Weighting Strategy of Observations for Kinematic Multi-GNSS PPP/PPP-AR Using Residual Approach

The proper weighting of the carrier phase and code observations has the potential to improve the performance of multiple global navigation satellite system precise point positioning (PPP)/PPP-ambiguity resolution (AR); however, the traditional empirical method of weighting results in additional computational burden. The purpose of this study is to propose and evaluate a weighting strategy using a residual approach for a PPP filter that can estimate the actual observation error efficiently and accurately using only one calculation. Generally, in pseudo kinematic PPP using static observation data, the proposed weighting method improved the position accuracy by 7–43% in the float solutions and 4–7 % in fixed solutions in the up-down direction after the PPP/PPP-AR solutions converged. Additionally, the convergence time was confirmed to be shortened by 8–20 % in the float solutions and 9–13 % in the fixed solution in most cases by using the proposed weighting method. Next, in kinematic PPP using observation data from the gravity recovery and climate experiment (GRACE) satellites, the ratio of the number of fixed solutions was increased by more than 22.5 % for GRACE C and 18.2 % for GRACE D, and especially the position accuracy of PPP/PPP-AR corresponding to GRACE D was considerably improved by 46.3 % for float solutions and 61.9 % for fixed solutions. From these results, the proposed PPP filter residual approach was found to be a more accurate and efficient method to tune the standard deviation of unknown observation errors in comparison with that of the popularly used weighting method. The proposed weighting method can be used to improve the convergence time and position accuracy of low earth orbit satellites and PPP in unmanned aerial vehicle navigation, as well as low-cost antennas and receivers.