Cascading PPP-RTK: a sequential network processing framework for product generation

Abstract Precise point positioning and real-time kinematic (PPP-RTK) extends PPP by incorporating the ambiguity resolution (AR) concept from RTK, enabling rapid and high-precision positioning supported by satellite phase bias and atmospheric delay products. This work proposes a cascading PPP-RTK framework that formulates two network models to sequentially estimate satellite phase biases and atmospheric delays. The first network model, designed for a backbone network with sparsely distributed stations, enables the estimation of satellite phase biases that can serve a wide area. The second network model, applied after fixing the estimated satellite phase biases, processes densified networks with closely spaced stations to generate high-precision and robust atmospheric products. Its high precision is achieved through weighted constraints on between-receiver single-differenced atmospheric delays. Its robustness arises from the network formulation, which enables atmospheric delays to rapidly reconverge after disturbances such as data interruptions, in contrast to the traditional single-station PPP-AR model that requires long reconvergence times due to independent station-wise processing. To validate the framework, GPS data from National Geodetic Survey reference stations in the United States are used, forming a backbone network, a densified network, and multiple users. Results show that, compared with single-station PPP-AR, the proposed network-based approach produces more accurate atmospheric products, especially when a satellite is newly tracked and ionospheric estimates are still initializing. When applied to user positioning, these products reduce the average time-to-first-fix from 8 min to 5 min, improving overall positioning performance.