Estimating multi-frequency satellite phase biases of BeiDou using maximal decorrelated linear ambiguity combinations

Improving ambiguity resolution (AR) in multi-frequency undifferenced and uncombined precise point positioning (PPP) benefits from accurate uncalibrated phase delays (UPD), which are often estimated from linear combinations of float ambiguities. The traditional linear ambiguity combinations for estimating these UPDs in case of triple-frequency observations are typically extra-wide-lane, wide-lane, and L1 combinations. We proposed the method for estimating UPDs from triple-frequency ambiguities using maximal decorrelated linear ambiguity combinations obtained by the least-squares ambiguity decorrelation adjustment Z-transformation. To validate the quality and availability of estimating UPDs for the BeiDou navigation satellite system, based on maximal decorrelated linear ambiguity combinations, tests using observations from stations of the Crustal Movement Observation Network of China and the Asia-Pacific Reference Frame project are performed using undifferenced and uncombined PPP-AR. The results show the internal precision of combined satellite UPDs estimated from the maximal decorrelated linear ambiguity combinations is better than that estimated from traditional combinations in terms of temporal stability and RMS of posteriori residuals. Furthermore, the statistical results also demonstrated that triple-frequency PPP-AR using the improved UPDs reduces the average convergence time by 8.9 and 12.3% in horizontal and vertical directions, and also improves the positioning accuracy for 3 h of observations by 11.1, 9.1 and 8.3% in the east, north and up directions, respectively, compared with triple-frequency PPP-AR using the UPDs derived from the traditional combinations.