Undifferenced and Uncombined PPP Ambiguity Resolution Combined with GPS/GLONASS Triple-Frequency Observations

Objectives Currently, two global navigation satellite system （GLONASS）-K1 and four GLONASS-M+ satellites transmit code division multiple access (CDMA) signals on the third frequency in addition to the traditional frequency division multiple access (FDMA) signals on the first two frequencies, making it possible for GLONASS joint use of FDMA and CDMA signals for precise point positioning (PPP). To follow with the trend of multi-frequency and multi-system, GPS+GLONASS triple-frequency uncombined PPP ambiguity resolution (AR) model is investigated.

Methods First, a GPS+GLONASS triple-frequency uncombined PPP model considering the inter-frequency clock bias (IFCB) of GPS and GLONASS systems is presented. Then we present the triple-frequency uncalibrated phase delay (UPD) estimation method and PPP-AR algorithm. However, limited to the number of GLONASS triple-frequency observations and its distribution, we combine GPS and GLONASS triple-frequency observations for PPP-AR, but only fix GPS triple-frequency ambiguities, while GLONASS ambiguity maintains its floating-point form. The IFCB and UPD products are estimated by more than 300 multi-GNSS experiment (MGEX) stations distributed around the world, and another 14 MGEX stations are used to evaluate PPP-AR performance.

Results Experimental results demonstrate that the best positioning performance has been achieved by our algorithm. Compared with GPS triple-frequency PPP-AR, the positioning accuracies of the static experiments in the east, north, up and 3D directions are improved by 80.7%, 60.0%, 61.0% and 63.8% respectively, and that of the simulated dynamic experiments are improved by 41.9%, 14.5%, 11.6% and 16.3%. However, if GLONASS IFCB errors are ignored, the stability of the convergence series of the combined triple-frequency PPP-AR will be harmed, causing the positioning performance even inferior to GPS single system. Moreover, our algorithm achieves rapid ambiguity resolutions. The average time to first fix time of static and simulated dynamic experiments of our model is about 12.3 and 12.9 min respectively, which is significantly improved compared with GPS, in which the improvement of the simulated dynamic experiment is 53.8%. Besides, compared with the scheme of combining GPS triple-frequency observations and GLONASS dual-frequency observations, after integrating GLONASS CDMA observations, the stability of the positioning time series of the simulated dynamic experiments is effectively improved, and the root mean square value of positioning errors in each direction can be reduced.

Conclusions These results demonstrate that the best positioning performance can be achieved by the proposed GPS+GLONASS triple-frequency PPP-AR. Moreover, GLONASS IFCB errors must be carefully investigated and calibrated beforehand. However, limited by the number of GLONASS CDMA datasets and other factors, it is difficult to perform GLONASS triple-frequency PPP-AR with FDMA and CDMA signals currently. In the future work, we will focus on the investigation of GLONASS triple-frequency PPP-AR.