Denoising ionospheric observables based on multipath error modelling with Tikhonov regularization

Abstract

Multipath errors, as one of the manifest unmodelled error types introduced by code measurements, are absorbed in ionospheric observables, which results in ionospheric pollution. In this work, in order to cancel out random noise by an adjustment algorithm, the modelling of multipath errors derived from code measurement residuals in undifferentiated and uncombined precise point position (PPP) mode is realized by solving a regularization problem, in which Tikhonov regularization (i.e. the first order difference) is taken into account. Furthermore, the Thomas update algorithm is employed to find the solution and a bootstrap method is used to determine the optimal regularization parameter. After the multipath error model was constructed, it was used to extract the ionospheric observables, thereby enabling the correction of the code measurements. In this research, three ionosphere-retrieval schemes were designed, namely the the alignment of the carrier phase to the code (1) before and (2) after the multipath errors were corrected (CCBM and CCAM), and (3) a PPP solution (PPPS). Based on colocation experiments, the effects of removing errors arising from the multipath effect on the code were comparatively assessed. Large differences were found between the three schemes when used in a short-baseline experimental setting, but only small differences were found with a zero-baseline setup. In the short-baseline experiment, CCAM was more reliable than CCBM, with an improvement in accuracy of about 50%, and reached close agreement with PPPS. In addition, 14 continuously operating reference stations in Hong Kong were selected for ionosphere modelling with differential code bias (DCB) estimations. Similar results were seen, as follows: (1) compared with CCBM, CCAM and PPPS had better modelling accuracies, with an improvement of 60%; (2) CCAM and PPPS had better performance at five fitting stations with respect to CCBM, which resulted in improvements in the accuracies ranging from 60% to 80%; (3) taking five-day-average values of the satellite DCBs, the difference between Center for OrbitDetermination in Europe (CODE) and CCAM was around 0.5 ns, which is consistent with the difference between CODE and PPPS, but about a 2 ns difference was verified between CODE and CCBM.