PPP-RTK: from common-view to all-in-view GNSS networks

Integer ambiguity resolution-enabled precise point positioning (PPP), otherwise known as PPP real-time kinematic (PPP-RTK), recovers the integer nature of ambiguities at a user receiver by delivering the satellite phase biases (SPBs) estimated from a global navigation satellite system (GNSS) network. Due to the rank-deficiency existing between the satellite and receiver phase biases and the ambiguities, the formulation of PPP-RTK model needs to choose a set of unknown parameters as the datum (or the S-basis). Despite the fact that there are non-unique datum choices, one prefers a PPP-RTK model where the estimable SPBs contain a minimum number of datum ambiguities. We will show that otherwise there will be discontinuities occurring in datum ambiguities that will lead to unfavorable jumps in the estimated SPBs and frequent ambiguity resolution (re-)initialization on the user side. For this to occur one normally restricts to a common-view (CV) network, where the satellites are commonly visible to all receivers involved, and constructs the PPP-RTK model by choosing the phase biases and the ambiguities, pertaining to one receiver, as the datum. In doing so the CV model is capable of estimating the SPBs with each bias containing only one datum ambiguity. In this contribution we extend the CV model to an all-in-view (AV) network case where the satellites tracked can differ across receivers, but at least one satellite is commonly visible; this is practical as the network size is normally consisting of baseline lengths of several hundreds of kilometers. Contrary to the CV model, in the AV model the phase biases and the ambiguities pertaining to one satellite is selected as the datum, such that, the number of datum ambiguities entering into the estimable SPBs is always at the minimum as the SPBs are formulated in a between-satellite single-differenced form. The benefits with AV model are that it relieves the stringent satellite visibility as required by the CV model and, at the same time, reduces to the best possible extent any jumps in the estimated SPBs as well as the necessary ambiguity resolution (re-)initialization on the user side. Experiments conducted using multi-GNSS data collected in both CV and AV networks verify that the AV model always outperforms the CV one, as measured by both the time-to-first-fix as well as the positioning accuracy when compared to very precise benchmark coordinates.