Multi-constellation and multi-frequency precise point positioning with fast ambiguity resolution on a global scale

To achieve global fast centimeter-level precise point positioning (PPP), ambiguity resolution (AR) is a prereq-uisite. We extended the PPP cascading AR method (PPP-CAR) to the GPS, Galileo, BDS-2, and BDS-3 all -fre-quency signals, in which more wide-lane (WL) ambiguities were fixed instantaneously to accelerate the narrow -lane (NL) AR. The performances of the multi-frequency PPP-CARs on a global scale were investigated in terms of the time to first fix (TTFF) of the NL ambiguities and convergence time (CT). The test results indicated that the TTFF and CT decreased significantly with increasing frequencies. The dual-frequency PPP-CAR achieved an average TTFF and CT of 9.4 and 7.8 min, respectively. The average TTFFs and CTs reached 7.6, 6.1, and 5.6 min, respectively, and 6.0, 4.4, and 4.3 min, respectively, for the triple-frequency, quad-frequency, and five-frequency PPP-CARs, with improvements of 19.1%, 35.1%, and 40.4%, respectively, and 23.1%, 43.6%, and 44.9%, respectively, compared to the dual-frequency PPP-CAR.