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Tropospheric delay is one main factor affecting the accuracy of precise point positioning (PPP) ambiguity-float and fixed solutions. Investigations mainly focused on evaluating the contributions of tropospheric corrections to the accuracy and reliability of PPP solutions. The tropospheric corrections generally contained the zenith tropospheric delay (ZTD) and the horizontal gradients estimated from relative positioning or PPP. However, the estimated tropospheric delays can be partly absorbed by the carrier phase residuals if the stochastic model is not well-defined. Therefore, along with the ZTD and horizontal gradients, the carrier phase residuals from PPP backward filter are considered to reconstruct slant tropospheric delay (STD). Based on the proposed STD model, its marginal effects on GPS PPP were investigated. Results indicated that the consideration of carrier phase residuals for STD modeling can improve the three-dimensional accuracy to 0.5 cm/1 cm/1.2 cm in the South/North/Up (N/E/U) components. Then, the effects of internal and external STD corrections on PPP float and fixed solutions were analyzed. Compared to the ZTD + gradients augmentation, STD corrections from the same station could improve the PPP accuracy by 51%/51%/60%; the large improvements were because the multipath error and observation noise were eliminated. In comparison, the improvement was 14%/28%/31% using external STD corrections, which indicated the effects of unmodeled tropospheric errors in the phase residuals. The ambiguity-fixing results indicated that the fixing rate of PPP ambiguity was increased by 30% with STD augmentation. As the BeiDou System (BDS) suffered longer convergence than that of GPS, the benefits of STD modeling to the BDS observations were also validated. Overall, the results validated the performance of STD-augmented PPP, which demonstrated the potential application of high-accuracy troposphere products.

Analysis on the Impacts of Slant Tropospheric Delays on Precise Point Positioning