Integer ambiguity resolution considerable improves the performance of precise point positioning (PPP). With the popularity of multi-frequency observations, multi-frequency PPP ambiguity resolution (PPP-AR) for GPS, BDS and Galileo has been well studied, whereas there is a lack of research on GLONASS triple-frequency PPP-AR. Fortunately, GLONASS currently transmits CDMA signals on the third frequency of two GLONASS-K and four GLONASS-M + satellites, making it possible to investigate the triple-frequency PPP-AR. To fully exploit GLONASS triple-frequency observation, this study proposes a CDMA + FMDA combined multi-frequency PPP-AR model with the careful consideration of GLONASS phase inter-frequency clock bias (IFCB) errors. The characteristics of GLONASS IFCBs and EWL UPDs are also well investigated. To verify our proposed model, tracking data of 14 stations is used to estimate uncalibrated phase delay (UPD) and another 6 stations are selected as users to perform PPP-AR. A time- and satellite-dependent IFCB of about 0.2 ~ 0.5 m is identified for GLONASS-M + triple-frequency observations. After the removal of the IFCB, the EWL, WL and NL UPDs of GLONASS satellites show remarkable stabilities at several hours. About 99.9% EWL, 98.7% WL and 99.4% NL residuals are within 0.15 cycles, which shows comparable accuracy compared with GPS. Based on the precise UPD products, GLONASS triple-frequency PPP-AR can be achieved. Compared with PPP float estimates, GLONASS triple-frequency PPP-AR improves the convergence time and 1-hourly positioning errors in the E, N and U directions from 14.5 min and [4.6 20.7 39.9] mm to 11.5 min and [3.1 4.6 14.1] mm, with an improvement of about 20.7% and [32.6% 77.8% 64.7%], respectively. However, limited by the number of datasets under current conditions, GLONASS triple-frequency PPP-AR exhibits insignificant improvement compared with the dual-frequency solution. After integrating GPS triple-frequency observations, results indicate that GLONASS + GPS triple-frequency PPP-AR exhibits significantly better positioning performance than the dual-frequency solution.
Integer ambiguity resolution considerable improves the performance of precise point positioning (PPP). With the popularity of multi-frequency observations, multi-frequency PPP ambiguity resolution (PPP-AR) for GPS, BDS and Galileo has been well studied, whereas there is a lack of research on GLONASS triple-frequency PPP-AR. Fortunately, GLONASS currently transmits CDMA signals on the third frequency of two GLONASS-K and four GLONASS-M + satellites, making it possible to investigate the triple-frequency PPP-AR. To fully exploit GLONASS triple-frequency observation, this study proposes a CDMA + FMDA combined multi-frequency PPP-AR model with the careful consideration of GLONASS phase inter-frequency clock bias (IFCB) errors. The characteristics of GLONASS IFCBs and EWL UPDs are also well investigated. To verify our proposed model, tracking data of 14 stations is used to estimate uncalibrated phase delay (UPD) and another 6 stations are selected as users to perform PPP-AR. A time- and satellite-dependent IFCB of about 0.2 ~ 0.5 m is identified for GLONASS-M + triple-frequency observations. After the removal of the IFCB, the EWL, WL and NL UPDs of GLONASS satellites show remarkable stabilities at several hours. About 99.9% EWL, 98.7% WL and 99.4% NL residuals are within 0.15 cycles, which shows comparable accuracy compared with GPS. Based on the precise UPD products, GLONASS triple-frequency PPP-AR can be achieved. Compared with PPP float estimates, GLONASS triple-frequency PPP-AR improves the convergence time and 1-hourly positioning errors in the E, N and U directions from 14.5 min and [4.6 20.7 39.9] mm to 11.5 min and [3.1 4.6 14.1] mm, with an improvement of about 20.7% and [32.6% 77.8% 64.7%], respectively. However, limited by the number of datasets under current conditions, GLONASS triple-frequency PPP-AR exhibits insignificant improvement compared with the dual-frequency solution. After integrating GPS triple-frequency observations, results indicate that GLONASS + GPS triple-frequency PPP-AR exhibits significantly better positioning performance than the dual-frequency solution.