An investigation into multi-frequency ambiguity resolution for real-time PPP time and frequency transfer

Abstract Precise point positioning with ambiguity resolution (PPP-AR) has been developed to restore the integer nature of estimated ambiguities, significantly enhancing time and frequency transfer performance. Since the end of 2019, the International Bureau of Weights and Measures has adopted PPP-AR for calculating integer PPP (IPPP) results in the time links of international atomic time. Dual-frequency (DF) ambiguity resolution method has been applied to IPPP time and frequency transfer. To incorporate multi-frequency observations into IPPP time and frequency transfer, this study adopts cascaded ambiguity resolution and cascaded cycle slip detection to investigate the performance of real-time multi-frequency IPPP in time and frequency transfer. The quality and availability of multi-frequency phase bias products were first assessed. Except for the GPS L5 frequency, the standard deviation (STD) of the phase bias products remained below 0.2 ns, with 78.79% of the narrow-lane fractional part residuals falling within 0.15 cycles, and 95.13% within 0.30 cycles. The IPPP time and frequency transfer performance of DF, triple-frequency (TF), and quad-frequency (QF) was systematically analyzed. Across both zero baselines and various baseline experiments, IPPP demonstrated reduced time transfer error fluctuations compared to float solutions. Furthermore, as the averaging time increased to several hours, IPPP demonstrated improved frequency stability. Following DF ambiguity resolution, the STD value of the zero-baseline common clock difference decreased by 5.5 ps, while the TF improved from 67.53 ps to 64.13 ps. Meanwhile, the frequency stability of the QF ambiguity-fixed solution reached 9.910 × 10 −17 at 2.84 d averaging. Furthermore, for both short and long baselines, IPPP led to a significant reduction in time transfer errors. As the averaging time increased, IPPP demonstrated further enhancement in frequency stability.