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Precise point positioning (PPP) can achieve high-accuracy point solution using un-differenced code and carrier phase observations. Many PPP models have a higher measurement noise and multipath effects, resulting in a long time to obtain sub-decimeter to centimeter positioning accuracy during a short duration. This paper will address a modified un-combined (MUC) model based on phase–phase geometry-free combination in addition to code–phase ionosphere-free combination and original carrier phase observations. The observation system composed by the new combinations has a lower measurement noise and orbit error level compared with the un-combined (UC) model, University of Calgary (UofC) model and standard un-differenced ionosphere-free combined (UD) model. Moreover, it can capture the changing characteristics of atmospheric delays between epochs as constraints to accelerate the filter convergence. We use the data sets from about 114 international GNSS service reference stations to analyze the performance of the MUC model. Numerical results show that the MUC model generally yields the best performance when the observation duration is short. For the 0.5 h duration observation data sets, about 70.2 % of all 6912 convergence tests are convergent, which is an increase by 19.2, 2.8 and 49.3 % points compared with the UC, UofC and UD models, respectively. For the common convergence parts of all the test data sets, the mean convergence time of the MUC model is significantly reduced by 22.9, 9.6 and 35.3 %, and the percentage of the 2D position biases within 0–5 cm is increased by 16.0, 3.4 and 55.0 %, respectively, compared with the UC, UofC and UD models. Therefore, the proposed PPP model is more beneficial for the PPP user to quickly obtain sub-decimeter to centimeter positioning accuracy during a short duration.

A modified un-combined model to improve the performance of precise point positioning: model and test results