. Firstly, raw GPS measurements from a global cluster of International GNSS Service (IGS) stations are corrected for the effect of second-order IONO. The corrected data sets are then used as input to the Bernese GPS software to estimate the precise orbit, satellite clock corrections, and Global Ionospheric Maps (GIMs). It is shown that the effect of second-order IONO on GPS satellite orbit ranges from 1.5 to 24.7 mm in radial, 2.7 to 18-6 mm in along-track, and 3.2 to 15.9 mm in cross-track directions, respectively. GPS satellite clock corrections, on the other hand, showed a difference of up to 0.067 ns. GIMs showed a difference up to 4.28 Total Electron Content Units (TECU) in the absolute sense and an improvement of about 11% in the Root Mean Square (RMS). The estimated precise orbit clock corrections have been used in all of our PPP trials. NRCan's GPSPace software was modified to accept the second-order ionospheric corrections. To examine the effect of the second-order IONO on the PPP solution, new data sets from several IGS stations were processed using the modified GPSPace software. It is shown that accounting for the second-order IONO improved the PPP solution convergence time by about 15% and improved the accuracy estimation by 3 mm.