Integer ambiguity resolution at a single station is prevented by the non-integer phase biases which cannot be separated from undifferenced integer ambiguities in a least squares adjustment. One method to estimate such phase biases is to average the fractional parts of all pertinent ambiguity estimates to determine the fractional phase biases, and the other is to assimilate the narrow-lane fractional parts into satellite clocks by fixing undifferenced ambiguities to integers in advance. While these two approaches have been well achieved for GPS, the phase bias estimation for GLONASS is difficult because 1) satellites do not share the same frequencies as a result of FDMA (Frequency Division Multiple Access) signals; 2) and even worse, pseudorange hardware biases of receivers vary in an irregular manner with manufacturers, antennas, domes, firmware, etc. which especially complicates GLONASS PPP-AR over inhomogeneous receivers. We hence propose a general approach where external ionosphere products are introduced into GLONASS PPP to estimate precise phase biases that are less impaired by pseudorange hardware biases of diverse receivers to enable PPP-AR. However, each GNSS asks for its own reference satellite to form resolvable ambiguities, namely intra-system PPP-AR. We further propose to estimate station-specific inter-system phase biases (ISPBs) and then form resolvable ambiguities between, instead of within, GNSS (i.e., inter-system PPP-AR) aiming at providing one more ambiguity candidate for more efficient partial AR.

Fig. 1 Geographical distribution of the station-specific RMS for the phase-bias-based method minus that for the integer-clock-based method. An RMS is computed over the residuals of ambiguity-fixed position estimates against the IGS weekly solutions for the East component over one year. This figure shows that the two PPP-AR approaches can generally produce similar results while the largest differences appear over remote regions such as oceans

Fig. 2 Distribution of the GLONASS wide-lane fractional parts after removal of phase biases at 105 BIGF stations equipped with LEICA GRX1200+GNSS receivers. The top six panels show the fractional parts for six exemplary satellites R01, R07, R15, R22, R23 and R24 with respect to R08 on day 152 without (in black) and with (in red) global ionosphere maps. The bottom three panels show the distribution of fractional parts of all GLONASS or GPS satellites over the 30 days. This figure shows that GLONASS phase biases can be separated by introducing external ionosphere constraints.

Fig. 3 Time series of differential wide-lane and narrow-lane daily inter-system phase biases (ISPBs), and the fractional parts of inter-GPS/BeiDou double-difference ambiguities after removal of ISPBs on all 24 days. Six station pairs are presented representing baselines with identical or mixed receivers. Station codes are displayed at the bottom of the left panels while receiver types shown at the top left corners and the mean (b_m and b_n) along with the standard deviations (cycles) of ISPBs shown at the top right corners. Here ISPBs are plotted after removal of the mean. Correspondingly, the fractional parts of double-difference ambiguities after removal of these ISPBs are shown in the right panels with the standard deviations and the percentages of those falling within ± 0.15~cycles exhibited at the top part of each panel. Note that the standard deviations (b_m and b_n) for CHKH--QXGZ are calculated after eliminating the jumps on day 70. Gaps are due to GNSS observation loss. This figure shows that ISPBs can be stable over a long time and thus can be extracted to enable inter-system PPP-AR. 

Related Works

1. Geng J*, Meng X, Dodson AH, Teferle FN (2010) Integer ambiguity resolution in precise point positioning: Method comparison. J. Geod.,  84(9):569-581

2. Geng J*, Bock Y (2016) GLONASS fractional-cycle bias estimation across inhomogeneous receivers for PPP ambiguity resolution. J. Geod. 90(4):379-396, doi:10.1007/s00190-015-0879-0

3. Geng J*, Li X, Zhao Q, Li G (2018) Inter-system PPP ambiguity resolution between GPS and BeiDou for rapid initialization. J. Geod. 93(3):383-398. doi: 10.1007/s00190-018-1167-6