Effectiveness of L1-norm regularization sidereal filtering for precise point positioning

Integer ambiguity resolution is critical for achieving positions of high precision and reliability of precise point positioning (PPP). However, as an important error source in global navigation satellite system (GNSS), multipath interference limits the ability of PPP in high-accuracy GNSS positioning applications. Thus, to guarantee the performance of PPP ambiguity resolution techniques in a multipath environment, a sidereal filtering technique based on sparsity promoting regularization is adopted to mitigate the multipath error. The key idea of the proposed strategy emphasizes the use of the L1 norm to extract multipath from noisy carrier phase residuals. The classical single-difference between-satellites method is used to fix PPP with the estimated phase clocks/bias products for obtaining carrier phase residuals in the previous period. Two GPS datasets are adopted to assess the denoising effect of the multipath model and the performance of the proposed strategy. The carrier phase residuals of static PPP ambiguity resolution and the positioning accuracy of kinematic float PPP after the application of the multipath model are used to reflect the final filtering performance. Results show that the multipath model based on first-order regularization can improve the RMS of carrier phase residuals by approximately 49.8% compared with the solution without multipath mitigation. In kinematic float PPP, a mean coordinate improvement of 49.7% for day of year (DOY) 273 and 57.8% for DOY 275 in 2017 could be achieved.