An undifferenced and uncombined phase-only PPP model for time transfer
摘要
Traditional precise point positioning (PPP) for time transfer relies on both code and phase observations, assuming receiver code biases are time-invariant. However, unmodeled code errors, such as time-varying receiver code bias and code multipath effects, can degrade time transfer performance. To overcome these issues, we propose a PPP model based solely on undifferenced and uncombined (UDUC) phase observations, thereby eliminating potential code-related errors. The exclusion of code observations renders the model rank-deficient, which we resolve using S-system theory to achieve a full-rank UDUC phase-only PPP model capable of capturing only the trend of the receiver clock rather than its absolute value. We evaluate the proposed model using BDS observations collected in China and from IGS stations in Europe that are linked to coordinated universal time (UTC(k)). Its performance is compared against the traditional PPP model and a modified PPP model that treats receiver code bias as a time-varying parameter (TVB-PPP). The results show that the phase-only solution improves daily frequency stability by 21.91% over traditional PPP and by 13.65% over TVB-PPP for the second-generation BeiDou navigation satellite system (BDS2). The larger gain over traditional PPP stems from significant code errors at both receiver-induced and satellite-induced, while the improvement over TVB-PPP mainly reflects satellite-induced code multipath. For BDS3, the phase-only and TVB-PPP solutions perform similarly, both surpassing traditional PPP, indicating that satellite-induced code multipath is negligible, though receiver code bias variations persist. When integrating BDS2 and BDS3 observations, the traditional PPP solution achieves frequency stabilities (averaged over the four time-links) of 1.76 × 10−15, 1.08 × 10−15, and 1.03 × 10−15 for averaging times of 1-3 days, respectively. The corresponding improvement ratios of the TVB-PPP solution are 3.80%, 9.64%, and 11.85%. The phase-only solution further enhances frequency stability by 11.44%, 13.81%, and 16.23%, respectively.