Abstract
The single-receiver integer ambiguity resolution-enabled variant of precise point positioning (PPP), namely PPP-RTK, has proven to be crucial in reducing the long convergence time of PPP solutions through the recovery of the integerness of the user-ambiguities. The proliferation of global navigation satellite systems (GNSS) supports various improvements in this regard through the availability of more satellites and frequencies. The increased availability of the Galileo E6 signal from GNSS receivers paves the way for speeding up integer ambiguity resolution, as more frequencies provide for a stronger model. In this contribution, the Galileo-based PPP-RTK ambiguity resolution and positioning convergence capabilities are studied and numerically demonstrated as a function of the number and spacing of frequencies, aiming to shed light on which frequencies should be used to obtain optimal performance. Through a formal analysis, we provide insight into the pivotal role of frequency separation in ambiguity resolution. Using real Galileo data on up to five frequencies and our estimated PPP-RTK corrections, representative kinematic user convergence results with partial ambiguity resolution are presented and discussed. Compared to the achieved performance of dual-frequency fixed solutions, it is found that the contribution of multi-frequency observations is significant and largely driven by frequency separation. When using all five available frequencies, it is shown that the kinematic user can achieve a sub-decimeter level convergence in 15.0 min (90% percentile). In our analysis, we also show to what extent the provision of the estimable satellite code biases as standard PPP-RTK corrections accelerates convergence. Finally, we numerically demonstrate that, when integrated with GPS, the kinematic user solution achieves convergence in 3.0 and 5.0 min on average and at 90%, respectively, in the presence of ionospheric delays, thereby indicating the single-receiver user’s fast-convergence capabilities.
Highlights
Integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is the global navigation satellite systems (GNSS) positioning mode that offers ambiguity-resolved parameter solutions on the basis of a single receiver
To obtain an understanding of the impact of the number and spacing of frequencies in standalone Galileo ambiguity resolution and an insight into the real data results presented we formally analyze the user’s ambiguity resolution performance
It is worth mentioning here that we focused on Galileo and its existing frequencies in our formal analysis, the concept and results discussed above are generally applicable to any GNSS system and can serve to show the achievable gain after ambiguity resolution when more than two frequencies are employed, e.g., with BeiDou-3 multi-frequency data
Summary
Integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is the global navigation satellite systems (GNSS) positioning mode that offers ambiguity-resolved parameter solutions on the basis of a single receiver. In the presence of ionospheric delays, fast and reliable ambiguity resolution with a single-GNSS dual-frequency model is known to be hindered, due to its inherent weakness in the sense of its IAR capabilities, and requires measurements over multiple epochs. This can be overcome, to a certain extent, with model strengthening by means of either using data from multiple systems and frequencies, or incorporating regional ionospheric corrections, or a combination thereof. The establishment of such dense networks, is not highly attractive because of the cost and complex operation requirements involved, and is difficult or even impossible in certain areas
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