Determination of optimal satellite phase bias combinations for BeiDou triple-frequency PPP-RTK

Abstract

The precise point positioning real-time kinematic (PPP-RTK) technique enables a single receiver to achieve high-precision and real-time positioning services, mainly relying on integer ambiguity resolution based on satellite phase bias (SPB) information. For the PPP-RTK technique based on uncombined observations, the SPBs of basic frequencies are available only at low precision because of high correlation and therefore need to be updated frequently. Thus, the most appropriate linear combinations of BeiDou triple-frequency SPBs with low update rates for transmission to users must be identified. To acquire combinations of BeiDou triple-frequency SPBs, we use the Z-transformation to process the covariance matrixes corresponding to SPB estimates to generate decorrelated SPB combinations. To meet different circumstances, geometry-free, geometry-fixed and geometry-plus-satellite-clock-fixed variants of PPP-RTK are applied to process data from the regional network. The computed results indicate that the primary stable, secondary and tertiary stable SPB combinations of B1, B2 and B3 frequencies are (0, −1, 1), (1, 2, −3), and (−33, −129, 163) for the geometry-free variant, (0, −1, 1), (1, 2, −3), and (−21, −95, 117) for the geometry-fixed variant, and (0, −1, 1), (1, 3, −4), and (−18, −84, 103) for the geometry-plus-satellite-clock-fixed variant. Furthermore, the statistical results of the SPB series provide stable periods of the primary stable combinations of longer than 7 d. For the secondary and tertiary stable combinations, the stable periods for the geometry-free variant are 12 h and 5 h, for the geometry-fixed variant 12 h and 8 h, and for geometry-plus-satellite-clock-offset variant 12 h and 10 h. These stable periods suggest how often the SPB information should be updated and provide meaningful insight for the allocation of the computing resources of the PPP-RTK server.