Stochastic modeling of between-receiver single-differenced ionospheric delays and its application to medium baseline RTK positioning

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is one of the key issues and challenges for precise relative positioning. For baselines greater than 10 km, integer ambiguity resolution becomes difficult because the ionospheric delay effects on the single-differenced (SD) observations are significant. One way to deal with this difficulty is to weight the ionospheric delays, instead of treating them in a deterministic way, giving rise to the so-called ionosphere-weighted model. With this model relative positioning technology is enabled to work with much larger inter-station distances than its current status. Here we seek to gain insight into how to reasonably weight the SD ionospheric delays, normally introduced in the ionosphere-weighted model as pseudo observables, which consists of two sequential steps. The first step seeks to construct realistic stochastic models for the GNSS observables with the ionosphere-fixed model where the SD ionospheric delays are assumed to be absent. With the results so obtained in the second step we estimate the variance of the SD ionospheric delays with the ionosphere-float model, in which the SD ionospheric delays are assumed to be fully unknown. Numerical tests based on GPS data from the National Geodetic Survey CORS network demonstrate a clear improvement in medium baseline real time kinematic (RTK) positioning performance, as compared to the ionosphere-weighted model that employs the unrealistic stochastic models for the pseudo SD ionospheric observables.