312 / 2023-10-13 09:59:46

Pivot-receiver-dependent PPP-RTK user positioning performance relieved by network integer ambiguity resolution

PPP-RTK; Pivot receiver dependency; Network integer ambiguity resolution; Global navigation satellite system (GNSS); Homogenous positioning performance

PPP-RTK, a synthesis of precise point positioning (PPP) and real-time kinematic (RTK) techniques, achieves fast integer ambiguity resolution-enabled positioning using, among others, the satellite clocks, biases, and ionospheric corrections generated in a reference network. When formulating a network model to estimate these products, one usually considers a receiver as the pivot and selects its receiver-related parameters as the datum to address the rank deficiency problem. As a result, the estimable satellite clocks absorb the pivot receiver clock error, and the estimable satellite phase biases absorb the code biases, phase biases, and ambiguities of the pivot receiver. Moreover, the estimable ionospheric delays absorb the code biases of the pivot receiver if one formulates the ionosphere-weighted model in regional networks. Hence, the estimable network products relate to the selected pivot receiver. With these clearly defined products estimated on the network side, users can properly correct their observation errors and formulate a full-rank user model for precise positioning.



In addition to the definition of network products, users also wonder how precise the products are. In this work, we demonstrate that the precision of ambiguity-float combined PPP-RTK products relates to the pivot receiver selection. The combined product encompasses the summation of satellite clocks, satellite phase biases, and ionospheric delays at a certain station. Specifically, we find that the precision of ambiguity-float combined products at the pivot receiver surpasses that at non-pivot receivers by a significant margin. Consequently, user positioning becomes inhomogeneous in the network, as users far away from the pivot receiver perform worse than those close to the pivot receiver. To relieve this pivot receiver dependency, we emphasize the necessity of network integer ambiguity resolution, which improves the precision of products and ensures the homogeneity of user positioning. For verification purposes, we performed a one-week experiment involving 12 global positioning system (GPS) receivers to generate network products and 23 receivers to perform user positioning. The results showed that the precision of ambiguity-float combined products at the pivot receiver was better than 2 cm, whereas that at non-pivot receivers reached several decimeters. With these ambiguity-float products employed on the user side, the time-to-first-fix (TTFF) of the positioning near the pivot receiver was less than 5 epochs, but that away from the pivot receiver exceeded 15 epochs. Network integer ambiguity resolution improved the quality of PPP-RTK products, as the precision of combined products at an arbitrary receiver reached several millimeters. User positioning with ambiguity-fixed products became homogeneous with an average three-dimensional root-mean-square (3D RMS) of 1.5 cm, and the mean TTFF decreased to 4 epochs.