An improved phase-smoothed-code algorithm using GNSS dual-frequency carrier epoch-difference geometry-free combination observations

The Hatch filter has been widely used in global navigation satellite system (GNSS) single point positioning (SPP). However, the classic phase-smoothed-code (PSC) method is vulnerable to ionospheric cumulative errors, resulting in filter divergence and accuracy degrada-tion in the positioning solution. In this paper, an improved method, i.e, phase epoch-difference geometry-free (GF) combination smoothed code (PESC), is proposed for SPP with raw GNSS measurements. In other words, the dual-frequency carrier-phase observa-tions are used to form epoch-difference GF combinations to obtain the precise between-epoch variations of ionospheric delays. Then, the ionospheric delays of code observations during a continuous satellite arc are converted to the initial epoch's value. Subsequently, the initial epoch's ionospheric delay of each arc, setting as a constant value, is estimated along with other parameters through the Kalman filter. GNSS measurements from 20 globally distributed stations from multi-GNSS experiment (MGEX) network on July 7 2021 are selected to validate the feasibility of the new algorithm. Results indicate that the average root mean square (RMS) of PESC-SPP errors is 0.404 m, 0.340 m, and 1.491 m in east (E), north (N), and Up (U) components, respectively, with the improvement of 30.5%, 50.5%, 52.1% and 36.5%, 55.1%, 54.3% in comparison with that of PSC-SPP and SPP, respectively. Data collected in the kinematic experiment on 28th November 2021 is used to evaluate the PESC positioning performance. Results demonstrate that the deviations of epoch-difference slant total electron content (STEC) derived from the PESC-SPP are much smoother and more stable than those of PSC-SPP during continuous satellite arcs, with the average RMS improvements of 33.5%, 66.9%, and 32.9% for GPS, Galileo, and BDS satel-lites, respectively. The PESC positioning solutions can converge after a few minutes, and the RMS of PESC-SPP errors is 0.779 m, 0.609 m, and 2.060 m in E/N/U components, which is 32.2%, 24.1%, 32.0%, and 27.8%, 18.2%, 16.5% lower than that of SPP and PSC-SPP results, respectively.(c) 2022 COSPAR. Published by Elsevier B.V. All rights reserved.